UNIVERSITÉ DE MONTRÉAL SIMULATION À ÉVÉNEMENTS DISCRETS POUR LA COMMANDE TEMPS RÉEL DE SYSTÈMES DYNAMIQUES COMPLEXES AMEL JAOUA

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2 UNIVERSITÉ DE MONTRÉAL SIMULATION À ÉVÉNEMENTS DISCRETS POUR LA COMMANDE TEMPS RÉEL DE SYSTÈMES DYNAMIQUES COMPLEXES AMEL JAOUA DÉPARTEMENT DE MATHÉMATIQUES ET DE GÉNIE INDUSTRIEL ÉCOLE POLYTECHNIQUE DE MONTRÉAL THÈSE PRÉSENTÉE EN VUE DE L OBTENTION DU DIPLÔME DE PHILOSOPHIAE DOCTOR (Ph.D.) (GÉNIE INDUSTRIEL) AOÛT 2009 Amel Jaoua, 2009.

3 UNIVERSITÉ DE MONTRÉAL ÉCOLE POLYTECHNIQUE DE MONTRÉAL Cette thèse intitulée: SIMULATION À ÉVÉNEMENTS DISCRETS POUR LA COMMANDE TEMPS RÉEL DE SYSTÈMES DYNAMIQUES COMPLEXES présentée par : JAOUA Amel en vue de l'obtention du diplôme de: Philosophiae Doctor a été acceptée par le jury d'examen constitué de: Mme. YACOUT Soumaya, D.Sc., présidente Mme. RIOPEL Diane, ing., Docteure, membre et directrice de recherche M. GAMACHE Michel, ing., Ph.D., membre et codirecteur de recherche M. COHEN Paul, ing., Ph.D., membre M. GHARBI Ali, ing., Ph.D., membre externe

4 À mon père. iv

5 v REMERCIEMENTS Je désire dans un premier temps, exprimer ma sincère et profonde gratitude à mes directeurs de thèse, les professeurs Diane Riopel et Michel Gamache pour leur encadrement remarquable tout au long de cette thèse. J aimerais les remercier pour leurs précieux conseils et leur implication totale dans le projet tout au long de ces quatre années. Je suis grandement reconnaissante au Pre. Riopel pour son soutien moral continuel et acharné. Je tiens aussi à remercier le Pr. Gamache pour l enthousiasme sans équivoque avec lequel il s est investi dans ce projet. Un grand merci aussi à Pre. Yacout à Pr. Cohen, à Pr. Gharbi et finalement à Pr. Marcotte pour avoir accepté de réviser cet ouvrage. Je profite de cette occasion pour remercier Monsieur Stéphane Alarie pour son précieux support qui a servi à éclaircir des points clés concernant l aspect pratique de la problématique au tout début de ce projet. Un grand merci aussi à toute l équipe du service informatique et du secrétariat du Département de mathématiques et de génie industriel. Finalement, je tiens à remercier la mission universitaire de Tunisie en Amérique du Nord pour son soutien et sa bienveillance vis-à-vis des étudiants Tunisiens.

6 vi RÉSUMÉ Plusieurs systèmes dans différents domaines d application comme la production, le transport ou les services sont aujourd hui considérés comme étant des systèmes à événements discrets et à comportement dynamique complexe. Pour satisfaire les contraintes grandissantes de qualité et de productivité, la maîtrise du caractère dynamique de ces systèmes évoluant dans des environnements stochastiques est essentielle. Grâce aux progrès réalisés dans les technologies de l information et de la communication, des données accrues concernant l état et la dynamique du système sont devenues continuellement accessibles. Plusieurs attentes ont été formulées autour d une intégration efficiente de ce type d information qui permettrait une commande agile et robuste. Cependant cette intégration demeure un problème ambigu et de ce fait, forme un champ ouvert à la recherche. La présente thèse porte sur cet axe de recherche en pleine expansion vu l émergence des avancées technologiques. L une des principales contributions de nos travaux est la proposition d une architecture qui permet la commande en temps réel de ce type de système. Pour cette architecture la stratégie de commande prédictive développée par les automaticiens est adoptée. Cependant pour garantir un modèle fiable de prédiction, le noyau de notre structure de commande est un modèle de simulation à événements discrets et non un modèle analytique. Bien que cette dernière approche soit proposée depuis deux décennies, peu de travaux l ont réellement implantés vu le manque de formalisme autour de cette structure de commande. Nos travaux viennent élucider plusieurs concepts nécessaires à une implantation efficiente d une structure de commande en temps réel. À cette fin, nous avons eu recours à une méthodologie orientée objet en utilisant le langage de spécification UML. L utilisation de cette méthodologie nous a permis de développer un système de commande répondant aux standards des applications temps-réel.

7 vii Dans notre architecture, la génération des lois de commande s effectue ainsi de façon concurrente durant la phase opérationnelle du système contrôlé. Le principe de cette commande est d amener le système à suivre la trajectoire de référence qui exprime les performances souhaitées. À cette fin, nous générons les lois de commande de sorte à continuellement minimiser l écart entre les performances atteintes et les performances désirées. Pour la résolution de ce problème de minimisation, nous avons intégré un module d optimisation intelligent basé sur la métaheuristique du recuit simulé. L utilisation d une métaheuristique pour l optimisation en temps réel des lois de commande constitue elle aussi une importante contribution. En effet dans des travaux antérieurs, le temps de calcul important et la problématique de l intégration ont été désignés comme étant deux complexités allant à l encontre de l utilisation des métaheuristiques pour la commande en temps réel. Dans nos travaux, nous avons démontré que le temps de recherche résultant du couplage de la simulation avec l optimisation peut considérablement décroitre en développant des modèles de simulation spécifiques à la commande. Quant à la problématique de l intégration, nous proposons de la résoudre par la programmation multiprocessus. Une application prototype de transport minier est choisie pour l implémentation de notre architecture. Le choix de ce domaine d application est principalement motivé par les critiques relevées dans ce domaine concernant les investissements lourds dans des technologies de l information qui se sont avérés peu profitables. Par exemple, des études récentes ont montré que des systèmes de positionnement très performants permettent de renvoyer à tout instant l emplacement exact des camions évoluant dans la mine à ciel ouvert, cependant cette information n est pas efficacement intégrée dans les systèmes de répartition de flotte. Ainsi des problèmes de congestion et de longues files d attente de camions sont engendrés à cause de la myopie des systèmes envers l état réel du trafic engendré lors de la génération des commandes de répartitions.

8 viii Pour commander en temps réel ce système de transport minier, nous avons tout d abord développé un modèle de simulation à événements discrets. Le développement d un tel modèle à fine granularité et dédié à la commande constitue l une des contributions de cette thèse. Pour cette fin nous avons dans un premier temps montré que l approche de modélisation classique des problèmes de répartition transport peut considérablement biaiser les résultats de simulation. Ensuite, nous nous somme basés sur une approche objet pour intégrer un simulateur de trafic microscopique à un modèle classique de simulation de transport. En effet, nous avons décelé que les problèmes de répartition de flotte ont principalement été traités par la communauté de recherche opérationnelle, tandis que la résolution des problèmes de trafic constitue généralement un champ de recherche en ingénierie civil. Nos travaux viennent alors rapprocher ces deux communautés en considérant le trafic dans le réseau comme étant une composante intrinsèque d un système de transport interne. Nous avons aussi décelé que les mêmes critiques concernant la faiblesse des modèles de répartition à considérer l état réel du trafic se retrouvent dans les travaux traitant le pilotage des réseaux de transport internes des terminaux à conteneurs. Ainsi pour que notre approche soit réutilisable dans d autres systèmes de transport internes, notre modèle de simulation se base sur un modèle conceptuel développé selon l approche objet. Suite à l implémentation et à la validation du modèle de simulation à fine granularité, nous avons expérimenté le potentiel de ce simulateur une fois intégré dans l architecture de commande comme observateur de l état du trafic. Les résultats obtenus montrent que notre simulateur peut fidèlement reproduire des phénomènes de trafic importants de formation et de propagation de peloton résultant de l interaction longitudinal des camions dans le réseau de transport fermé. Par l augmentation de la loi de commande de répartition initiale par une seconde dimension de routage, nous avons alors abouti à un système de commandes permettant la répartition et le routage temps réel des camions. Finalement, l efficacité d un tel routage en temps réel en termes de contrôle et de réduction de congestion dans les réseaux de transport fermés est démontrée.

9 ix ABSTRACT Several systems involved in different application fields such as production, transportation or services are now considered as discrete event systems with complex dynamic behavior. In order to meet the increasing requirements of quality and productivity, the control of the dynamic nature of those systems during operation level in stochastic environment is essential. With the advancements made in information and communication technologies, a large amount of data related to the dynamic status of these systems become continuously available. Thus, many expectations have been raised around an efficient integration of such accurate information that can lead to a robust and agile control of the complex and dynamic systems. However, such integration appears complex and remains an active field of research. Our thesis is directed towards this growing research area which seems to attract a lot of interest since the emergence of technological advances. One of the major contributions of our work is the proposed architecture for real-time control of these systems. This architecture is mainly inspired form the model-based predictive control scheme developed by the automation scientist. However, to ensure a reliable prediction model of the complex and dynamic systems, our control scheme is based on a discrete event simulation rather than an analytical model. Even though two decades have now passed since this approach was proposed, very few industrial implantations have been reported. The scarcity of this promising approach is mainly due to the lack of a formal specification of such control architecture. The purpose of our work is to open up new generic architecture avenues for the implementation of an efficient simulation-based real-time control system. The structural design and the behavior of the proposed architecture are built upon the object-oriented modelling methodology. This methodology is based on the Unified Modelling Language (UML), standard for efficient deployment of real-time systems. The purpose of this control scheme is to bring the system to follow a reference trajectory defined according to the desired performance.

10 x In the architecture, control laws are computed concurrently with the objective of minimizing the deviation between the controlled system achieved performances and the off-line forecasted performances. To solve this minimization problem, we incorporated an intelligent optimization module based on the simulated annealing metaheuristic. Another important contribution of our work is the effective use of a metaheuristic (the simulated annealing) in the optimization module to achieve intelligent control. Previous researches discard the use of metaheuristics at this control stage due to the following limitations: integration complexity and the long simulation based optimization run-time. In our work, we demonstrate how this long run-time could substantially be decreased by developing a specific simulation model designed for the control purpose. Furthermore, we propose to resolve the integration problem by embedding a multiprocessing technique. A prototype application of mine transportation system is chosen to experiment the capability of the control architecture. This choice is mainly motivated by the critics formulated around the unprofitable huge investments made on information technologies acquisition in the mining industry. For example, recent studies demonstrated that accurate online data delivered from positioning systems and sensors is provided for tracking instantaneous state of trucks, but this information is not effectively used in the real-time dispatching systems. Thus, a problem of high unpredictability level caused by truck bunched together in platoons remains elusive in the mining industry. In order to embed the real time control architecture in the mining environment, we first developed a discrete event simulation model. The development of a high fidelity simulation model dedicated to the control purpose constitutes an important issue in our work. For this purpose, we firstly demonstrate that the classical modelling approach of the considered transport dispatching problems could lead to biased simulation results. Then, based on the object oriented methodology, we integrate a microscopic traffic model in the classical transportation model. We have noticed that the fleet dispatching

11 xi problem was mostly addressed by the operational research community while this problem of traffic constitutes a civil engineering field of research. Thus, our work comes to bring those two communities by considering the traffic in the network as an inherent part of the internal transportation systems. The same critics concerning the weakness of the dispatching models in considering the actual traffic state in the internal transportation networks are also founded for the transport of containers at transhipment terminals. Thus, in order to ensure the reusability of our approach, we provide the conceptual model based on the object-oriented approach. After the implementation and validation of the high granularity simulation model, we investigated its capability as an observer of the traffic state in the control scheme. Results proved that our simulator could indeed reproduce important traffic behaviors of platoon formation and propagation due to the longitudinal trucks interactions in the internal transportation network. With the addition of a routing decision to the original control law of truck dispatching, it results in an interesting control system for real-time dispatching and routing. Finally, we demonstrate the efficiency of such real-time truck routing in alleviating traffic congestion problems arising in vehicle-based internal transport systems.

12 xii TABLE DES MATIÈRES DÉDICACE. iv REMERCIEMENTS v RÉSUMÉ...vi ABSTRACT...ix TABLE DES MATIÈRES... xii LISTE DES TABLEAUX...xvi LISTE DES FIGURES... xvii LISTE DES ANNEXES...xix INTRODUCTION...1 CHAPITRE 1 REVUE CRITIQUE DE LA LITTÉRATURE Caractérisation des systèmes complexes Définition Approches de modélisation Formalisme de spécifications Présentation de l application prototype : transport minier Présentation des opérations minières Cartographie du processus d exploitation du gisement Processus de chargement et de transport Présentation de l article de conférence...19 CHAPITRE ARTICLE A FRAMEWORK FOR REALISTIC MICROSCOPIC MODELLING OF SURFACE MINING TRANSPORTATION SYSTEMS Introduction State of the art on modelling approaches for urban road and mining transport systems Modelling approaches used in road transportation systems...25

13 xiii Modelling approach used in mine transportation systems Design and development of mining transportation micro-simulator Mining transportation micro-simulator framework design Mining transportation micro-simulator development First validation study: macroscopic versus microscopic behavior Dunbar s model description Model implementation Model validation Second validation study: sensitivity analysis Midsize model description Factors investigated by sensitivity analysis and performance measures ANOVA results and discussion Case studies, results and analysis Extended model description First case study: simulation results Second case study: simulation results Findings Conclusion and future work...53 CHAPITRE 3 59 ARTICLE SPECIFICATION OF AN INTELLIGENT SIMULATION BASED REAL TIME CONTROL ARCHITECTURE: APPLICATION TO TRUCK CONTROL SYSTEM Introduction Literature Review Simulation-based optimization Implementation issues Review of application Specifications of the simulation-based real-time control system The UML use cases model of the control system...69

14 xiv Behavior specification of the control system Prototype implementation of a truck control system Application context Simulator development Implementation of Sensor and Actuator classes Optimizer development Experimentations and results Mine networks layout Control system under nearly steady-state dynamics Control system reactivity under aperiodic stimuli The response time of the control system Conclusion...88 CHAPITRE 4 93 ARTICLE EFFICIENT SIMULATION MODEL FOR REAL-TIME FLEET MANAGEMENT PROBLEMS IN INTERNAL TRANSPORT SYSTEMS Introduction Literature review Review of traffic modelling approach Implementation of the microscopic modelling approach Review of applications Specification of the proposed conceptual model The conceptual difference in modelling system static structure Modelling dynamic system behavior Implementation and validation of the transportation model Implementation of the proposed internal transportation model Validation of the model behavior under constrained traffic Experimentation and analysis of the real-time truck routing Real-time truck routing under road blockage upset...115

15 xv Real-time rerouting from highly congested roads Conclusion CHAPITRE DISCUSSION GÉNÉRALE CONCLUSION ET RECOMMANDATIONS LISTE DES RÉFÉRENCES ANNEXES...152

16 xvi LISTE DES TABLEAUX Table 2.1. Parameters in the macroscopic model...38 Table 2.2. The design summary for the ANOVA experiment...45 Table 2.3. ANOVA results...46 Table 4.1 Truck performance Table 4.2 Path table Table 4.3 Generated control law...118

17 xvii LISTE DES FIGURES Figure 1.1 Processus de chargement et de transport : source Fayad et Nabavi (2001)...17 Figure 2.1 Representation of a typical macroscopically modeled transport benchmark problem Figure 2.2 UML class diagram of the micro-simulator framework...33 Figure 2.3. Graphical representation of the layout s basic components Figure 2.4 Dunbar s model representation under the macroscopic approach...38 Figure 2.5 Dunbar s model representation under a microscopic approach...39 Figure 2.6 Midsize model s network topography Figure 2.7 Abstraction graph of midsize mine model...42 Figure 2.8 Truck movement on the mine road section Figure 2.9 Variation of performance measures with the number of trucks...45 Figure 2.10 Extended model network topography...48 Figure 2.11 Abstraction graph of extended mine model...48 Figure 2.12 Evolution of ore, leach and waste production level: original vs. new designed network Figure 2.13 New alternative route layout...50 Figure 2.14 Road section occupancy level: original vs. new designed network...51 Figure 2.15 Layout path1 and path Figure 2.16 Evolution of Shovel production: dispatching with vs. without rerouting...52 Figure 3.1 The use case model...69 Figure 3.2 Sequence diagram...71 Figure 3.3 Simulation-based control scheme...74 Figure 3.4 Pseudo code of Simulated Annealing...79 Figure 3.5 Abstract graph of mines...80 Figure 3.6 Behavior of the system under Open-loop versus Closed-loop Control...82 Figure 3.7 Behavior of the system under different Control Horizon...83 Figure 3.8 System performance under Aperiodic Stimulus...85

18 xviii Figure 3.9 Neighbourhood generation...87 Figure 3.10 Evolution of the simulation-based optimization searching process...87 Figure 4.1 Example of a UML class diagram from (Knapp and Page [45]) Figure 4.2 UML class diagram of a surface mine model, provided by Jaoua et al. [26] Figure 4.3 Statechart diagram Figure 4.4 Time-distance diagrams Figure 4.5 Our simulation-based control scheme Figure 4.6 Abstract graph of the medium scale mine Figure 4.7 Simulation output according Decision Figure 4.8 Abstract graph of the large-scale mine Figure 4.9 Space occupancy on road sections Figure 4.10 Transported tonnage under fixed versus flexible routing...122

19 xix LISTE DES ANNEXES ANNEXE A Article de Conférence MOSIM ANNEXE B Diagrammes de Processus...165

20 1 INTRODUCTION Cadre théorique et problématique Les systèmes considérés dans cette thèse sont les systèmes dynamiques à événements discrets. De nos jours, les systèmes de ce type à dynamique complexe sont devenus très répondus. On retrouve sous cette catégorie les systèmes flexibles de production et les systèmes de transport. La complexité de ces systèmes émane de leur structuration connexe, leur caractère dynamique et de leur interaction avec l environnement dans lequel ils évoluent. Avec les besoins grandissants de qualité et de productivité auxquels vient s ajouter la criticité des contraintes temporelles, la maîtrise et l optimisation continue de ces systèmes deviennent nécessaires. Implanter une commande en temps réel permettrait alors d instaurer une telle conduite des systèmes dynamiques complexes. Durant les deux dernières décennies, l émergence des technologies de l information a fait accroître l espoir de disposer de structures de commande agiles et robustes pour faire face à des environnements dynamiques et stochastiques. De tels systèmes de commande devraient non seulement faire face à des perturbations internes, mais de plus réagir, au cours de leur fonctionnement, aux aléas provenant de l extérieur. Il en découle une nécessité de disposer d une structure de commande permettant l adaptation continue à l environnement du système contrôlé. L instauration d une structure de commande permettant à un procédé de faire face aux perturbations de l environnement externe est un problème qui a largement été étudié par les automaticiens. En effet, plusieurs procédés industriels sont aujourd hui commandés en temps réel grâce à la stratégie de commande prédictive. Dufour (2000) décrit le potentiel de cette structure de commande prédictive et revoit les domaines d application qui en ont bénéficiés, tels que les procédés chimiques et de raffinage. Étant donné qu il est impossible de prévoir toutes les perturbations à l avance, le principe de ce type de commande consiste à résoudre en temps réel un problème d optimisation pour générer

21 2 des lois de commande permettant la correction continue des perturbations. La formulation de ce problème d optimisation concerne la poursuite d'une trajectoire de référence qui exprime les performances souhaitées du procédé. Cette commande doit être basée sur une structure en boucle fermée afin de capturer l état du procédé en temps réel et de le réguler. Cette structure de commande prédictive nécessite l existence d un modèle très fiable du procédé afin de générer les lois de commande optimale qui vont amener le système à suivre la trajectoire de référence désirée. En effet, le succès même de cette stratégie est contraint par la pertinence de ce modèle de prédiction. Il est vrai que cette structure de commande est performante pour des procédés simples, mais son adaptation pour les systèmes à événements discrets complexes s avère compliquée. L un des premiers obstacles relevés par Banks (1998) est la faiblesse des modèles mathématiques à reproduire finement des systèmes complexes comme les systèmes manufacturiers ou de transport. La solution proposée était d adopter des modèles de simulation comme modèle de prédiction. Bien que cette solution ait été approuvée, les travaux récents d Iassinovski et al. (2008) et ceux de Mirdamadi et al. (2007) rapportent que l application effective de cette approche dans l industrie reste très limitée. L handicap de cette approche de commande est sa complexité d intégration. En effet, dans les travaux de Sivakumar et Gupta (2006) ainsi que ceux de Cardin et al. (2008), les auteurs traitent des cas particuliers d ateliers et ne présentent aucun formalisme de leur structure de commande. Ce manque de spécification représente une limitation qui va à l encontre de l adaptation de cette approche de commande en temps réel pour les systèmes complexes. Dans cette thèse, la notion de système complexe est caractérisée dans la revue de littérature complémentaire présentée au chapitre 1. Plus spécifiquement, les caractéristiques du système de transport minier, qui est considéré comme application pilote tout au long de nos travaux, sont exposées. Le choix de cette application est principalement motivé par les critiques récentes de plusieurs responsables miniers qui remettent en cause les énormes investissements pour les technologies de l information

22 3 qui se sont avérés peu profitables. L étude de Krzyzanowska (2007) démontre que même si des systèmes très performants de positionnement permettent de localiser chaque camion à tout instant dans la mine, les logiciels de répartition n exploitent pas ce type d information en temps réel afin d optimiser des problèmes très courants de trafic et de congestion dans les mines à ciel ouvert.

23 4 Objectifs Dans ce contexte, les principaux objectifs de cette thèse sont de : 1. analyser l écart entre les performances théoriques des algorithmes de répartition, et les performances réelles reportées par les praticiens; 2. évaluer la pertinence de la modélisation des problèmes tests pour la répartition de flotte de camions, en réseau de transport minier, comme des problèmes de répartition classique dans un graphe; 3. considérer l application du transport minier dans l environnement complexe des mines à ciel ouvert; 4. développer un modèle plus réaliste des systèmes de transport minier permettant la prise en compte accrue de comportements connexes; 5. spécifier une structure pour la commande en temps réel des systèmes complexes, tel que le système de transport minier; 6. développer les différents modules de cette structure de commande tout en garantissant leur généricité; 7. évaluer l efficacité de ce système de commande pour la répartition en temps réel des camions dans les mines à ciel ouvert; 8. évaluer la flexibilité de ce système de commande à intégrer le routage comme nouveau composant dans la loi de commande; 9. et étudier le potentiel de l intégration du routage temps-réel dans les réseaux de transport fermés caractérisés par des problèmes de congestion.

24 5 Organisation de la thèse La présente thèse sous articles est structurée en six chapitres, dont trois sont des articles de revues à comité de lecture publiés ou soumis. Le chapitre 1 est structuré en deux parties. La première partie présente une revue complémentaire de littérature (de celle des articles) pour introduire le contexte global de la thèse et clarifier la sémantique utilisée dans nos travaux. La seconde partie renvoie les lecteurs vers un article de conférence. Cet article de conférence a lui aussi été accepté et publié. Il traite des deux premiers objectifs cités plus hauts. Il montre que la modélisation des problèmes tests pour la répartition de flotte de camions en réseau de transport minier, comme des problèmes de répartition classique dans un graphe peut considérablement biaiser les résultats. D où cette approche de modélisation utilisée engendre l élargissement de l écart entre les performances simulées et celles réellement retrouvées par les praticiens. Les recommandations de ce premier chapitre, nous ont ainsi amené à concevoir et implanter un modèle de granularité plus fine, présenté dans le chapitre 2. Lorsque le problème d obtenir un modèle fiable pour un système réel est résolu, le développement d une structure de commande pour ces systèmes de nature distribuée et complexe est présenté au chapitre 3. La contribution originale du chapitre 3 est de répondre aux cinquième, sixième et septième objectifs cités ci-haut. Une architecture inspirée de la structure de commande prédictive en automatique, mais basée sur un modèle de simulation comme modèle de prédiction, est développée. Cette architecture est implantée et validée pour la commande en temps réel de la flotte de camions dans le système de transport minier. La structuration modulaire de cette architecture de commande est exploitée au chapitre 4. Ce chapitre répond aux deux derniers objectifs et démontre le potentiel de l architecture de commande dans le routage en temps réel pour faire face aux complexités du trafic. Ce problème de trafic est fortement critiqué dans les systèmes de transport internes comme dans le cas d une mine ou dans les terminaux à conteneurs, cependant il est ignoré par les modèles de répartition proposés.

25 6 Le chapitre 5 discute le choix du modèle de simulation ainsi que l importance de la cartographie préliminaire qui a permis d aborder le transport en tenant compte de l environnement. Finalement, nous clôturons cet ouvrage en résumant les principales conclusions de cette thèse et en présentant des recommandations pour des travaux futurs.

26 7 CHAPITRE 1 REVUE CRITIQUE DE LA LITTÉRATURE Ce chapitre est divisé en deux parties. La première partie présente une revue de la littérature permettant d introduire le contexte global de cette thèse. Le but ici est de complémenter et non de reprendre les revues réalisées dans nos articles. En effet, le premier objectif de ce chapitre est d élucider certaines notions nécessaires pour la compréhension ultérieure des caractéristiques de l environnement. Le second objectif est d amener le lecteur à comprendre nos choix de méthodologie, à travers une revue critique des autres méthodes d analyse. Le troisième et dernier objectif de ce chapitre est de clarifier la sémantique utilisée dans le cadre de nos travaux. Cette revue de la sémantique est nécessaire pour la compréhension ultérieure de certaines notions généralement propres à d autres disciplines d ingénierie. La deuxième partie de ce chapitre est exposé sous forme d article de conférence présenté en (Annexe A). 1.1 Caractérisation des systèmes complexes Cette section permet de situer les lecteurs par rapport à la notion de système complexe dans lequel émerge la structure de commande que nous proposons. Elle caractérise les systèmes complexes et revoit les approches proposées pour la modélisation des cette classe de systèmes. Le formalisme permettant la spécification de ces modèles y est également discuté Définition Fishman (2001) décrit les systèmes dynamiques à événements discrets comme étant des systèmes complexes dont l état change instantanément de façon discrète dans le temps. Ce changement d état est régi par l occurrence instantanée d événements. Ces événements peuvent avoir lieu à des instants connus ou aléatoires. Selon la définition

27 8 donnée par Lemoigne (1990), un système complexe est caractérisé par le nombre de ses composants ainsi que par les relations de dépendance entre ces différents composants. Cette classe englobe les systèmes manufacturiers, les systèmes de transport, etc. Reaidy (2003) met l accent sur la complexité des systèmes manufacturiers. Il explique que l environnement actuel dans lequel émerge ces systèmes est dynamique, perturbé et le nombre des composants, c est à dire les acteurs, est susceptible de changer, engendrant une nouvelle composition. De plus, il se rajoute une complexité structurelle qui émane de l interaction et des relations de dépendance entre les produits lors de leur fabrication. La complexité des systèmes de transport est, selon Burckert (1998), reliée à leur nature intrinsèquement distribuée et dynamique. De plus, ces systèmes évoluent généralement dans des environnements fortement stochastiques. D après la caractérisation faite par Fleury et al. (2007), les systèmes considérés sont principalement inaccessibles et ne sont pas décomposables. La notion d inaccessibilité est reliée au phénomène circulatoire interne qui n est pas retraçable étant donné que ces systèmes ne peuvent pas être décomposés en sous-systèmes indépendants. Pour étudier ces systèmes complexes, il faut alors disposer d un modèle permettant de les appréhender. Les approches de modélisation généralement utilisées sont présentées dans le paragraphe suivant Approches de modélisation Pour ces systèmes à événements discrets, deux types de modèles sont généralement utilisés : les modèles analytiques et les modèles de simulation. Les modèles analytiques consistent à formaliser le système à l aide d équations mathématiques. Habchi (2001) résume cette démarche analytique en trois principales étapes : la recherche d un ensemble d équations qui peuvent décrire le système, la définition des hypothèses adaptatives du système réel et enfin l implémentation et l exploitation du modèle. Ainsi, pour que cette méthode puisse être utilisée, il faut d abord trouver le modèle mathématique et ensuite trouver les outils mathématiques

28 9 permettant d étudier ce système. Parmi ces outils on retrouve : la programmation linéaire, la programmation dynamique, etc. Les modèles de simulation, plus précisément les modèles de simulation à événements discrets, se basent sur la création d un modèle de comportement. Ce modèle essaie d imiter l'évolution au cours du temps de l'état du système réel. La logique de changement d état va alors reproduire temporellement et spatialement le comportement des différents éléments du système. Cette reconstitution ordonnée des évènements se fait par un ordinateur qui fera ainsi évoluer l état du modèle. Cardin et Castagna (2006) expliquent que l analyse de cette suite ordonnée d événements va permettre de faire des prévisions sur le comportement futur du système réel. La simulation consiste alors à développer un modèle informatique qui reconstitue le comportement d un système dynamique. Dans ce modèle informatique, le temps évolue de façon discrète par déclenchement d événements. À chaque événement est associé un ensemble de fonctions à exécuter qui peuvent modifier l état du système ou encore créer eux-mêmes un autre ensemble d événements. La gestion de ces événements est généralement faite à l aide d un ordonnanceur. Cet ordonnanceur maintient une liste d événements prévus avec la date de leur arrivée. En se basant sur cet échéancier, il déclenche les actions correspondantes. Pour une revue plus approfondie de ce principe de gestion d événements, les lecteurs peuvent consulter l ouvrage de Fleury et al. (2007). En terme plus spécifiques à la simulation, Boimond (2004) définit un tel modèle comme étant composé de variables, d objets et de relations entre ces objets. Les objets sont caractérisés par des attributs fixes ou variables. L'état du système est ainsi donné, à tout instant, par l'ensemble des valeurs, des variables et des attributs des objets. Ainsi, la reproduction de l évolution du système réel se fait par le modèle sous l'effet des activités qui y sont réalisées. Les avantages de ces modèles de simulation, lorsque comparés aux modèles analytiques, sont énumérés dans plusieurs ouvrages tels que ceux de Cardin et al. (2008), Fleury et al. (2007) et Hollocks (2006). Ces jugements se basent principalement sur la faiblesse des

29 10 méthodes analytiques à traduire la complexité des systèmes étudiés. Cette complexité implique des modèles analytiques avec un niveau d abstraction élevé. Ces modèles sont ainsi jugés considérablement synthétiques, ce qui engendre leur manque de fidélité dans la reproduction de la réalité. En conséquence, la conformité des résultats générés par ces modèles est remise en doute. Les modèles de simulation, quant à eux, attirent aujourd hui aussi bien les académiciens que les industriels. L avantage de cette méthode se résume par son aptitude à modéliser finement le comportement temporel des systèmes complexes et de grande taille et sans pour autant recourir à un degré élevé d abstraction. Cependant, Habchi (2001) précise que ces deux méthodes ne doivent pas nécessairement être considérées comme étant opposées. En effet, il explique que les modèles analytiques peuvent êtres d une grande utilité aux premières phases d analyse des systèmes. Par exemple, durant la phase de conception, ils peuvent fournir des configurations de base qui seront ultérieurement précisées à l aide de la simulation. Dans le cadre de nos travaux, étant donné que les aspects temporels et de synchronisation sont fondamentaux pour la commande, nous choisissons les modèles de simulation. Il faut noter cependant que ces modèles de simulation se retrouvent critiqués, vu leur manque de reproductibilité. Pour pallier cette lacune, Robinson (2004) précise qu il est nécessaire de développer un modèle conceptuel du système basé sur un formalisme de spécification approprié. La sous-section suivante décrit les formalismes utilisés dans ces modèles conceptuels Formalisme de spécifications Au cours de ces deux dernières décennies la notion de formalisme de spécification est devenue cruciale pour juger de la cohérence et de la validité de tout système informatique. Cette notion de spécification a été discutée par Demuynck et Meyer (1979). Ces auteurs ont affirmé que les langages de programmation sont impropres à la spécification. Ils ont ainsi expliqué que même si ces langages de programmation sont en

30 11 train d acquérir un haut niveau de normalisation qui leur confère un grand degré d interopérabilité entre les machines et les systèmes d exploitation un programme informatique reste toujours insuffisant en termes de reproductibilité et de fiabilité. Ils définissent alors la notion de formalisme de spécification comme étant la méthode de «fournir un cadre précis pour constituer sous une forme fiable et rigoureuse, pouvant éventuellement être traitée automatiquement, l'exposé d'un problème que l'on envisage de résoudre sur ordinateur.». Au fil des années, avec le nombre grandissant des langages de programmation, il est alors devenu fondamental de trouver un cadre standardisé permettant la compréhension et l analyse de tout programme informatique proposé. Billon et al. (2007) définissent ce cadre comme étant le modèle conceptuel qui permet de représenter, grâce à une méthode de spécification formelle, des concepts complexes du modèle informatique et ceci sans erreurs d'interprétation possibles. Deux principales méthodes sont généralement utilisées pour la spécification les modèles informatiques de simulation: les réseaux de Pétri et le langage UML (Unified Modelling Language). Un réseau de Petri est défini comme un graphe orienté comportant deux types de nœuds, nommés place et transition. Les places permettent de décrire les états et les transitions décrivent les changements d état ce qui correspond aux événements. La notion de jeton est associée à ces éléments. À tout instant, l état du système est alors donné par la répartition des jetons dans les places. Les réseaux de Petri décrivent ainsi la dynamique d un système en associant des graphes au comportement. Plus précisément, leur sémantique, s avère adéquate pour décrire le changement d état des systèmes à événements discrets. En effet, ce changement d état se trouve modélisé par le franchissement des transitions. L adaptation des réseaux de Petri comme formalisme de spécification des systèmes à événements discrets est décrit dans les travaux d Ernest (1994). Bien que l utilisation des réseaux de Petri s est avérée d une grande utilité lors de la spécification des systèmes à événements discrets; des récents travaux de Knaak et Page

31 12 (2006) critiquent les limitations de cette méthode pour les systèmes complexes et distribués. De même, Xu (2001) trouve que les réseaux de Petri sont incapables de modéliser correctement un système de production flexible. Habchi (2001) précise que la tendance actuelle est orientée vers le concept objet. En effet, il explique que cette vision objet est considérée aujourd hui comme étant la plus proche de la perception des programmeurs et des utilisateurs. Perret et al. (2003) considèrent aussi que l adaptation de ce paradigme objet permet de répondre aux besoins d extensibilité, de réutilisabilité et ainsi au standard de qualité logicielle. Pour adopter ce paradigme objet dans les modèles conceptuels, le formalisme de spécification UML est alors utilisé. Roques et Vallée (2007) expliquent que grâce à ce langage de modélisation unifié, les concepteurs considèrent aujourd hui la notion objet comme un standard au niveau industriel. En effet, UML propose de modéliser le système suivant deux modes : statique ou structurel et dynamique ou comportemental. Ces deux aspects sont nécessaires pour schématiser les composants du système ainsi que leurs interactions au cours du temps. Habchi (2001) considère UML comme étant la méthode appropriée pour la spécification des modèles de simulation vu qu elle permet la prise en compte accrue de l aspect dynamique indispensable en simulation. Un autre atout de cette méthode est la considération des objets selon leur structure, leur fonctionnement ainsi que leur évolution spatiale et temporelle. Un dernier avantage est la représentation graphique qui simplifie considérablement la compréhension. En effet, UML s articule autour de 13 diagrammes. Selon les objectifs et les champs d application, des diagrammes sont implantés. Pour le cas de spécification des modèles de simulation à événements discrets, Page et al. (2005) présentent les concepts nécessaires à modéliser ainsi que les diagrammes correspondants. Sans vouloir être exhaustif, les éléments syntaxiques relatifs à deux principaux diagrammes, les diagrammes de classe et les diagrammes d état, sont explicités dans ce qui suit.

32 13 Le diagramme de classe est considéré comme le fondement de toute modélisation objet. Il permet de représenter une vue interne statique du système. Cette vue décrit, par un graphe, les éléments intervenant du système et leurs relations. Dans ce graphe, le facteur temporel n est pas pris en compte. Ainsi cette vue traite principalement les classes et leurs relations. Une classe regroupe des objets partageant les mêmes caractéristiques de structure et de comportement, ainsi que les mêmes relations. Elle est représentée par un rectangle. Une association est une relation entre deux classes, elle représente par défaut une relation structurelle symétrique. Elle indique donc qu il peut y avoir des liens entre des instances des classes associées. À cette définition conceptuelle d une association, UML rajoute des notions complémentaires de relations d agrégation et de généralisation. La relation d agrégation forte, aussi appelée composition, décrit une contenance structurelle entre instances. La destruction du composite implique la destruction de ses composants. Cette notion sert à indiquer que le cycle de vie des objets composants est lié à celui du composite. Graphiquement, cette relation est représentée à l aide d un losange plein du côté de l agrégat. La généralisation permet d intégrer la notion de relation entre une classe spécialisée et une classe générale. Cette notion sert à introduire le concept d héritage. Elle est symbolisée par un trait dont la terminaison est un triangle qui se dirige vers la classe générale. Les diagrammes d état décrivent la dynamique interne des objets. Ils permettent de décrire les changements d'états d'un objet en réponse aux interactions avec d'autres objets. Ce type de diagramme se base sur trois principaux concepts : état, transition et événement. Il montre ainsi les états potentiels visités par un objet au cours de son cycle de vie. Le passage d un état à un autre se fait par transition instantanée qui est déclenchée par un événement. Les états ont des durées, tandis que les événements sont de type discret. Page et al. (2005) expliquent que cette notion d état et d événement est d une grande utilité pour spécifier la dynamique des modèles de simulation à événements discrets. Ces diagrammes servent ainsi à décrire le comportement des classes réactives.

33 Présentation de l application prototype : transport minier Cette section présente les caractéristiques de l environnement minier afin de présenter aux lecteurs notre application prototype. Elle revoit les opérations minières et permet de présenter la cartographie que nous avons réalisée du processus d exploitation des gisements minier. Cette cartographie sert à situer le problème de transport minier dans l environnent d exploitation des mines à ciel ouvert Présentation des opérations minières La méthode classique d exploitation des mines à ciel ouvert comporte les procédés suivants : exploration du site, préparation des surfaces, exploitation du gisement et enfin la restauration du site. L exploration du site consiste à faire des sondages pour définir le profil géologique du terrain et préparer des plans d exploitation afin d extraire les minéralisations tout en réduisant au maximum les coûts relatifs à l extraction. Ces plans sont contraints par les caractéristiques géologiques et minéralogiques du terrain. La préparation des surfaces concerne la mise en place de l infrastructure nécessaire comme les routes et les canalisations ainsi que les installations de traitement comme les concasseurs et les raffineries. L exploitation du gisement est la phase productive de tout le cycle et peut durer plusieurs années (5 à 20 ans). Cette phase consiste principalement à déplacer hors de la fosse, éventuellement vers les centres de traitement, les matériaux détachés des fronts de taille. Une fois que les minéraux sont extraits et la teneur du gisement est exploitée, la restauration du site est nécessaire pour remblayer la fosse et remettre en état le terrain et les végétations. Cette industrie nécessite de lourds investissements, ainsi pour rentabiliser et faire des profits, les sociétés minières essayent continuellement d augmenter la productivité, en

34 15 cherchant à optimiser les opérations de déplacements durant la phase d exploitation du gisement. Dans cette perspective, ce secteur minier a pleinement adopté les nouvelles technologies de l information permettant de délivrer les informations en temps-réel sur l état d avancement des opérations d extraction et de transport dans le gisement. Cependant, bien que l optimisation des opérations durant cette phase a suscité, depuis des décennies, l intérêt de plusieurs chercheurs, des travaux récents de Krzyzanowska (2007) ou encore de Lewis et al. (2004) s accordent sur le besoin inhérent de projets de réingénierie. En effet, des études de terrain menées par Krzyzanowska (2007) et Chen (2005) prouvent le manque de mise à profit des nouveaux logiciels et des nouvelles technologies intégrées. Afin de comprendre ces lacunes, la première étape de nos travaux est de mener une analyse détaillée du processus complexe d exploitation du gisement Cartographie du processus d exploitation du gisement Cette phase consiste à élaborer une cartographie détaillée du processus. La complexité de ce dernier émane en effet du nombre important des tâches et des intervenants ainsi que des interactions connexes entre eux. Ainsi, une activité de collecte d informations et de documentations sur le rôle des diverses parties intervenantes dans ce processus est menée. Pour cette cartographie, nous avons eu recours aux diagrammes de processus. Un diagramme de processus permet de représenter les responsables des tâches du processus, leurs activités respectives ainsi que l ordre chronologique de ces activités. La cartographie réalisée de l exploitation du gisement est alors composée des quatre diagrammes de processus suivants : mesure en teneur; abattage; terrassement; chargement et transport.

35 16 Ces quatre diagrammes de processus sont présentés en Annexe B. Le processus de mesure en teneur consiste à mesurer et vérifier la teneur en minerai pour la zonéographie précise des corps minéralisés. L abattage aux explosifs est l étape qui permet de fragmenter les roches. Le processus de terrassement consiste à entretenir et à nettoyer les pistes de roulage, les tirs et les verses. Le processus de chargement et de transport concerne le chargement des matériaux détachés par des pelles et mis dans des camions pour être transporter du front de taille vers les lieux de déversements. Plusieurs intervenants rentrent dans ce processus : opérateurs de pelles, répartiteur, service d entretien, service de planification, aiguilleur et camionneur. L élaboration de cette cartographie a permis de déceler la forte interconnexion caractérisant l exploitation du gisement. Elle a de plus dévoilé la complexité du processus de chargement et de transport. Dans ce projet, nous nous intéressons spécifiquement à ce processus. Cet intérêt est suscité par plusieurs travaux de recherches, par exemple Wang et al. (2006) ainsi que Alarie et Gamache (2002) estiment que l optimisation du processus de transport minier permettra une diminution des coûts opératoires, ceux-ci pouvant atteindre jusqu'à 50% des coûts. Ainsi, comme notre intérêt porte sur le transport minier, sans intégrer d autre processus d exploitation minière à dominante continue, nous classifions alors le système étudié comme étant discret Processus de chargement et de transport L objectif de ce processus est d assurer le déplacement des minéraux vers les installations de traitement. Au début du quart de travail, des pelles sont placées dans le gisement pour l excavation des matériaux depuis le front de taille. Chaque godet est ensuite déversé dans le camion. Une fois le camion chargé, il va se déplacer sur une piste de roulage pour atteindre le point de culbutage et déverser sa charge pour ensuite revenir à une pelle de chargement. Au cours d un quart de travail, le comportement du

36 17 camion est ainsi cyclique entre les pelles placées à des endroits fixes et les lieux de déversement préalablement fixés. La figure suivante (Figure 1), extraite de Fayad et Nabavi (2001), présente une vue montrant les camions et les pelles dans le processus de chargement et de transport d une mine à ciel ouvert. Figure 1.1 Processus de chargement et de transport : source Fayad et Nabavi (2001) Plusieurs travaux de recherches ont proposé des outils pour optimiser ce processus complexe : Wang et al. (2006), Ta et al. (2005), Bissiri (2003), Temeng et al. (1997) et Elbrond et Soumis (1987). Le principal objectif de ces travaux est de mettre en place des systèmes informatisés pour une répartition efficiente des camions dans les mines à ciel ouvert. Ces outils doivent allouer les camions aux pelles, afin de déplacer le plus rapidement possible les roches et les minéraux détachés depuis les fronts de taille jusqu aux lieux de déversement. Dans ces travaux, les trois composantes suivantes sont généralement considérées : camion, pelle et répartiteur. Cependant, la cartographie réalisée indique que l environnement dans lequel ces systèmes de répartition émergent est caractérisé par une grande hétérogénéité de flux et une affluence de composants de nature diversifiée en forte interaction : camions, pelles, conducteurs, routes, équipements, conditions climatiques, objectifs de production, répartiteurs, système de maintenance, etc.

37 18 Dans ce contexte, les récents travaux de Burt et Caccetta (2007) et Krzyzanowska (2007) critiquent la faiblesse des logiciels de répartition face à l environnement dynamique ainsi que fortement stochastique. En effet, Kheddar et Coiffet (2002) définissent cet environnement comme étant complexe et déstructuré. De plus Dessureault et al. (2004) mettent l accent sur le besoin de redéfinir ces systèmes de pilotage des mines pour répondre à des besoins accrus en flexibilité, agilité et robustesse. Ainsi, l inadéquation des logiciels de répartitions des camions avec la réalité des opérations parait comme l une des faiblesses qui engendre d énormes coûts. Nos premiers objectifs ont été de comprendre et d analyser ce large écart entre les résultats théoriques qui montrent la performance des algorithmes de répartition de flotte sur des problèmes tests et ceux réels, fortement critiqués par les praticiens. Dans ce contexte, une première phase d étude a permis de déceler dans la littérature que pour les systèmes de transport deux approches de modélisation différentes peuvent êtres utilisées, l approche macroscopique et l approche microscopique. La modélisation macroscopique décrit le trafic des véhicules comme un flux continu. Ainsi le déplacement du véhicule n est pas représenté mais seul compte le fonctionnement à un niveau agrégé. La propagation des véhicules est alors décrite à travers des variables globales : le débit, la concentration (nombre de véhicules par unité d espace) ou bien la vitesse du flot (vitesse moyenne des véhicules) (Cohen, 1990). À l opposé, la modélisation microscopique, offrant des modèles à granularité fine, tente de s approcher le plus possible du comportement réel des véhicules. Cette approche microscopique vise l analyse des composants du réseau de transport. Elle s appuie sur des notions d entités (tronçon, intersection, conducteur, véhicule, signalisation, etc.), chacune caractérisée par des attributs pour modéliser leurs interactions (Krauß, 1997). Ainsi, dépendamment des objectifs de l étude le choix d une granularité fine ou élevée doit être établi. Les travaux portant sur cette étude ont été publiés dans l article présenté ci-dessous.

38 Présentation de l article de conférence Cet article, voir Annexe A, intitulé : «Comparaison d approches de modélisation de problèmes tests pour le pilotage du transport : application aux mines à ciel ouvert» a été accepté et présenté dans la : 7e Conférence Internationale de Modélisation et Simulation - MOSIM 08 Paris- France. La référence de cet article est : A. Jaoua, M. Gamache et D. Riopel, " Comparaison d approches de modélisation de problèmes tests pour le pilotage du transport : application aux mines à ciel ouvert", 7e Conférence Internationale de MOdélisation et SIMulation, Éditions Tec&Doc Lavoisier ISBN :

39 20 CHAPITRE 2 ARTICLE 1 A FRAMEWORK FOR REALISTIC MICROSCOPIC MODELLING OF SURFACE MINING TRANSPORTATION SYSTEMS Présentation : Suite aux résultats de l article précédent portant sur l inconsistance des modèles macroscopique pour la résolution des problèmes de commande de flotte; l objectif de cet article est de développer un simulateur microscopique réaliste pour les systèmes de transport minier. Étant donné que le succès de la structure de commande prédictive que nous visons à implanter est contraint par la pertinence du modèle de prédiction, cette phase de développement du modèle paraît alors d une grande criticité. Ainsi nous proposons la structure conceptuelle permettant l implantation de tel modèle dans l environnent minier. L implantation de cette structure aboutit à un modèle robuste pour l analyse et le pilotage des systèmes de transport minier. Les premières expérimentations montrent l utilité de notre micro-simulateur dans la conception du réseau de roulage minier. Un autre apport concerne le potentiel de notre simulateur une fois intégré dans une structure de pilotage pour la gestion proactive des problèmes d allocation de flotte en temps réel. D autres potentiels relatifs au contexte environnemental, comme la réduction de consommation de carburant, sont aussi soulignés. Cet article qui a été accepté et publié dans «International Journal of Mining, Reclamation and Environment».

40 21 La référence de cet article est : A. Jaoua, D. Riopel and M. Gamache, "A framework for realistic microscopic modelling of surface mining transportation systems." International Journal of Mining, Reclamation and Environment 23 (1), (2009).

41 22 A framework for realistic microscopic modelling of surface mining transportation systems A. Jaoua, D. Riopel and M. Gamache Group for Research in Decision Analysis (GERAD) Department of Mathematical and Industrial Engineering, Polytechnique Montréal, Canada Abstract: This paper presents a recently developed realistic microscopic simulator for surface mining transportation systems called SuMiTSim. In the road transport sector recent researches proved that for proper deployment of Intelligent Transportation Systems (ITS), the use of microscopic simulation modelling rather than the conventional macroscopic ones is critical. Microscopic simulators emulate realistically the dynamic traffic on a road network. A conceptual framework for the development of a surface mining micro-simulator is then proposed. The implementation of this framework led to SuMiTSim which is a robust tool for truck traffic analysis and control. Two cases study have been conducted. The results obtained from the first case study show clearly the benefits that can be derived when using SuMiTSim as a laboratory for more efficient haul roads design. The second finding concerns the integration of SuMiTSim as a proactive updater for real-time allocation. Other potential uses of SuMiTSim are highlighted, such as for sound environmental management through controlling fuel consumption and reducing truck bunching effects on mine network. Keywords: Transport, micro-simulator, traffic, open-pit mine. 2.1 Introduction The prevalent technology used for loading and hauling material in surface mining operations is based on shovel-truck systems. With the integration of Information Technology (IT) including GPS and sensors to track the movement of in-pit materials, several approaches for minimizing the high cost of open pit mine transport systems have been proposed [1,2]. In this context, with the objective to use real-time data provided to increase profitability, we propose to develop a realistic microscopic simulator for surface mining transportation systems. This new simulator we have called Surface Mining Transportation Simulator, SuMiTSim. The purpose of this paper is first to present the

42 23 capabilities of SuMiTSim as a simulation laboratory for mine transportation network design and analysis. Furthermore, we demonstrate how it could be used as a real-time support tool by capturing the actual network traffic interaction and its attendant problems, as well as a tool for proposing more efficient haulage paths to which trucks could be re-routed for improving mine productivity. The adoption of this microscopic paradigm is mainly inspired from advanced research into implementation of Intelligent Transportation Systems (ITS) in the urban road environment. By studying the deployment of IT systems on road transportation, a need is revealed for adoption of simulation modelling and more specifically microscopic simulation modelling approaches to ensure a robust traffic and congestion control. The main difference between macroscopic and microscopic approaches is the level of modelling detail. The macroscopic approach is a low level detailed modelling; it describes the traffic process with aggregate quantities, such as flow and density. In comparison, the microscopic approach is known as a high level detailed modelling (single-vehicle level); it describes the dynamics of the elements, such as the vehicles and the road, and their interaction in the traffic network [3]. Previous research [4-7] has proved that the conventional macroscopic models lack the capability of modelling detailed functions and features of transport control and management and thus are unable to take advantage of a new generation of transport information technology. In [8] authors explained that for the investigation of ITS, the use of a microscopic model, which reproduces each individual vehicle movement and captures the dynamic interaction on road networks, is compulsory. In order to control the complex and nonlinear traffic phenomena like cluster formation, models must be able to capture information delivered from network component sensors. Therefore, researchers in road transport agree on the fact that the macroscopic approach is not capable of modelling causal connections between traffic situations and the vehicle, and thus cannot deal with an effective integration of IT in complex and dynamic transport systems.

43 24 The aim of our present work is therefore to integrate this microscopic paradigm into mine transportation systems by providing a robust framework for more realistic surface mining transport modelling. The conventional macroscopic approach widely used in modelling surface mining transport systems is unable to reproduce the dynamic aspect caused by truck interaction on mine haulage networks. This shortcoming of the macroscopic modelling will be addressed by our newly proposed microscopic model. By descending to the single truck-driver level modelling, we provide a simulator with a high degree of accuracy. Hence, SuMiTSim will give more robust analyses and decisions at not only the design stage for haul road network or equipment selection, but also at the planning and the real-time dispatching stages. Our model is capable of capturing and elucidating important traffic phenomena such as congestion or formation of bunches. Although these dynamic traffic effects are important, they have never been studied before in mining transport. In recently published research [9], authors pointed out the importance of a true measurement of bunching effects, which remains elusive in the mining industry as the issue is yet unresolved. Furthermore, in [10] we proved that simulation results generated by these macroscopic models could be biased when traffic interaction on mine haul road networks is ignored. Even though microscopic modelling has a great potential, this approach is known to be complex which could explain the ultimate resort to the macroscopic approach. In order to counter this complexity, the object-oriented approach is adopted for the conceptual design in order to simplify the reusability of the micro-simulator framework. Moreover, according to [3], scalability is another key factor if microscopic modelling is adopted. For this purpose, we will explain how our developed generic components could be adopted to model all sizes of mining networks. Furthermore, the usage of SIMAN/ARENA [11] overcomes the black box phenomenon of common urban road traffic micro-simulators [12].

44 25 This paper deals with development and implementation of an efficient microscopic simulator for open-pit mine transport systems. This work is presented as follows. In Section 2 the literature related to macroscopic and microscopic modelling in road and in mine transportation systems is analyzed. Section 3 deals with the micro-simulator framework design and development. Section 4 presents the first conducted validation study of SuMiTSim behavior in a mining environment. Another validation study is presented in Section 5, which is based on the sensitivity analysis technique. Section 6 presents experimentation and results undertaken on two case studies; the main findings are also discussed. The last Section 7 summarizes the main tasks required to develop this microscopic simulator, presents conclusions drawn from the research and gives guidance for future work. 2.2 State of the art on modelling approaches for urban road and mining transport systems Simulation modelling has gained great popularity as a modelling paradigm for robust control of transportation systems. Analytical approaches cannot deal with complex and dynamic transport process [13]. Assumptions behind mathematical formulation affect the accuracy as well as the applicability of results in the field of transportation. During the last decade, a great advancement has been accomplished in the field of urban road transportation. The aim of the following literature review is to study and focus on these advancements in road transportation for eventually adopting a new concept to mining transportation systems Modelling approaches used in road transportation systems Modelling approaches applied to road transportation are split into two research themes. The first theme concerns road traffic management, whereas the second concentrates on fleet management (Dynamic Vehicle Dispatching problems). For road traffic

45 26 management modelling there are two modelling approaches: macroscopic and microscopic. For fleet management, macroscopic modelling is most often used. Below, we first describe modelling for road traffic management then we go on to depict modelling for road fleet management. Traffic management Traffic management on road transportation has been a field of research since the 1950s. With the continuous increase in transportation demand, the planning and management of this dynamic process has become essential [14]. For this purpose, there are two primary types of modelling: macroscopic (low fidelity) and microscopic (high fidelity) approaches. Some recent research has focused on a mixed fidelity modelling, called mesoscopic, this approach will not be addressed in this paper; for more details readers could refer to [15]. Originally, only the macroscopic approach was available. Over the past twenty years, the advancement of computational capability has led to a wider implementation of the more accurate microscopic modelling approach. Furthermore, the development of ITS applications has emphasized the need for more dynamic and high fidelity models [8]. The macroscopic approach consists principally of describing traffic as flows defined by behavioral rules based on the mechanics of fluids. The evolution of traffic over time and space is expressed using a set of differential equations. The most popular macroscopic traffic model goes back to [16], which assumes that the flow is simply the product of the density and the average velocity. [17,18] have developed variants of the Lighthill- Whitham model. For an overview of the state of the art in macroscopic modelling research, see [19]. The main advantages of this approach are its good agreement with empirical data and less coding effort. In fact, the data needed for such models (flow counts, speeds) are at the same level of aggregation as the data supplied by the measurements. However, according to [3,6] this steady state approach is unrealistic when describing the more complex aspects of dynamic interaction between the

46 27 components in a transportation system s network. Thus, time-dependent microscopic models are required. These models provide individual representations of the vehicles driving along the network, and emulate the interaction of vehicles with each other and with the road infrastructure. In order to emulate the vehicle s movement in the system, two types of traffic flow are commonly reproduced: free flow and following flow modes. In free flow mode, the distance between the lead vehicle and the following one is assumed to be large enough, so there is no influence of preceding vehicles. In this mode, the driver seeks to reach and maintain his cruising speed. In the case of following flow mode, the interaction between the following and preceding vehicles must be reproduced. This behavior is captured in sets of rules which determine when and how a vehicle accelerates, decelerates, changes its route and so on. Other algorithms take into account the network characteristics which influence vehicle behavior, such as lane changing (in multi-lane roads, and gap acceptance (in intersections). The mainly embedded formulations are cellular automata (CA) [20] and car-following (CF) models [21]. In the literature these two model types are widely used on approved micro-simulator traffic software. As an example, in [22] CA was implemented into TRANSIMS, (TRansportation ANalysis and SIMulation System), and in [23] CF was embedded into CORSIM, (CORridor SIMulation). Although microscopic models allow an accurate emulation of traffic networks and lead to a more effective management and control of transport systems, there are drawbacks for this approach. Drawbacks include the large data requirements (road network, vehicle type, etc), significant development effort (object-oriented programming language, simulation language, etc) and finally the calibration of the model parameters [15]. Real-time dispatching In the literature, the macroscopic approach is commonly used to validate real-time dispatching algorithms on benchmark problems. The Solomon benchmark problems are in particular the most used [24]. Performance of dynamic vehicle dispatching algorithms presented in [25-29] are evaluated on a weighted graph G = (V, E), where V = {1,

47 28 2,..m,..n} is the vertex set and E is the edge set. Vertices i =1,...,m correspond to customers, whereas the remaining (n-m) vertices are depots. The assigned cost to each edge (i, j) E represents the travel time t ij. Depending on the dynamic degree of the studied problem, this travel time could be deterministic or stochastic. The objective then is to minimize, over all vehicles, a weighted summation of this travel time. In [7] authors pointed out this simplistic approach of translating the map of the city road network to a directed graph representation with nodes and links as depots and customers. Moreover they explain how the travel time in real traffic networks could no longer be Euclidean. The design and development of such separate dispatching software, outside of any transportation network management and control environment is criticized in [30]. A large gap between the pretended (i.e. simulated on macroscopic models) and the realworld performance of these dynamic dispatching algorithms was deplored in [31]. Hence, unlike for traffic management, the proposed modelling approaches for fleet management are mainly restricted to macroscopic modelling. The developed dynamic dispatching algorithms are evaluated on models in which interaction on the transport network is not effectively emulated Modelling approach used in mine transportation systems Simulation modelling is widely recognized as a powerful tool for mine design and planning. [32-34] give a literature review on the potential of simulation models in mining engineering. We focus on the use of simulation models for materials handling in open-pit mines with several excavation sites and a fleet of trucks carrying material (ore, leach or waste) from loading stations to a number of unloading stations. By studying modelling approaches used on these mine transportation systems, we notice that all of the developed or at least published research uses the macroscopic approach. In the literature, these simulation models can broadly be classified into two categories: simplistic and extended models.

48 29 Simplistic models The simplistic simulation models are adapted as benchmark models to evaluate the performance of truck dispatching algorithms like those proposed in [2,35-37]. The common logic behind these models assumes a mine can be represented as a graph consisting of nodes representing loading, unloading or waiting stations. The resulting problem corresponds to an algorithm for solving a minimum cost flow optimization problem on graph. In which the associated weight (cost) to each directed arc is generally a stochastic distribution of an estimated travel time between each pair of nodes (sites). The following example tends to encompass the common assumption made behind these macroscopic transport system models. An open-pit mine (figure 1) has a fleet of N trucks, 4 ore shovels and 2 waste shovels which are placed on loading sites (l i ). Ore is hauled to a crusher (u 1 ) and waste to a waste dump (u 2 ). After dumping, trucks at the crusher are ready to be assigned only to shovels 1 to 5, whereas trucks at the waste dump are ready to be assigned to shovels 2, 5 and 6. Truck from shovel 2 (l 2 ) could not dump at waste dump (u 2 ) thus, there is no direct arc from node l 2 to node u 2. A cost (Ĉ) is associated to each possible path. Cost Ĉ l1, u1 is higher than cost Ĉ u1,l1, empty trucks coming from the crusher are faster than the loaded ones from the shovel. Then, with such logic, allocation and dispatching decisions are based on off-line estimations of truck cycle time and performances are tested on unrealistic models which do not effectively reproduce truck motion (acceleration, deceleration, speed up, etc) and their dynamic interaction within the mine haulage network (rule based n-way intersection, etc).

49 30 l4 l2 u2 Ĉ u2,l6 l6 Ĉ u2,l2 Ĉ l6,u2 Ĉ u1,l2 Ĉ l2,u1 u1 Ĉ u1,l1 l1 Ĉ l1,u1 Ĉ u1,l5 l5 l3 Figure 2.1 Representation of a typical macroscopically modeled transport benchmark problem. Extended models On the other side, the extended models like those proposed in [1,38-40] tend to represent more detailed components than those addressed in the simplistic models. For example, [1] take into account the different rolling resistance of a haulage segment. The objectoriented approach used in [40] takes into account hoppers and surge levels, conveyor velocity, maintenance station capacity, etc. These extended models aim to analyze the system design and its capability for accurate prediction and deployment of equipment or haulage layout. The principle behind these models is to aggregate material flow with truck flow and to consider trucks as virtual entities moving in the network. With such assumptions the interaction of individual trucks with each other and within the network traffic is totally ignored and the travel times of trucks are generally estimated as a mean time delay.

50 31 From this investigation into modelling approaches used on road and mine transportation systems, we perceive that microscopic modelling has not yet been introduced in the mining field. Unlike the road transportation case, there is no research in mine transportation concerning the dynamic traffic interaction on the mine haul road network. According to [9] a true measure of the bunching effect remains elusive in mining industries. Furthermore, although the macroscopic modelling of benchmark problems for fleet dispatching is used in road and mining fields, recent research on road transport strongly criticizes this choice. Moreover in [10] we proved that the development of separate dispatching software, with no adequate modelling of the real-time haulage network constraints or traffic congestion and truck interaction, can lead to biased results, and thus can significantly increase the gap between simulated vs. practical algorithm performance. When the use of a macroscopic approach on urban road fleet management could be explained by the complexity of gathering real time data, in mining fleet management this complexity no longer exists as trucks are already fitted with GPS systems. Therefore, in order to give more robustness and accuracy to the management and control of mine transport systems, we propose to develop a realistic microscopic surface mining transportation simulator. The main stream of the methodology used to develop this micro-simulator is presented in the following section. 2.3 Design and development of mining transportation micro-simulator In this work the object-oriented approach is adopted for design of surface mining transportation simulator framework. Using this object paradigm ensures a high level of scalability and reusability to the developed software [41]. We use the Unified Modelling Language (UML) for the modelling notation. The UML is a set of object-oriented modelling notations that has been standardized by the Object Management Group in order to represent every kind of software system [42].

51 32 The second part of this section will deal with the SIMAN/ARENA implementation. This choice is mainly motivated by the recent work [12] in which they explain that using SIMAN/ARENA in transportation system traffic modelling insures a great level of flexibility and procures the label of open architecture to the developed software. However, it is important to note that the use of the high level ARENA construct does not allow capturing the complexity of the microscopic behavior, which is why we need to approach the problem with SIMAN lower-level language. ARENA was used basically as a developing environment interface Mining transportation micro-simulator framework design The UML class diagram is used to develop the conceptual model of the system. This diagram depicts the classes within our micro-simulator framework and their interrelationships. This class diagram is considered as the mainstay of object-oriented analysis and design [43]. First, we define the object model and depict the object classes to implement. Then, we discuss the following relationships implementation: association, generalization and composition. The description of the object-oriented framework using class diagram is presented in figure 2.

52 33 Figure 2.2 UML class diagram of the micro-simulator framework. Classes are depicted as boxes; they form the main building blocks of an object-oriented application. A link connecting two classes is called an association. It reproduces the relation between classes if an instance of one class must know about the other in order to perform its work. A triangle pointing from subclass to the superclass is called a generalization and it models an inheritance relation; one class is a superclass of the other. It reproduces similarity relationships (attributes, methods) between classes, and thus enables the reusability of existing data and code. A filled diamond at the whole end, called a composition, is a strong association in which an object is made up of other objects and that the part object cannot exist without the whole one. Our proposed framework is mainly based on these five reference classes: LoadingSite, UnloadingSite, Equipment, HaulroadNetwork, and Dispatcher. The LoadingSite and UnloadingSite classes are both generalization of three subclasses. LoadingSite inheritance hierarchy captures the similarities between OreFace, LeachFace and WasteFace classes. Depending on the classification of mining material, each production

53 34 face is specialized on stripping the predefined type of material. Let s assume the following three main classes: high grade ore, low grade ore and waste. The corresponding unloading sites to these three types of material are represented at the second level of specialization of the UnloadingSite superclass. They are referred to as: OreCrusher, StockPile and WasteDump. Equipment class is composed of two classes: Truck and Shovel. This composition relation indicates that the considered mining transport system is based on truck shovel operation. Shovel class is associated to subclasses of LoadingSite for modelling shovel affectation to production faces. HaulroadNetwork is a class from which objects are instantiated. This class is associated by a composition relation to Section and Node classes. These classes model the open-pit mine geometry and layout of the mine haul roads. The accuracy of the network segments modelling lead to a more effective microscopic tracking of the traffic interaction phenomenon on the haul road network. One of the main attributes in HaulroadNetwork class for microscopic tracking is capacity. In fact, the logic behind SuMiTSim truckdriver behavior simulation consists of defining this capacity in terms of cell numbers. The decision control of the system is embedded in a class named Dispatcher. One purpose of this class is to maintain coordination between a set of dispatcher objects, this coordination is represented by the recursive association. Truck allocation-dispatching is modeled in this set of dispatcher objects. To model dispatching task generation between Dispatcher and Truck classes, we introduce DispatchingTaskOrders which is an association class. The introduction of this association class is due to the valuable dispatching information that needs to be clearly defined such as: haul path, Shovel identification, etc. This Dispatcher class is connected to all other classes with binary association, in order to ensure a robust real-time dispatching while controlling all other components of the system. With such architecture, the control decision takes into account the complex dynamic nature of the mining environment. As an example, the

54 35 impact of bad weather conditions on rolling resistance will be tracked on HaulroadNetwork class, and it will be used accordingly by Dispatcher class in dispatching order generation. Later in this paper, other scenarios will be depicted such as detection of congested sections and the possibility of real-time truck re-routing Mining transportation micro-simulator development The implementation of our software framework is based on three main stages. The first stage is HaulroadNetwork class coding. For this purpose we introduce 'Intersections', 'Links' and 'Networks' from SIMAN elements. This first stage is the most complex one; as an example, the direct use of Intersections for Node class implementation with default SIMAN affected parameter to the node object prevents control of node instances. So, it is compulsory to resort to the IntersectionNumber method from SIMAN object code for proper specification. Another difficulty at this stage is how to govern the following two conflicting objectives: on one hand an accurate representation of the haulage network geometry must be defined, whereas on the other side we must provide scalable software which can be adopted to model all sizes and topologies of mining networks. For this purpose, we provide two generic components which reproduce the corresponding logic on LoadingSite and UnloadingSite classes. Each component will then be replicated as often as the corresponding studied open-pit mine has loading and unloading sites. Furthermore, we establish a component logic which avoids deadlock situations. Graphical representation is given in Figure 3. Two portions of the haulage network are represented. Each portion is segmented into cells. The cell length ( ) represents the average length a single truck could occupy.

55 36 Figure 2.3 Graphical representation of the layout s basic components. The second stage consists of defining attached resources to the three following classes: LoadingSite, UnloadingSite and Equipment classes. Two types of resources exist: static and dynamic resources. Shovel, crusher, stockpile and waste dump are static resources. They are considered as fixed during a shift. Trucks are the dynamic resources. In fact, in our model we consider trucks as physical entities navigating on the network as an independent flow. Unlike previously proposed models [38,40,44] in which trucks were identified as entities with characteristics as attributes, our model considers the class Truck. This class represents physical objects (i.e. trucks) which occupy and move through cells on haul road segments. In SuMiTSim truck-driver motions are implemented by a following behavior inspired from the CA model in addition to rules for crossing n-

56 37 way intersections. Finally, in the last stage we establish the logical control module through implementation of Dispatcher class. In this stage, different control strategies will be implemented for potential evaluation and analysis. An important step in building a robust simulator after its development and coding is validation. The following two sections will deal with SuMiTSim validation. The first validation study consists of checking the ability of the micro-simulator to reproduce macroscopic behaviour. The second study is based on sensitivity analysis technique proposed in [45] for increasing the validity and credibility of general purpose simulation models. 2.4 First validation study: macroscopic versus microscopic behavior Checking the ability of a micro-simulator to reproduce macroscopic behaviour is a commonly used technique for validation of road traffic micro-simulators and was proposed by a research team from Robert Bosch GmbH, [46]. For this purpose, we use the macroscopic model studied by Dunbar [36] Dunbar s model description The model used an open-pit mine transport system is composed of two loading shovels and one crusher. This simplified hauling configuration was used by [2] for assessing the performance of their stochastic optimization model. It was also used in [36] to evaluate their proposed real-time truck dispatching algorithm. In this system, shovels are affected at two distinct ore faces. Empty trucks at the crusher are dispatched to shovels in order to be loaded. When an empty truck arrives at the face depending on the shovel state (idle or busy), it may spot for loading or wait in the corresponding shovel waiting area. Once the truck is loaded, it will travel to the crusher for dumping. For this purpose, trucks

57 move through two fixed haul road segments defined between loading sites (l 1, l 2 ) and unloading site (u 1 ). In Dunbar s model, it was assumed that loading and dumping times are constant. Truck travel times vary stochastically according to a triangular distribution (minimum, mode, maximum). Thus, the resulting problem is reduced to a network with two nodes associated to shovels l i and one node u 1 associated to the crusher. For each node l i, there is an incoming arc from node u with an arc cost of Ĉ u,li. There is also an outgoing arc with an arc cost of Ĉ li,u. The corresponding values for the parameters of this macroscopic model are presented in Table Figure 2.4 Dunbar s model representation under the macroscopic approach. Table 2.1 Parameters in the macroscopic model Parameter Value (in minutes) Path Cost (Ĉ) Ĉ u1,l1 Tri (9,10,11) Ĉ u1,l2 Tri (4,5,6) Ĉ l1,u1 Tri (10,11,12) Ĉ l2,u1 Tri (5,6,7) Operating Time Shovel 1, ( l1) Constant : 3 min Shovel 2, ( l2) Constant : 3 min Crusher, (u1) Constant : 2 min Given the objective of satisfying an equal number of truck loads from the two shovels after a shift of 12 hours and under fixed assignment (i.e. trucks are assigned to a specific shovel for the duration of the shift), cycle time for shovel 1 is then equal to 26 minutes and cycle time for shovel 2 is equal to 16 minutes. Thus, the optimum number of trucks

58 39 assigned to Shovel 1 is eight and the optimum number of trucks assigned to Shovel 2 is five. Additional details can be found in [36] Model implementation After reproducing this macroscopic model on ARENA, we found that the number of truckloads was consistent with the results obtained in [36]. For the microscopic model implementation, we first define the haul network. The mine topography is composed of two disjoint sections between loading sites (l i ) and unloading site (u 1 ) (Figure 5). We define the velocity distribution of truck-driver couple on each segment. In order to take the inconsistency of driver behavior into account, truck-driver velocity is modeled based on Gaussian distribution. A mathematical analysis of this assumption can be found in [47]. For example, in section u 1 - l 1, the velocity of a loaded truck under free flow conditions is modeled using a normal distribution with a mean of km/h and standard deviation of 0.21 km/h. When empty the truck velocity will be higher, the mean of the normal distribution is assumed to be 36 km/h and the standard deviation 0.24 km/h. l2 V(t) N(36,0.24) 3 km u1 X (t) 6 Km l1 V(t) N(32.72,0.21) X (t) Figure 2.5 Dunbar s model representation under a microscopic approach.

59 Model validation We simulate the developed microscopic model and we compared performance, expressed as the evolution of total truckloads, to those realized by simulation with a macroscopic model. Simulation results are presented in [10]. We have thus demonstrated the capability of our microscopic simulator to reproduce macroscopic behavior. However, we noted a small performance gap which did not exceed 7%. This gap is due to delays caused mainly by acceleration and deceleration of trucks under microscopic modelling. We have also analysed the impact of changing the haulage layout by changing the section between the crusher placed on (u 1 ) and shovel 2 on (l 2 ) to a common section for all trucks. From this experiment we noticed that the performance gap grew from 7% with the first configuration to 13% with the modified configuration. Truck interaction is more abundant in haul road with a common segment. The point here was to investigate how this type of interaction is totally ignored in the macroscopic model and how the addition of only one common segment had increased the disparity between the macroscopic and microscopic performance results by 6%. Further details on this issue can be found in [10]; the main conclusion was that when researchers on fleet management adopt a macroscopic approach in modelling benchmark problems they could bias their simulation results. Furthermore, we proved that in these macroscopic models, the dispatching order generated by the dynamic routing algorithms could be ineffective when traffic interaction on a mine network is ignored or not effectively emulated. 2.5 Second validation study: sensitivity analysis For this sensitivity analysis study we used analysis of variance (ANOVA) to identify the model factors that have significant effects on the system performance. The first part of this study was carried out in [48]. Below we will present the main points and the results

60 41 of our work. For conducting this sensitivity analysis study we use a more elaborate openpit mine configuration, a midsize model Midsize model description The model used an open-pit mine composed of three shovels (l 1,l 2,l 3 ), one ore crusher (u 1 ) and one waste dump (u 2 ). The simulated mine road network topography is illustrated below (Figure 6), with the corresponding abstraction graph (Figure 7). Each road section consists of two one-way lanes. A lane carries truck traffic in the same direction and between two lanes the flow is opposed (Figure 8). Unlike in highways, on a mine road lane, overtaking a slower truck is not possible in mine traffic. This phenomenon of faster trucks bunching up behind the slower ones induces a creation and an increase in the size of the formed platoon in mine haul road network. Figure 2.6 Midsize model s network topography.

61 2,8 km 42 l3 7,5 km l2 u1 u2 4,4 km l1 4,2 km Figure 2.7 Abstraction graph of midsize mine model. Figure 2.8 Truck movement on the mine road section Factors investigated by sensitivity analysis and performance measures The following factors have been investigated in the sensitivity analysis: Number of trucks; Number of shovels; Distance between loading and unloading sites; Fleet heterogeneity ratio; Dispatching rules; Target variability ratio. The fleet heterogeneity ratio is related to the mixture of truck types within the fleet. This mixture characterizes the reality of open-pit mine operations. We introduce this ratio as a controllable factor in order to track and assess the dynamic interaction caused by different types of trucks moving in the same one-way segment. When a truck of type A encounters a slower truck of type B it enters the following flow mode. In this mode, the truck A decelerates and adjusts its velocity according to the headway with the preceding slower truck B. We assume in this study that the fleet is composed of two truck types: truck type A is a 360 ton trucks and truck of type B is a 240 ton truck. We define a heterogeneity scale ranging from 0 to 1. A scale of 0 corresponds to a complete

62 43 homogeneous fleet of truck type A or B and a scale of one corresponds to a half mixed fleet of each truck type. In this study the following dispatching rules are investigated: Fixed truck assignment; Minimizing shovel waiting time; Longest waiting shovel; Minimizing shovel production requirement. With the strategy of minimizing shovel waiting time, a truck is assigned to the shovel that is expected to be idle next. The longest waiting shovel policy consists of assigning a truck to the shovel that has been waiting the longest. The rule minimizing shovel production requirement assumes that shovels have predefined production targets and trucks are assigned to the shovel which is most behind its production schedule while taking into account the en route trucks. A detailed explanation of these rules is given in [37]. For these analytical studies we compute the following measures of performance from the system output: - Shovel utilization; - Truck utilization; - Total production; - Occupancy level. The first three measures are widely used in previous work [37,40]. However, the occupancy level is newly introduced and associated to our microscopic developed approach. Furthermore, although truck utilization has been used in previous studies, we compute this measure differently in our present work. In fact, with the adopted microscopic paradigm, we efficiently assess this measure that we depict for each

63 44 individual truck in the system. By truck utilization, we do not mean the state of the truck (busy, idle) but we look to consider useful truck movement. Let us assume that a hauled truck travels from the shovel to the crusher with the above defined free flow mode. Once it arrives there, it finds the shovel idle so the truck utilization would be 100%. This truck utilization decreases when non desirable delays occur due to: bunching on the haulage network, waiting for a busy loading or unloading station, stopping to give passing priority at a n-way intersection, etc. We also define total production as a ratio of realised tonnage versus a predefined target tonnage from the production plan. The occupancy level is a more complicated measure to compute. To assess traffic congestion, we define this measure for each haul road mine segment and also globally for the mine network. The occupancy level encompasses two measures, the first is a measure of concentration over space and the second measure is concentration over time. The number of occupied cells is then weighted by the proportion of the occupied time. When traffic is congested in one segment, which is characterized by slower speeds then this occupancy level will increase as a consequence of longer truck travel times. This measure of performance will then be an accurate traffic state indicator. The benefit of this two dimensional indicator will be emphasized in situations where free flow traffic is not automatically affected by the number of trucks, because when the fleet is homogeneous the smooth flow of traffic would not be affected. This occupation level will be of great importance for managing traffic on the mine haul road network ANOVA results and discussion The design experiment consisted of 720 minutes as length for each run (12 hours were chosen by Dunbar as the continuous work period) and the confidence level is set to be 95%. Table 2 lists the investigated factors and their assigned levels for this experiment. Each design point is experimented with 10 simulation replications.

64 45 Table 2.2. The design summary for the ANOVA experiment Factors Levels Number of trucks 10 levels; [2,..,20] Number of shovels 3 levels; (1,2 and 3) Distance between loading and 7 levels; [2km,..,8km] unloading sites Fleet heterogeneity ratio 6 levels; [0%,..,100%] Dispatching rules 4 levels; Fixed truck assignment Minimizing shovel waiting time Longest waiting shovel Minimizing shovel production requirement Target variability ratio 6 levels; [0%,..,100%] An example of simulation results is given below in Figure 9, which illustrates the variation of shovel and truck utilization, the percentage of the achieved total production from the target and the occupancy level for the different numbers of trucks. Truck utilization Shovel utilization Total production Occupancy level Performance (%) Number of trucks Figure 2.9 Variation of performance measures with the number of trucks

65 46 It is clear from the graph that the increase in occupancy level is not linear with the increase in the number of trucks. This behavior is attributed to the nonlinearity of the traffic phenomenon, which is created from interaction within the network. Simulations for each design point were then conducted and results were analysed using ANOVA method. ANOVA results for all of the response variables are presented in Table 3. In this analysis the following codification is adopted: *** corresponds to p-value <0.001; ** corresponds to p-value < Table 2.3. ANOVA results Source of variation Shovel utilization Truck utilization Total production Number of trucks *** *** *** *** Number of shovels *** *** *** *** Distance between loading and unloading sites Occupancy level *** *** *** *** Fleet heterogeneity ratio *** *** *** Dispatching rules *** *** *** *** Target variability ratio *** *** ** *** The ANOVA results showed that the majority of the investigated factors have significant effects on the system performance. It appears that fleet heterogeneity has a significant effect on all of the measured performance except for shovel utilization. It makes sense that the shovel performance would not be affected by the fleet heterogeneity factor due to the assumption that the shovel loading time remains the same for every truck type. This assumption is made only in this section to respect the requirement for a one-way analysis of variance study. Target variability has less effect on the total production, in fact target variability may affect each production site but since total production is computed as an average, this average is not greatly affected.

66 47 These ANOVA results support the previous finding that the traffic condition and the resulting interaction have a great impact on the entire system performance. In fact, the occupancy level is shown to be dependent on the investigated factors. This confirms the importance of considering the mining traffic as a critical component when studying open-pit mine transport systems. Moreover, dispatching rules have a significant effect on Total production; since a change in dispatching rules corresponds to a change of truck dispersion over the network, controlling this factor will be of great importance to improve traffic conditions and on haulage system performance. In conclusion, in this section we have asserted the importance of using a microscopic simulator for emulating traffic phenomena which appear to have significant effect on the performance of mining transportation systems. After investigating the validity of SuMiTSim, we move on to experimentation. 2.6 Case studies, results and analysis Two case studies are performed on an extended and realistic open-pit mine to explore potential application of SuMiTSim. The aim of the first case study is to investigate the capability of our micro-simulator, as an off-line tool for testing alternative design for the original haul road network. This issue has been pointed out as a problematic one in surface mining operations [49]. The second case study explores the potential improvement that could be reached by integrating SuMiTSim, as a realistic emulator of the haul road network traffic interaction in real-time truck dispatching systems Extended model description The selected mine consists of 10 shovels (l i, with i=1..10), one ore crusher (u 1 ), one stockpile (u 2 ) and one waste dump (u 3 ). We also introduce a departure station (d) which could be considered as truck parking area. The road network topography is illustrated below (Figure 10) together with the corresponding abstraction graph (Figure 11).

67 48 y Figure 2.10 Extended model network topography. 5,1 km 6 km Figure 2.11 Abstraction graph of extended mine model. For the dispatching system, we choose to implement the multilevel approach proposed in [50]. The upper level consists of defining each shovel production target while taking into account operational constraints (blending requirements). This production plan is

68 49 optimized by linear programming, while other approaches could be used (goal programming, non linear programming, etc). Once shovel targets are defined, we insert these values on the sublevel for real-time dispatching. An empty truck at the dispatching point is assigned to the shovel which is the most behind in its instantaneous target value; many other variants such as en route trucks and congested roads are also taken into account. The following assumptions are then formulated from the production plan: Shovels 1, 2, 4 and 5 are assigned to ore faces. Shovels 3, 6, 7 and 8 are working in the leach area. Shovels 9 and 10 are assigned for stripping waste First case study: simulation results This first case study focuses on measuring the impact of integrating a new haul road section between loading site 4 (l 4 ) and crusher (u 1 ). The objective herein is to know if the implementation of this modified design of haul road network improves transportation system throughput. Simulation results of the original and new designed throughput production are displayed below (Figure 12). From the simulation results we conclude that adding this route could improve the total production by 26%. Improvements are observed not only in ore production but delivered waste and leach levels have also increased. In fact, this new route has decreased network traffic congestion by reducing the road section occupancy level. Trucks from l 4 and l 5 bypassed congested sections by using the new alternative route rather than the old path (Figure 13). Dispatched trucks from u 3 to l 9 also took the new shortest path.

69 50 Original network New designed network Production level (%) 75% 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% Crusher Stock Pile Waste dump Figure 2.12 Evolution of ore, leach and waste production level: original vs. new designed network. Figure 2.13 New alternative route layout. This newly designed haulage network will thus keep truck traffic flow close to free flow mode. Figure 14 shows the decrease of road section occupancy level. By adding this new route not only do we improve shovel and truck productivity, but we also decrease fuel consumption. In fact, according to [51], by keeping vehicle flow on a given section close to free flow (i.e. by minimizing deceleration and acceleration due to congested areas) the fuel consumption rate could be reduced by 22%.

70 51 Figure 2.14 Road section occupancy level: original vs. new designed network Second case study: simulation results In this second case study, an incident is placed in the road section linking l 8 and l 6. This upset will not completely block the route but it will oblige the trucks to slow down when they move through this section. Two scenarios are simulated. At first, the dispatcher does not take into account this upset and trucks will move through this section even though it is congested. In the second scenario, we insert a traffic indicator in the dispatching module which allows rerouting trucks from the predefined shortest path in case of increasing congestion. Trucks dispatched to l 7 will then be rerouted to another less congested but longer path. The original minimal path (path 1) between u 2 and l 7 has a total length of 13.9 km. The dispatcher will reroute trucks to a longer alternate path (path 2) with a total length of 14.9 km (Figure 15).

71 52 Figure 2.15 Layout path1 and path2. Simulations results are shown in Figure % Dispatch with rerouting Dispatch without rerouting 70% Shovel target completion (%) 60% 50% 40% 30% 20% 10% 0% Shovel 1 Shovel 2 Shovel 3 Shovel 4 Shovel 5 Shovel 6 Shovel 7 Shovel 8 Shovel 9 Shovel 10 Figure Evolution of Shovel production: dispatching with vs. without rerouting. The experiments showed that by rerouting trucks to avoid bunching caused by disturbed traffic on path 1 due to slowing of other trucks, we improve total throughput production by 7%. More remarkably, shovel 7 production increases by 12%. Although path 2 is longer than path 1 so under normal conditions the corresponding truck cycle time used to be higher but when unpredictable events happen the truck cycle changes greatly. Then, basing dispatching decisions on an off-line past period predicted truck cycle could significantly decrease system performance.

72 Findings These simulation experiments conducted with SuMiTSim have led to two major findings. The first case study demonstrates how taking into account the microscopic behavior of trucks and their interaction on the haul road network can, at the design stage, lead to a more reliable evaluation model and thus to a more robust decision tool for mining transport system design. The second study proves the importance of considering real-time traffic conditions, not only at the dispatching stage but also at the allocation stage. Even though [2] have addressed this issue and proposed to use an updater, the main drawback of this updater is that it uses collected past period data. The delivered probability distribution of truck cycle time will then be based on the previous state of the mine and not on the real-time state. If platoon is formed on the network due to an upset which occurs during the last period at a giving road section, and if this disturbance is then fixed, the past period gathered data on truck cycle time will no longer be valid for the next period. In this context, we propose that instead of using the simple low-pass filter as an updater, a proactive approach for more robust real-time allocation will be to use predictive data produced by SuMiTSim. Our micro-simulator will take a snapshot of the actual state of the mine (truck position, traffic condition, etc) and then, it will generate more realistic estimations of truck cycle times for the next period. Indeed, SuMiTSim will not only address breakdown of shovels or crushers but also events such as haul road urgent maintenance activities or other upsets which directly affect the smooth flow of truck traffic. 2.7 Conclusion and future work In this research, we developed a realistic microscopic simulator for surface mining transportation systems. We provided the main principles of the methodology used to

73 54 develop this software framework. The object-oriented approach is adopted for the framework conceptual design. We also define generic components to ensure scalability to our microscopic simulator. This component has been tested in solving different openpit mine scales: basic, midsize and extended mine. Our developed framework can then be expanded to include every size of open-pit mines. Furthermore, two validation studies have been conducted to ensure a high level of credibility to our developed microsimulator. Potential uses of SuMiTSim as an accurate off-line decision tool for open-pit mine design have been highlighted. It could also be used as a simulation test bed to evaluate alternative mining traffic management strategies. Moreover, we propose a new advance for real-time allocation and dispatching by incorporating SuMiTSim as an on-line updater. By using this realistic emulator, it would be possible to control the dynamics of traffic phenomena. Furthermore, given that the technology required for real-time data acquisition in open-pit mines already exists, such as GPS systems for trucks positioning, the low cost of implementation of such application would be very profitable. Decreasing fuel consumption is another important improvement reachable with implementation of SuMiTSim at the control stage. In fact as we explained in the first case study, an increase in bunching is closely tied to an increase in fuel consumption. Furthermore, controlling pollution emissions is another important microscopic modelling issue; in fact, the ad hoc integration of a microscopic simulator with dynamic emission models appears to road traffic researchers as the most accurate way to truly measure pollution emissions [52]. With our micro-simulator, it would then be possible to calculate emissions for each individual truck according to its current driving mode: acceleration, deceleration, cruising, stopping, etc. In future work, we intend to investigate the implementation of an intelligent mining transport system, by integrating a real-time decision module based on an occupancy

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78 59 CHAPITRE 3 ARTICLE 2 SPECIFICATION OF AN INTELLIGENT SIMULATION BASED REAL TIME CONTROL ARCHITECTURE: APPLICATION TO TRUCK CONTROL SYSTEM Présentation : Suite à la phase de développement du noyau de la structure de commande prédictive qui a constitué le sujet de l article présenté dans le chapitre précédent, cet article a pour objectif de spécifier par un formalisme propre à la modélisation objet l architecture de commande proposée. Pour cette architecture, la stratégie de commande prédictive développée par les automaticiens est adoptée. Ainsi plusieurs concepts nécessaires à une implantation efficiente d une structure de commande en temps réel sont élucidés. Un module d optimisation intelligent basé sur la métaheuristique du recuit simulé est intégré pour la génération des lois de commande permettant la minimisation de l écart entre la performance réalisée et la trajectoire cible. Une phase d expérimentation est aussi effectuée pour examiner le potentiel de cette architecture dans la résolution des problèmes de répartition en temps réel de flotte de camions. Le contexte de transport minier dans un environnement stochastique est choisi comme cadre d expérimentation. La référence de cet article est : A. Jaoua, M.Gamache and D. Riopel, " Specification of an intelligent simulation based real time control architecture: Application to truck control system", soumis à INFORMS Journal on Computing en Juin 2009.

79 60 Specification of an intelligent simulation based real time control architecture: Application to truck control system Amel Jaoua Department of Mathematical and Industrial Engineering, Polytechnique Montréal, Montréal, Québec, Canada Michel Gamache Department of Mathematical and Industrial Engineering, Polytechnique Montréal, Montréal, Québec, Canada Diane Riopel Department of Mathematical and Industrial Engineering, Polytechnique Montréal, Montréal, Québec, Canada This paper presents a new generic architecture for the implementation of an intelligent simulation-based real-time control in large-scale discrete-events systems. The structure of the proposed control methodology is mainly inspired from the model-based predictive control scheme. Fundamental characteristics of real-time applications, timeliness, concurrency and reactiveness, are clearly specified and embedded to ensure the conformity of our online control architecture with the real-time systems standards. The feasibility of this new architecture is demonstrated through a complete implementation of a truck control system in an emulated mine transportation environment. In the experimentations that were conducted, results showed the capability of the provided closed-loop control in dynamic environment to achieve efficient real-time truck dispatching. We also present the used methodology that allows the integration of the intelligent metaheuristics search for an effective real-time fleet management, even under operational time constraints. The novelty of this work lays in the usage of concepts from computer science and software engineering in complex real-life problems generally addressed by the operation research community. Key words: generic architecture, control theory, simulation, fleet management, real-time system.

80 Introduction In the field of control theory, the model-based predictive control technique, introduced since the 1970s, is an approved and efficient control scheme. The purpose of this technique is to implement during the operational phase, control laws that minimize the deviation of the system output from the reference trajectory. According to Spyros et al. (1997), the success of this control method is due to its capability to face uncertainties, as it operates in real-time and optimizes the control law on a moving horizon based on closed-loop corrections. Camacho and Bordons (2004) state that, as this type control uses a model of the process to predict the future system outputs; its efficiency is then strongly related to the fidelity of this prediction model. In this context, Banks (1998) has proposed to adopt this model-based predictive control scheme for complex and distributed systems, such as manufacturing and transportation systems. However, he chooses to embed the high fidelity simulation model as a prediction model rather than an analytical one. He stated that, for this emergent class of large-scale discrete-event systems, simulation is known as the most accurate modelling approach. Thus, he established a new control approach for this class of systems named the simulation-based real-time control. Even though two decades have now passed since this approach was proposed, recent articles of Mirdamadi et al. (2007) and Yoon and Shen (2006) state that very few industrial applications are reported. In fact, according to Iassinovski et al. (2008), the reason of the scarcity of this promising simulation-based real-time control approach is the lack of, a formal specification methodology, leading to a generic architecture integrating the simulation model into the control system. The purpose of this paper is to open up new generic architecture avenues for the implementation of an intelligent simulation-based real-time control system. The structural design and the behavior of the proposed real-time control architecture are built upon the object-oriented modelling methodology. This methodology is based on the Unified Modelling Language (UML), recognized by the software engineering

81 62 community as a standard for deployment of real-time systems (Douglass 2003). In order to prove the viability of our architecture, a prototype implementation of a truck control system in mine environment is conducted to experiment the capability of the system in a real-time truck dispatching problem. The novelty of this research is to provide an effective real-time control system, in which fundamental characteristics of timeliness, concurrency and reactiveness are properly designed and implemented. Even though this type of control belongs fundamentally to the class of real-time applications, we could not find in any formerly proposed simulation-based control system, as those encountered in Iassinovski et al. (2008), Lee et al. (2007) or Young et al. (1999) a proper specification related to the system temporal behavior. From a computer scientists point of view the correctness of a real-time system is strongly related to the way in which time is handled. Levi (1990) has proved the criticity of the temporal reasoning and the management of temporal proprieties to ensure real-time application validity. We demonstrated how those characteristics are tracked in our control architecture to ensure that the control law is both accurate and timely. As an example of the considered control law: job assignment in the semiconductor back-end scheduling problem, dispatching of trucks in a mine transportation system, reroute jobs from production bottlenecks, etc. Such control law must be specified under short term control horizon within the range of few minutes. Another important feature of our control architecture is the use of a metaheuristic (the simulated annealing) in the optimization module to achieve intelligent control. Former researchers agree on the superiority of metaheuristic search techniques, but discard their use at this control stage due to the following limitations: integration complexity and the long simulation run-time (Robinson 2005, Gosavi 2003). To counter the integration complexity we embed a multiprocessing technique. For the second limitation, we demonstrate how the simulation run-time could substantially be decreased by developing a specific simulation model designed for the control purpose. This paper is organized as follows; Section 2 reviews the concept of simulationbased optimization and discusses existing simulation-based control systems. Section 3

82 63 deals with the specification phase of the proposed real-time control systems. Section 4 details the implementation and gives an overview of the control scheme. Section 5 includes simulation experiments and discusses results. Finally, Section 6 summarizes the findings and the main conclusions. 3.2 Literature Review The principle of the control architecture is to find, for the next control horizon, the control actions that minimize the deviation from the defined reference trajectory. For this purpose an optimization search must be performed. In the proposed architecture the discrete event simulation model is used as a prediction model, and the simulation-based optimization technique is chosen to find those control actions. The following sub-section mainly discusses this fundamental part of the control architecture Simulation-based optimization The integration of simulation and optimization is also referred as optimization for simulation or more shortly simulation optimization in the existing literature (Fu 2002). Herein, we opted for the taxonomy of a book written by Gosavi (2003) dedicated to this subject and entitled simulated-based optimization. The Simulated-based optimization is optimization where the value of the objective function is given by the output of a simulation model. The aim of this search process is to find values of a vector of input variables with the highest contribution to the objective function s value. Many comprehensive review of this mechanism are presented in Tekin and Sabuncuoglu (2004), Fu (2002), and Swisher et al. (2000). Depending on the nature of these input variables this optimization problem in large-scale stochastic systems belongs to two categories: parametric and control optimization. Even though simulation-based optimization has widely been studied in the literature, it is only recently that this fundamental distinction has been established by Gosavi (2003). In fact,

83 64 he states that a parametric optimization, also called static optimization, is performed to find a set of parameters that optimize the performance measure. It is referred to as static because the solution is a set of values for the design parameters for all states visited during the operational level by the dynamic system. Those variables are determined before the beginning of the system run and then remain constant. For example the number of Automatic Guided Vehicles (AGVs) is typically constant during the short term execution phase of a Flexible Manufacturing System. On the other hand Gosavi (2003) explains that in control optimization, also called dynamic optimization, the solution is a set of actions which are state dependant; i.e. this solution changes as the state of the studied dynamic system changes. Then the performance metric is a function of the selected actions in all the states. In a similar way, Gupta and Sivakumar (2005), made a clear differentiation between simulation models developed for the parametric optimization and simulation models developed for the control optimization. They state that, contrary to the highly stochastic simulation model for parametric optimization, the simulation model for control optimization must be partially stochastic. In other words, as those models must be used at the control stage, the introduced stochasticity must be relevant to the time scale of the prediction horizon. In Section 4, we highlight the issue of providing a dedicated simulation model for the control purpose. After defining the process of the simulationbased optimization the next sub-section discusses some implementation issues for this coupling technique Implementation issues The implementation issues outlined below concerns the optimization algorithms used for parametric purposes and the relative architectural design of the coupling technique. The second part exposes the same issues but for the control stage. Simulation-based parametric optimization appears to be very practical for the design and configuration of complex discrete event system, (Ghiani et al. 2007). For this

84 65 purpose the use of a metaheuristic (e.g., genetic algorithms, tabu search, simulated annealing) as an optimization method was widely discussed by Tekin and Sabuncuoglu (2004) and by Olafsson and Kim (2002). Their main conclusion was that even if the academic research community criticizes the convergence properties of metaheuristic approaches, such methods take precedence over other methods in term of generation of good solutions in simulation optimization practice. Although metaheuristics are not guaranteed to produce optimal solutions, asymptotic convergence appears to have limited relevance in practice. That explains the ultimate resort to metaheuristics as the methodology of choice of commercial simulation software with optimization packages: OptQuest uses scatter search, tabu search, and neural networks (Glover et al. 1999) AutoStat (Olafsson and Kim 2002) uses evolutionary and genetic algorithms and Optimizer that use simulated annealing and tabu search. According to Page et al. (2005), the successful use of the metaheuristic at this parametric stage is based on viewing the simulation model as a black-box evaluator of a complex function which cannot be given in a closed form. Then the optimizer is completely separated from the simulation model. The advantage of such architecture is in the flexibility of using generic optimization packages. For the control purpose, Mirdamadi et al. (2007) explain that the technique of simulation-based optimization is based on two different concepts: off-line versus online. As depicted by Gupta and Sivakumar (2005), most of the simulation-based control systems reported in the literature are off-line systems. In those systems, at a first stage an optimal or a sub-optimal scheduling is defined by an off-line simulation-based optimization technique and then this schedule will be stored and used later during the runtime of the system. This category of off-line control optimization could be viewed as parametric and executed under the black-box design. In fact, the simulation-based optimization resolution is not timely constrained. However, this off-line architecture, also called open-loop control, is inefficient for applications where the system performances are tightly related to the short-term control decision in a highly dynamic environment. Then, for an effective on-line/real-time control the simulation-based

85 66 optimization technique that is used must allow the on-line interaction between the environment and the simulation model. The control system needs this continuous environmental feedback to ensure that the control loop is acting properly and to define the control law for the next prediction horizon. Thus, the black-box coupling technique is no more relevant for this type of on-line control. The lack of controllability under this black-box design is also criticized by Persson et al. (2006). The next sub-section reviews the proposed control architecture for handling this real-time concept Review of application According to Banks (1998), the real-time control technique via on-line simulation appears of great potential towards the very challenging closed-loop control of the emerging class of large-scale discrete-events systems. Gosavi (2003) states that finding an adequate architecture for executing simulationbased optimization in real-time for control purpose is a complex issue. He proposes a solution that consists of coding the optimizer based on Reinforcement learning algorithm as an integral part of the simulator. But this solution remains viable only for small-scale application. Besides, the widely approved simulation packages could not be used and the development of a simulator with a general purpose language is required to integrate the optimization algorithm into the simulator. Another type of architecture is used by Son et al. (2002) and Young et al. (1999). The proposed simulation-based control architecture is embedded with the Arena software. A mechanism of multipass simulation is used. Two computers are needed to embed the two simulation models. At each decision point a task generator developed under Arena RT runs the latter simulation model in a fast-mode to evaluate different control policy and then feeds the real-time system with the best strategy found. This architecture has been tested on an emulated shop floor and promising results were identified for controlling dynamic flexible manufacturing systems. Even if this architecture seems simpler than the one that we propose, we could not find any formal

86 67 specification of timing constraints proving that it can lead to an effective real-time control system. Furthermore, the scheduling problem is solved only by evaluating scheduling alternatives and selecting the best scheduling control law. The works of Sivakumar and Gupta (2006) is one of the rare real word applications. They propose the implementation (in the C++ language) of an on-line simulation-based control system at a semiconductor back-end site. They reported performance improvement due to significant robustness under a stochastic environment. However, the authors did not provide a clear formalism of the developed architecture. Moreover, as an optimization technique they only selected the best evaluated scheduling rules. From the review of recent applications, we made two main observations. Our first comment is consistent with the one formulated by Iassinovski et al. (2008) and is related to the need of a more formal methodology for robust specification of a simulation-based real-time control system. According to Gérard and Terrier (2004), a proper real-time systems development cannot be achieved efficiently without methodological support tools such as the UML standard. Our second observation concerns the extensive use of simple rules as optimization method rather than the metaheuristics. The recent paper of Ouelhadj and Petrovic (2009) prove that the use of metaheuristics as dynamic scheduling/control technique is more appropriate than dispatching rules and heuristics. Robinson (2005) and Gosavi (2003) consider that it is difficult to use metaheuristics in simulation-based real-time control optimization because those methods are time consuming. In Section 5, we will demonstrate how our proposed architecture could support an intelligent metaheuristic optimizer while ensuring that the control law is generated with respect to system-response time requirement. The next section provides the design and the behavior specification of our proposed control system. 3.3 Specifications of the simulation-based real-time control system Prior to the specification phase, we begin by defining the main purpose of the system. The purpose of the proposed simulation-based real-time control system is to establish an

87 68 intelligent closed-loop control for a discrete-event system. This closed-loop control has to ensure that the operations are performed according to the predefined production plan. This production plan is considered as a reference trajectory and is computed off-line. It was assumed that this system target performance is already defined by an off-line planning/scheduling technique as the simulation-based off-line control optimization introduced in the second section or as the solution of an analytical model. As in the real environment the operating condition will seldom be stationary, the controller must continually monitoring the system state by generating new control laws and sending the specified control actions to be executed. The fundamental objective behind the control law generation is to minimize the deviation between the controlled systems achieved performances and the off-line forecasted performances. As pointed earlier this control system belongs by its nature to the category of realtime application. As for real-time system our proposed control architecture must respect the following fundamental properties: timeliness, concurrency and reactiveness. Zendler (1997) defines those notions as follows: timeliness is the most crucial part which insures that the system response is produced on time. A real-time application is intrinsically a concurrent system, thus modelling this concurrency concept is fundamental. The reactiveness is the ability to continuously respond to periodic as well as aperiodic events by providing interaction of the system actors with the environment. Since UML (Unified Modelling Language) has become a widespread standard for software engineering (Gérard and Terrier 2004) then we assume in this paper that readers are already familiarized with this standard. We propose an object-oriented architecture of the system expressed in the UML use case model. This model emphasises the reactiveness of the proposed control architecture with external environment. The system timeliness and concurrency requirements are depicted in the sequence diagram presented in the Section 3.2.

88 The UML use cases model of the control system For real-time systems the set of external objects and their interactions with the system are captured by the use case model. A use case is a named capability of a structural entity in a model. An actor is an object outside the scope of the system but has significant interaction with it. In Figure 1, we present the use case mode. It defines the functional requirements of the control system in terms of actors and use cases. The icon for an actor is a stick figure and the use cases are presented using an ellipse form. Simulation-based Real-Time Control System Get Stimulus Sensor Simulate «extends» Controller «includes» «includes» «includes» Formulate New Control Law Capture Environment Status «includes» «includes» Reference Input Actuator Implement Control Action Optimize Setup Parameter Figure 3.1 The use case model In the use case model the following actors are defined: Sensor, Actuator, Controller, Reference Input and Setup parameter. The actors Sensor and Actuator are defined as the main features of the real-time system. Sensors provide information to the application about the state of its environment. This environmental feedback is used to know how the control loop is acting. Actuators are used to change the system s environment according

89 70 to the received control law. Both actors Sensor and Actuator infer the required reactiveness to our developed Real-Time application. The main capability of the proposed simulation-based real-time control system is to implement Control action. The principle behind this control system is to continuously monitor the system state under the specified control actions until a new/better control law is formulated. When the system state deviate from the forecasted one or the prediction time horizon is achieved, the Controller has to find a new control law while considering the real-time environment and system status. In order to specify the control actions, two capabilities are required: Formulate New Control Law and Get Stimulus. This is shown as an «includes» relation. When searching for a new or better control law, the intelligent simulation-based optimization technique is used. Thus, both Simulate and Optimize capabilities are needed. The Optimize use case needs data from actors Reference Input and Setup parameter. The Simulate use case needs the capability Capture Environment Status. This use case relation is fundamental to record the realtime environment and system state. Finally, the control system can optionally use the capability Get Stimulus, it is shown as an «extends» relation. This relation is optional because it depends on the chosen policy in face of the exogenous stimulus. From a software engineering point of view, two types of stimulus exist in Real-Time application: periodic and aperiodic stimuli. When the actor Controller has control over periodic stimuli occurring at predictable time intervals, the consideration of aperiodic stimulus will be relative to the chosen policy. The following example gives a practical view of this point. In industrial engineering literature, we found the concept of aperiodic stimulus under the taxonomy of unexpected event occurrence; see (Ouelhadj and Petrovic 2009). In this context, some of these events in manufacturing environment could be: machine failure, processing time delays, urgent job arrival, shortage of materials, etc. Depending on the technical constraint of each manufacturing plant, some of those unexpected events could be considered as having insignificant impact and then be ignored. Thus, the use case Get Stimulus will depend on the classification of the Stimulus/Event. After specifying the

90 71 structural design of our control architecture, the next section provides an in-depth level of specification: the behavior specification Behavior specification of the control system For specifying the system behavior and the critical timing issue involved in our real-time control architecture, we use the UML sequence diagrams; see Figure 2. According to Gérard and Terrier (2004), those diagrams are the most powerful tools on behaviour modelling of a real-time system. We also use the branching improved concept provided in UML 2.0. These new concepts are well documented in Pender et al. (2003). Figure 3.2 Sequence diagram

91 72 Active objects involved in the interaction are: Actuator, Sensor and Controller. This concept of active object is related to concurrency propriety. The defined active objects run concurrently and each one owns its proper control thread. The Optimizer object belongs to a passive class and runs under the call of the Contoller object. Although the Simulator with the stereotype «process» is created by the Controller object, it is an active object and must run on its own and not shared address space. This concept of spawning child process is crucial for the proper implementation of the proposed realtime control architecture. The principle of our closed-loop is to operate periodically under the system steady state and to react to aperiodic stimulus to face the transient behavior of the system. For this purpose at a specified regular time intervals, called control horizon, a ControlLoop periodic signal is sent in order to compute new control law. Then the ControlLoop.period is set equal to the control horizon. This control horizon is domain and system specific. Nevertheless it must be well expressed as it represents a crucial characteristic in the control concept. Later in the implementation phase this notion of ControlLoop.period will be expressed under the studied transportation system. When ControlLoop signal is received, the real system state is recorded and the simulationbased optimization mechanism is launched to find new control law, minimizing the deviation of the system performance over the specified prediction horizon. For this purpose the Controller must spawn the Simulator as a child process. With this multiprocessing technique the Controller will be the parent process, and then remains active, listening to the external environment tracked via sensors feedbacks. Concurrently the fragment of simulation-based optimization is under a loop operator. This fragment will iterate until Stop Command (StopCND) is received from the Controller object. This Stop Command is constrained by the time-response requirement expressed as the NewControlLaw.execTime. The searching process completion time must be shorter than the tracked system state variation. This constraint is properly expressed in the sequence

92 73 diagram with the use of the sendtime propriety of the asynchronous messages Sensor_In and Sensor_Out. When the Controller stops the execution and gets the best found solution, this parent process destroys the child and sends the NewControlLaw to be executed by Actuators in the next control horizon. This fragment will be executed only if Aperiodic Stimulus is not taken into account. This condition is expressed on the guard of the alt operator. Then if during the control law processing an external Stimulus disturbs the real system state, the Controller destroys the former simulator child, gets the real-time environment state and spawns a new Simulator child process. Another timeliness constraint is captured in the requirement called quality of service (QoS). This time is imposed by software provider of the communication channel between the control and the controlled system. It is obvious from this specification phase that we propose a new architecture different from the previous ones provided by Lee et al. (2007), Son et al. (2002) and Young et al. (1999). Those simulation-based control architectures used to switch between the task generator and the fast-mode plan evaluator. Even if their approach seems simpler, they do not provide any timing specification to support the real-time system requirements. Furthermore, with our architecture we are no more confronted to the problem formerly reported in Banks (1998) of statistical consistency when initiating simulation to a different state. We are indeed under a more consistent approach which provides the same initial state and thus, the output analysis is similar to that for a terminating simulation. After the specification phase of the proposed generic control architecture, the next section deals with its implementation in a mining transportation system.

93 Prototype implementation of a truck control system The global control scheme discussed in this section is illustrated in figure 3 below. This scheme is adopted from the typical structure in control theory of a model-based predictive control. In this control scheme, we also provide the programming language used for each module. The core of this control system, in which an optimizer is embedded, is developed using the C programming language. A mine emulator is constructed for conducting tests; this application is coded with Visual Basic, which gives an ease interface to build applications. The mine observer module is based on a simulator model developed with SIMAN and ARENA RT. This observer has to reflect the state of the real mine system. Thus it must be synchronized and progress concurrently with the real system, i.e. emulated mine. The communication channel between this module and the mine emulator is established with C++ language, this language is imposed by ARENA RT to benefit from highly efficient response time. The mine predictor contains the simulator developed using the SIMAN simulation language (Pegden et al. 1995). Figure 3.3 Simulation-based control scheme The purpose of this phase is to discuss important issue for the implementation of this control scheme, based on the lastly provided object-oriented specification. The

94 75 following sub-section elucidates the context of the chosen application and the next subsections depict the implementation of the different classes into the control scheme Application context Material transportation is one of the most important expenditures in surface mine operation. In this environment, pickup and delivery operations involve a fleet of trucks transporting materials from loading sites (pickup stations) to unloading sites (delivery stations) through a haulage road network. At pickup stations shovels are continuously digging during a shift according to a predefined production plan. Trucks are moving in a cyclical manner between shovels and dumping areas. After dumping, truck receives its dispatching order expressed as its next assigned shovel. Those orders must be generated continuously during a shift. In mining operations the truck cycle time (10 25 min) is short comparatively to the length of the shift (8 to 12 hours). Also, the request of a truck assignment at each delivery point is particularly frequent (each 3 5 min). A large number of papers have been produced on this topic (Burt and Caccetta 2007, Ta et al. 2005, Alarie and Gamache 2002). The fundamental complexity of this class of problem consists on the generation of the truck dispatching order under highly stochastic and dynamic environment. It was demonstrated that for efficient management of this transportation system, the trucks assignment to shovels must be conducted concurrently with the real-time environment. For this purpose, huge investment has been made for the integration of GPS and sensors to provide real-time tracking of the transportation system state. However, recent works (Jaoua et al. 2009, Burt and Caccetta 2007) prove also the need of more effective control software to integrate and to make use of this accurate and online delivered data. Thus, in our present work we choose this complex transportation system as a prototype application for our real-time control system.

95 Simulator development In the proposed simulation-based control architecture, the simulation model plays a fundamental role since it is embedded into the mine predictor and the mine observer modules of the control scheme. Thus its accuracy is crucial for a proper closed-loop control. An important issue is the simulator development consists on providing a model which can be initiated to the state of the physical system. As explained by Gonzalez and Davis (1998), a problematic issue in most developed simulation models is that the used variables are different from those defining the state of the real system. For example, in the context of our application, in order to reproduce trucks travelling, a simple approach consists on assuming this activity as an entity flow through the system during a time period. A simulation model developed under this approach could be sufficient at earlier design stage. However, it does not capture neither indicates the physical position of each truck in the network. Thus, for the real-time truck dispatching and control such simulation model is inefficient. The conceptual design of a highly reliable simulator for surface mining transportation systems has already been provided in our previous works; more details could be found in Jaoua et al. (2009). In our model, five reference classes are mainly enrolled: LoadingSite, UnloadingSite, Equipment, HaulroadNetwork and Dispatcher. Equipment class is composed of two classes: Truck and Shovel. HaulroadNetwork class models the surface mine geometry and layout of the transportation network. The control law, i.e. truck dispatching orders, is embedded in the Dispatcher class. In our model a truck is defined as an autonomous object with capability to perceive control actions, i.e. dispatching orders and to react according to a behavioural map. Two simulators were coded: one for the mine observer module and another one for the mine predictor module. For this purpose we opted for the Siman/Arena simulation language (Kelton et al. 2007). This simulation language allows benefiting from the robustness of approved software in term of model building and statistical consistency.

96 77 Furthermore, this software offers, with Arena RT features, the possibility to establish a communication channel for exchanging messages with external applications. Further details on Arena RT functionality is given in (Young Jun and Wysk 2001). A simulator for the observer module is than provided under Arena RT. The simulator for the mine predictor module is built using SIMAN. The main issue, when coding this simulator is that it will be compiled only once. The predictions processing during the control loop execution are carried out by a simple calling from a C function of an executable file. In order to construct this model, we use a technique which allows us to generate an executable SIMAN program file. For this purpose, it is fundamental to separate the control and the state structures from the rest of the modelled component; they must be coded separately as a global variable and linked to external files. With this technique, we do not need to run the simulation software anymore nor compile the simulation model at each evaluation. We then, eliminate the time consuming actions in simulation-based optimization evaluation process. With this modelling construction, the Controller gets this state structure as a feedback from the Sensor object and creates the Simulator object with a pointer to the state structure as input. In this state structure, we mainly code each truck position in the network, their actual velocity and the different affectations. The achieved shovel productions are also reported. The control structure concerns the control law, i.e. dispatching order Implementation of Sensor and Actuator classes The active Sensor class must communicate in real-time with the controlled transportation system components. This class is then implemented in the simulator for the observer module. As the goal of the closed-loop is to monitor the transportation system action Actuator objects in this application are trucks. To monitor the transportation system, we notice that the state of the real system could be well tracked in the observer by the entering and leaving events in pickup and delivery stations. Sensors

97 78 are then placed at the entering and leaving zone of each station. A Sensor_In message is sent when a truck enters a delivery station. After dumping the truck departs from this site, a Sensor_Out message is then transmitted when crossing the placed sensor at the leaving zone of this station. To express those sensors the TASKS element from SIMAN templates are used. Aperiodic stimuli, such as trucks decelerations due to bad weather, are also integrated. Those stimuli are specified in the ARRIVALS element. Those signals synchronize the observer module with the controlled system state, i.e. the state of the mine emulator. The mine emulator module is developed with a standard programming language (Visual Basic 6). It is an external client application emulating a real mine environment, developed to test the functionalities and performances of our closed-loop control system Optimizer development For large-scale real-world optimization problems, metaheuristics are powerful algorithms. In our work, we are mostly interested by the viability of these algorithms for the simulation-based real-time control, and then the discussion of convergence is beyond the scope of this paper. Thus, we choose the Simulated Annealing (SA), introduced by Kirkpatrick (1984), as an optimization algorithm. In order to guarantee that our optimization procedure provide at least one feasible solution the initial solution is generated using classical dispatching rules in miming operation. In order to implement the SA algorithm, we need to define the problem-specific parameters and to determine the annealing parameters. Problem-specific parameters are the evaluation function and the neighbourhood structure. The chosen neighbourhood move will be discussed in the following experimentation section. The evaluation function expresses the gap between the target and the actual production achieved at each shovel. This function is related to the multilevel approach proposed in (Alarie and Gamache 2002). The upper level defines an optimal production plan for each shovel by a linear programming technique. This production plan is considered as a reference input

98 79 trajectory, in our control scheme, to be achieved during the operational level. In our application, we are interested by this operational lower level. We assume at the beginning of the shift that each target shovel production is already defined; and the production from each shovel is nearly linear with time. The objective is then to minimize the gap between the achieved and the instantaneous target. The annealing parameters are: the initial and final temperatures (T 0, T f ), the cooling schedule and the epoch length (E). There is a different cooling schedule for decreasing the temperature, we choose the geometric one. With this geometric cooling the temperature T l at iteration l is defined as: T l =T 0 (α) l. With α is the cooling rate ranges between 0.5 and The Figure 4 presents the used pseudo code of the SA algorithm: Figure 3.4 Pseudo code of Simulated Annealing As the evaluation mechanism is based on stochastic simulation, the value f i is the mean of outputs estimation from the required number of replications. The adequate number of replication is provided according to a confidence level of 95%, as defined in (Banks 1998) for the case of terminating simulation. After the implementation phase, the next section describes the experimentations and explores the potential of the control system.

99 Experimentations and results In this section the real-time control system capability in terms of reactiveness under periodic and aperiodic stimuli as well as time-response requirement are exposed Mine networks layout In order to conduct experimentation, two different realistic scales (medium and large) of surface mines are used. The corresponding abstraction graphs are presented below ,8 2 2,5 5,3 5,1 3,2 Figure 3.5: Abstract graph of mines. The medium-scale simulated mine (Figure 5a) has three pickup stations (shovels: S 1,S 2,S 3 ), one crusher (C) and one waste dump (WD). A departure station (D) is considered as a truck parking area. The haulage network is composed of the road sections with the corresponding distance presented in the graph. A fleet of 15 trucks is used in this medium mine. The large-scale simulated mine (Figure 5b) has 10 pickup stations (shovels S i, i=1,,10) and three delivery stations: crusher (C), waste dump

100 81 (WD) and stockpile (SP). A fleet of 60 trucks is used in this large mine. As stated earlier, the purpose of the dispatcher is to assign trucks to shovels. After dumping its load at delivery station, truck receives its dispatching order expressed as its next assigned shovel (pickup station). We formulate the control law as an allocation set to be computed and maintained for each delivery station at every specified control horizon. The following example explicits the formulation of this allocation set for the crusher delivery station (C). Let us assume a control horizon of 10 minutes, i.e. ControlLoop.period=10. Given that only one truck could dump at a time and the operation of dumping takes at least 4 minutes for positioning the truck, dumping the hauled material and leaving the dumping area; the cardinality of the crusher allocation set C is then C = 3. This cardinality is an upper bound on the number of possible truck assignment requests at the crusher during the time interval of 10 minutes. For example, let C={S 1,S 3,S 3 } be the generated control law. This indicates that the first truck leaving this delivery station during the next 10 minutes will be assigned to the Shovel 1, the second truck to Shovel 3 and so on Control system under nearly steady-state dynamics In this subsection, two types of study are conducted. The objective of the first one is mainly to show the effect of open-loop versus closed-loop control on a medium-scale mine system. The second objective is to examine the behavior of the large scales-mine under different control horizon. For the following experimentation, we assume that the operation of dumping in delivery station C takes at least 4 minutes, the same operation in other delivery stations WD and SP takes 3 minutes. Thus, in order to respect the previously defined time specification constraint: {NewControlLaw.execTime<= Sensor_out.sendTime - Sensor_In.sendTime}, an upper bound on the time allowed for finding new control law is set equal to 3 minutes. We then allow an execution time of 2 minutes for the simulation-based optimization searching. This time is also constrained by the validity of the starting system state under nearly steady-state dynamics. During

101 82 this time interval of 2 minutes, we assume that no abrupt state change as a breakdown of equipment (i.e. shovel, truck) occurs. Then if such event occurs, an aperiodic signal is sent to the controller to stop the searching, dismiss the last simulator and get the new disturbed state. The handling of such aperiodic events is discusses in the next subsection. To study the impact of the open-loop control versus closed-loop control, we choose to emulate the medium-scale mine for a period of 150 minutes. We impose a small perturbation on this real mine model, fluctuation of the truck-driver velocity by about 20%. Three simulation studies are conducted. In the first case, the system evolves under open-loop control. In the second and third cases, sensor feedback is used for the closedloop control of the mine. A periodic stimulus is generated at each specified ControlLoop.period to compute a NewControlLaw, i.e. allocation sets, according to the real, slowly disturbed, state of the mine. Two different control horizons of 20 and 40 minutes are tested. A warm-up period of 30 minutes is considered. Results are shown in Figure 6. Figure 3.6 Behavior of the system under Open-loop versus Closed-loop Control

102 83 From these first results we can easily detect the deterioration of the system performance under the open-loop control. This is in agreement with the expectation in the literature on the superiority of the closed-loop control. However in this medium-scale mine there is not a significant difference between a ControlLoop.period of 20 or 40 minutes. This indicates that even if a closed-loop is better than the open-loop control for this case we could not deduce that a small control horizon increases system output. Under this slowly perturbed environment it could be useless to define new trucks allocation sets at every relatively small control horizon. In the next experimentation the impact of different ControlLoop.period on the largescale mine, is tested for the same period of 150 minutes. The same velocity perturbation is also applied to the real large-scale mine. Results are presented in Figure 7. Figure 3.7: Behavior of the system under different Control Horizon The simulation outputs presented in Figure 7, show how the difference in control horizon infers a substantial variation on the large-scale mine performance. This system output variation in the large-scale mine is 40% greater than the one in the medium-scale mine.

103 84 In fact, in the medium mine only 15 trucks are used when in the large one the fleet is composed of 60 trucks. This larger fleet leads to greater volumes of traffic throughout the shared transportation network. Then under longer control horizon, the system becomes more unpredictable due to the stochastic nature of the traffic behaviour. Even trucks velocity in the real mine is slowly disturbed due to the highly dynamic traffic the state appears to deviate from the desired one when the control horizon increases. Thus, for more efficient real-time truck dispatching in this highly dynamic large-scale mine, the controller must set the ControlLoop.period to 20. As we explained formerly, the choice of this control horizon is related to the nature of the real-time dynamics of the studied system Control system reactivity under aperiodic stimuli The objective of this sub-section is to investigate the control system reactivity when an aperiodic stimulus occurs. The unpredictable event considered is the weather deterioration. When such event occurs in real surface mine system the trucks drivers decrease their velocity by about 50% for secure operation. In this context, two different experiments are conducted on the medium-scale mine. In the first case, this stimulus is ignored. In the second case, the capability of the Get Stimulus use case will be experienced. For experimentation purposes, we assume that this Stimulus/Event occurs after elapsing time equal to the eighth of a specified ControlLoop.period=40. Experimental results are shown in Figure 8.

104 85 Figure 3.8 System performance under Aperiodic Stimulus Obviously from the simulation graphs (Figure 8), system performance is deteriorated when this disturbance event is ignored. We notice performance degradation when the controller maintain the previously defined allocation set for truck dispatching; and do not react to change this control law even under the weather perturbation. The control system waits for the next ControlLoop periodic signal to get the new disturbed environment state into account. In the second case, when the Controller reacts to this Stimulus, a lost of 4.7% in production is prevented. In fact, this abrupt velocity change appears to greatly affect the traffic conditions. Thus, the truck dispatching orders computed before this upset occurrence are no more efficient to cope with this new state of the transportation environment. We prove that our control system has the capability to react in real-time and generate new efficient truck dispatching orders, leading to a substantial gain in performance. For this purpose, a classification of the Stimulus/Event must be established according to the

105 86 real application specificity. It is important to understand that, with our control system architecture it is possible to consider every transportation request as an aperiodic stimulus; and then generating within a time interval of 2 minutes, the appropriate next affectation for each truck. Such classification of Stimulus may be interesting if a problem occurrence induces very transient system behavior. After studying reactiveness of our real-time control system the following sub-section concerns the timeliness characteristics The response time of the control system In order to respect timeliness properties of our control system, the time generation of a new control law has an upper bound of 3 minutes. To conserve the validity of the starting system state we allow a maximum execution time of only 120 seconds for the simulation-based optimization searching. This sub-section shows how it is indeed possible to take advantage of the metaheuristic intelligent searching, even under realtime constraint. For this purpose in the first step a solution is computed by the classical dispatching rule of assigning trucks to the longest waiting shovel. In the second step the SA performs several evaluations with the objective to find a better solution. The neighbourhood move is performed by randomly choosing 3 ranges on each allocation set and shifts the corresponding assignment to the next shovel. An example of neighbourhood move is shown in Figure 9. In the large-scale mine with 10 shovels, the cardinality of the waste dump allocation set W under a control horizon of 20 minutes is W = 7. If the second element of this set is selected, then the number of the associated shovel will be incremented in cyclical manner.

106 87 Figure 3.9 Neighbourhood generation The following experimentations give an example of the conducted searching. In the first test the SA parameter set (T 0, T f, epoch) is equal to (10, 0.1,5), in the second test the set is (10,0.01,2). Results are exposed below, Figure 10. Figure 3.10 Evolution of the simulation-based optimization searching process

107 88 From these experimentations, we firstly deduce the use of metaheuristic leads to better performance than the use of simple dispatching rule. The choice of the SA leads to find dispatching orders which ameliorates the system performance by at least 17% comparatively to the achieved performance when basing the control action on a simple dispatching rule. Furthermore the convergence of the search to the found best value with the second SA parameter set is quicker than the first one. In fact in the first case it takes 179 seconds for the algorithm to find the same solution reached just after 105 seconds with the second parameter set. In our application, in order to find the appropriate epoch length we used the two counters AcceptCount and RejectCount used by Abdelsalam and Bao (2006). As it is well illustrated in the literature, the performance of such metaheuristic, in finding a good solution after a relatively small number of iterations, is very sensitive to the chosen parameter. It seems more appropriate for our considered application to opt for a set with less temperature. With this second SA parameters set, our control system satisfy the time constraint, (NewControlLaw.execTime = 105), and found a better dispatching than the one delivered by the classical dispatching rule. 3.6 Conclusion This paper presented a new architecture for embedding the simulation-based control in complex discrete-events systems. A truck control system in transportation mine environment has been used as a prototype implementation, to demonstrate the viability and the potential of our control architecture for efficient real-time truck dispatching. Nevertheless, the formal methodology used for the specification of the control scheme proves that our approach is generic and can be applied to other applications contexts. We have demonstrated the great potential of the closed-loop control when considering concurrently the real state of the system environment and computing the control law, i.e. dispatching orders for the next control horizon. For this purpose, the specified

108 89 concurrency and reactiveness proprieties of the proposed control system are fundamental. We confirmed that using the UML standard based on the object-oriented modelling methodology leads to efficient deployment of real-time system. In fact, our real-time control system could indeed generate an accurate and timely control law. We have noticed that in the formerly proposed control architecture important issues such as timeliness had rarely been considered. In fact, we found that those works were mainly provided by the Operations Research community; whereas building a real-time system is a task mostly addressed in the discipline of Computer Science. When concepts behind real-time system deployment could be ignored for solving earlier design problems or for offline planning; they are indeed fundamental, for effective online control of complex manufacturing and transportation systems. Our works open new avenues for Operations Researchers to integrate fundamental and approved concepts from computer and also from automation science to reach the widely desired effective real-time control. Another achievement presented in this paper consisted on the effective use of a metaheuristic (the Simulated Annealing) at the control stage. When the use of metaheuristics for an intelligent search of control law has been discarded in former works, we have provided solutions to facilitate their integration even when the simulator is coded with simulation software. In fact, the use of an approved commercial software in coding the prediction simulation model significantly facilitates the embedment of the control architecture. An interesting direction of future research would be to add other type of control law. In this first stage only dispatching has been considered, integrating real-time routing in complex and shared road network could also enhance the system performance. However, such two dimensional control law generation may infer a larger searching time. Thus, another interesting field of research consists on investigating the potential of parallel and distributed simulation for the intelligent real-time control of this class of discrete-events systems.

109 REFERENCES Abdelsalam, H. M. E., H. P. Bao A simulation-based optimization framework for product development cycle time reduction. IEEE Transactions on Engineering Management Alarie, S., M. Gamache Overview of solution strategies used in truck dispatching systems for open pit mines. International Journal of Surface Mining, Reclamation and Environment Andersson, M., G. Olsson Simulation based decision support approach for operational capacity planning in a customer order driven assembly line. Proceedings of the 1998 Winter Simulation Conference. IEEE Piscataway NJ United States, Washington, DC. Banks, J Handbook of simulation: principles, methodology, advances, applications, and practice. Wiley Engineering & Management Press, New York ; Toronto. Burt, C. N., L. Caccetta Match factor for heterogeneous truck and loader fleets. International Journal of Mining, Reclamation and Environment Camacho, E. F., C. Bordons Model predictive control. Springer, Berlin ; New York Douglass, B. P Real-time Design Patterns Robust Scalable Architecture for Realtime Systems. Addison-Wesley, Boston ; Toronto. Fu, M. C Optimization for simulation: Theory vs. practice. Informs Journal on Computing Gérard, S., F. Terrier UML for Real-Time. Pages UML for Real. Ghiani, G., P. Legato, R. Musmanno, F. Vocaturo A combined procedure for discrete simulation-optimization problems based on the simulated annealing framework. Computational Optimization and Applications Glover, F., J. P. Kelly, M. Laguna New advances for wedding optimization and simulation. Winter Simulation Conference Proceedings (WSC). IEEE Piscataway NJ United States, Phoenix, AZ. Gonzalez, F. G., W. J. Davis Initializing on-line simulations from the state of a distributed system. Proceedings of the 1998 Winter Simulation Conference, WSC. IEEE Piscataway NJ United States, Washington, DC. Gosavi, A Simulation-based optimization : parametric optimization techniques and reinforcement learning Kluwer Academic Publishers, Boston. Gupta, A. K., A. I. Sivakumar Conjunctive simulated scheduling. International Journal of Advanced Manufacturing Technology Hughes, C., T. Hughes Professional multicore programming : design and implementation for C++ developers. Wiley Pub., Indianapolis, Ind. Iassinovski, S., A. Artiba, C. Fagnart A generic production rules-based system for on-line simulation, decision making and discrete process control. International Journal of Production Economics Jaoua, A., M. Gamache, D. Riopel Comparaison d approches de modélisation de problèmes tests pour le pilotage du transport. 7ème Conférence Internationale de Modélisation, Optimisation et Simulation des Systèmes MOSIM 08, France. 90

110 Jaoua, A., D. Riopel, M. Gamache A framework for realistic microscopic modelling of surface mining transportation systems. International Journal of Mining, Reclamation and Environment Kelton, W. D., R. P. Sadowski, and D. T. Sturrock Simulation with Arena. McGraw-Hill Higher Education, Boston. Kirkpatrick, S Optimization by simulated annealing: quantitative studies. Journal of Statistical Physics Lee, J. J., P. A. Fishwick Simulation-based real-time decision making for route planning. Proceedings of the 1995 Winter Simulation Conference, WSC'95. IEEE Piscataway NJ United States, Arlington, VA. Lee, S., Y.-J. Son, R. A. Wysk Simulation-based planning and control: From shop floor to top floor. Journal of Manufacturing Systems Levi, S Real-time system design. McGraw Hill College Div. Mirdamadi, S., F. Fontanili, L. Dupont Discrete event simulation-based real-time shop floor control. 21st European Conference on Modelling and Simulation. European Council for Modelling and Simulation. Olafsson, S., J. Kim Simulation optimization. Proceedings of the 2002 Winter Simulation Conference. Institute of Electrical and Electronics Engineers Inc., CA, United States. Ouelhadj, D., S. Petrovic A survey of dynamic scheduling in manufacturing systems. Journal of Scheduling. Page, B., W. Kreutzer, B. Gehlsen The Java simulation handbook : simulating discrete event systems with UML and Java. Shaker, Aachen, Allemagne. Pegden, C. D., S. Robert E, S. Randall P Introduction to Simulation using SIMAN McGraw-Hill, New York Pender, T., E. McSheffrey, L. Varveris UML bible Wiley Pub., Indianapolis. Persson, A., H. Grimm, A. Ng On-line instrumentation for simulation-based optimization. Proceedings of the 2006 Winter Simulation Conference. IEEE Place of publication:piscataway NJ USA Material. Prudius, A. A Adaptive random search methods for simulation optimization. Georgia Institute of Technology, Georgia. Reithofer, W., J. Raczkowsky, E. Canuto HIMAC- Hierarchical Management and Control in Manufacturing Systems. cimmod94, Torino. Robinson, S Discrete-event simulation: from the pioneers to the present, what next? Journal of the Operational Research Society Rosen, S. L., C. M. Harmonosky An improved simulated annealing simulation optimization method for discrete parameter stochastic systems. Computers and Operations Research 32: Sanbuncuoglu, I., O. B. Kizilisik Reactive scheduling in a dynamic and stochastic FMS environment. International Journal of Production Research. (UK) Sivakumar, A. I., A. K. Gupta Online multiobjective Pareto optimal dynamic scheduling of semiconductor back-end using conjunctive simulated scheduling. IEEE Transactions on Electronics Packaging Manufacturing

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112 93 CHAPITRE 4 ARTICLE 3 EFFICIENT SIMULATION MODEL FOR REAL-TIME FLEET MANAGEMENT PROBLEMS IN INTERNAL TRANSPORT SYSTEMS Présentation: Dans le chapitre précédent, une structure de commande est proposée et aussi expérimentée pour la répartition temps réel des camions dans le réseau de transport minier. L article présenté dans ce chapitre vise à améliorer cette loi de commande de répartition par une dimension de routage. Dans les réseaux de transport fermés, comme ceux des mines à ciel ouvert ou bien des ports à conteneurs, nous avons décelé la gravité du problème de congestion du trafic, largement critiquée. Nous proposons alors d intégrer le routage comme composante connexe à la répartition de flotte en temps réel. Des expérimentations prouvent la pertinence de notre simulateur comme observateur reproduisant fidèlement des phénomènes de trafic importants de formation et de propagation de peloton résultant de l interaction longitudinale des véhicules. De même, on démontre que l utilisation de notre structure de commande permet un routage en temps réel tenant compte de l état du trafic réel et permettant d améliorer considérablement la productivité tout en minimisant la congestion dans le réseau. La référence de cet article est : A. Jaoua, D. Riopel and M. Gamache, "Efficient simulation model for real-time fleet management problems in internal transport systems", soumis à Simulation Modelling Practice and Theory en juin 2009.

113 94 Efficient simulation model for real-time fleet management problems in internal transport systems Amel Jaoua, Diane Riopel, Michel Gamache Group for Research in Decision Analysis (GERAD), Department of Mathematical and Industrial Engineering, Polytechnique Montréal, Montréal, Québec, Canada Abstract: This paper presents an efficient approach for realistic modelling of internal transport systems. The weakness of the former methods in tracking the traffic when solving fleet management problems in container terminals and in surface mining is strongly criticized. Thus we provide a new conceptual model integrating notions borrowed from the traffic engineering field. The difference between our model and the classical ones is demonstrated. Our model reproduces important traffic behaviors such as the platoon formation and prorogation. Experimentations results showed the substantial improvement realized with the real-time trucks rerouting to face problems such as closed road and highly congested paths. Keywords: Container terminal, Surface mine, Congestion, Simulation model, Real-time routing. 4.1 Introduction This paper focuses mainly on the simulation models for real-time vehicle routing and dispatching problems used in internal transport systems. More precisely, we are concerned with transportation activities exposed to the stochastic outdoor environment. In the present work internal transport includes vehicle-based transport systems that are confined to a closed network limited within boundaries defining the operating area. A

114 95 large number of applications belongs to this category of internal and outdoor system, such as the transport of containers at transhipment terminals, earthmoving in construction area, material transportation in surface mine and carrier, etc. Several papers in the literature have discussed the dynamic vehicle fleet management problems arising in internal transport systems. According to Van der Meer [1] the main goal of those works is to maximize efficiency, by moving loads, as quickly as possible, from pickup to delivery stations under operational constraints. Recently, Anh [2], Grunow et al. [3] and Vis [4] explained that those works mainly concerned the indoor manufacturing environment. Hence, they criticize the adoption of the proposed methods under other more complex networks and outdoor stochastic environment. As Grunow et al. [3] highlight, the path network in a seaport container terminal is of much larger size and height complex structure than the simple and well structured one in a manufacturing system. Also, Katta et al. [5] explain that the network in a container terminal is very often congested due to the large number of trucks operating simultaneously. They also emphasize that this traffic congestion significantly increases the ship turnaround time. In surface mine haulage network we also found the same critics related to the traffic complexity. Burt and Caccetta [6] and Krzyzanowska [7] point out that the problem of the high unpredictability level caused by truck bunched together in platoons; remains elusive in the mining industry. Obviously, more efficient modelling approaches for resolving this type of dynamic fleet management problem have to take into account the traffic behavior and the vehicle congestion. For this purpose, Vis [4] expresses the need to develop more accurate analytical or simulation models for this specific class of internal transport systems. However, to our knowledge and as noticed by Steenken et al. [8] we could not find any specification of a conceptual model allowing the integration of the dynamic traffic within classical models related to vehicle-based pickup and delivery internal operations. In this context, we propose a framework based on the powerful discrete-event paradigm. This framework integrates an extremely detailed model of traffic within a simulation model of internal transportation systems. The capability of the resulted model

115 96 to accurately reproduce interaction between vehicles and the resulted traffic behavior in internal road network is demonstrated. Finally, we embed this simulator in formerly developed simulation-based real-time control architecture where it will act as a predictor and an observer module. In fact, this paper is part of a more general research project aiming to provide a generic architecture, adopting the advanced model-based predictive control technique, for large-scale discrete-event systems. Then, we show how our highly accurate simulation model tracks real-time traffic states, detects congested roads and identifies less occupied path for achieving more effective real-time truck routing and dispatching. This issue of routing vehicles according to the real-time state of the internal network traffic and the online delivered information concerning their physical position has rarely been considered. Grunow et al. [3] affirm that providing routing flexibility in those shared internal path networks with highly congested traffic could greatly enhance the operation performance. This online rerouting allows avoiding problems that may be caused by the traffic volume, the stochastic nature of the outdoor environment (bad weather, road condition, and closed road), the variability of human driver behavior that causes bunching, etc. Our conceptual model is based on the object-oriented specification methodology using the Unified Modelling Language (UML) standard, presented in Page et al. [9]. In this paper, we also clearly emphasise how the classical used object-oriented conceptual model for the internal transport systems must be changed. This conventional approach, which models the vehicle travelling between stations as an activity processing with a specified time, fails to reproduce important traffic behaviors. In this context, we have already demonstrated in [10] that the validation of dedicated algorithms to truck dispatching optimization on such conventionally modelled benchmarks problems could lead to substantial inconsistency. This paper is organized as follows. Section 2 reviews the traffic modelling approach and discusses some previous applications which have considered the issue of traffic. Without a loss of generalisation for internal transportation application, this review is restricted to the transport of containers at transhipment terminals and material

116 97 transportation in open-pit mines. Section 3 deals with the specification phase of the proposed conceptual model. Section 4 details the implementation and the validation phase of the proposed simulation model. Section 5 includes experimentation and discusses results. Finally, Section 6 summarizes the findings and the main conclusions. 4.2 Literature review As the objective is to integrate a traffic model with a discrete-event simulation model of a vehicle-based internal transport system, the following literature review firstly presents the traffic modelling approach developed for urban transportation planning. The second subsection discusses implementation issues of the highly detailed microscopic modelling paradigm. Finally, the last subsection presents some works, which have considered the traffic behavior when studying outdoors vehicle-based internal transport systems Review of traffic modelling approach Modelling traffic flow for design, planning and management of transportation systems in urban and highway area has been addressed since the 1950s mostly by the civil engineering community. The following definitions and concepts of traffic simulation modelling can be found in works such as Gartner et al. [11]. Depending on the level of detail in modelling the granularity of traffic flow, traffic models are broadly divided into two categories: macroscopic and microscopic models. According to Gartner et al. [11], a macroscopic model describes the traffic flow as a fluid process with aggregate variables, such as flow and density. The state of the system is then simulated using analytical relationships between average variables such as traffic density, traffic volume, and average speed. On the other hand, a microscopic model reproduces interaction of punctual elements (vehicles, road segments, intersections, etc) in the traffic network. Each vehicle in the system is emulated according to its individual characteristics (length, speed, acceleration, etc). Traffic is then simulated, using

117 98 processing logic and models describing vehicle driving behavior, such as car-following and lane-changing models. Those models reproduce driver-driver and driver-road interactions. Despite its great accuracy level, for many years this highly detailed modelling was considered a computationally intensive approach. Since the last twenty years, with the improvements in processing speed, this microscopic approach becomes more attractive. In fact, Ben-Akiva et al. [12], Barcelo et al. [13] and Liu et al. [14] claim that using microscopic approach is essential to track the real-time traffic state and then, to define strategy to decrease congestion in urban transportation networks. For the control of congestion, they explain that the models must accurately capture the full dynamics of time dependant traffic phenomena and must also track vehicles reactions when exposed to Intelligent Transportation Systems (ITS). From the latter assertions, in order to control traffic congestion in internal transportation networks it appears that the microscopic modelling will be more appropriate. A common definition of congestion is the apparition of a delay above the minimum travel time needed to traverse a transportation network. As stated in Taylor et al. [16], this notion is context-specific; and complex because a delay may always appear in dynamic transport system, but this delay must exceed a threshold value in order to be considered. In our context of internal transport system, the formation and propagation of congestion is mainly due to the longitudinal interaction between vehicles. In fact generally speaking in mining haul road network as well as in the road network inside a container terminal, internal trucks are not allowed to bypass each other. Their movement is similar to vehicles in a one-lane scenario without overtaking. Thus the major manifestation of congestion under this traffic flow behavior is in platoons formation due to the longitudinal interaction. Tampere [17] defines platoons are sequences of one leader vehicle which is driving unconstrained followed by a number of constrained vehicles. From this review, we deduce that for efficient truck traffic and congestion control in internal transportation system, the microscopic paradigm appears of great potential.

118 99 Subsequently, the following subsection discusses the implementation issue of this highly detailed approach Implementation of the microscopic modelling approach In the recent decade, as the microscopic traffic modelling appears as the most effective way to study and integrate complex ITS applications, several microscopic traffic simulation software have been commercialised; among them CORSIM, DRACULA, AIMSUN, FLEXSYT, etc.. An extensive review and a comparison study of those micro-simulations commercial software are provided in Bernauer et al. [18]. For developing those tools, two approaches of simulation modelling are used: time-based and/or event-based models. According to the definition related to traffic engineering community, and given in the Highway Capacity Manual [19], a model is time-based if time progresses explicitly from one point in time to the next one. A model is event-based if time advances from one event to the next one while skipping over irrelevant points in time. This same definition is found in computer science discipline for developing simulation software but more under the taxonomy of event-driven and time-driven simulation models. In this context, Page et al. [9] state that researchers as well as practitioners agree that the event-driven approach is often more efficient than the time-driven one with fixed time step t. Also, the traffic engineer community Gartner et al. [11] and Middelham [20], agree on the efficiency in term of the highly improvement in the execution time of discrete event simulations comparatively to discrete time simulation models. In fact, contrary to the time-based traffic model, in which at every discrete interval the state of all vehicles is calculated, in the fully event-based traffic model like, FLEXSYT [21] when an event occurs only the changes for the affected vehicles are calculated. That makes this latter microscopic simulator very fast comparatively to the time-based traffic software. As in our work we intend to use the simulator as a prediction model for real-time control, the fast event-based modelling approach will be more appropriate. Besides, the

119 100 integration of an event-based microscopic traffic model with the original discrete-event model of pickup-up and delivery operations will be straightforward Review of applications As stated earlier, few works have considered the traffic behavior when studying outdoors vehicle-based internal transport operational problems. In the surface mining environment, pickup and delivery operations involve a fleet of trucks transporting materials from excavation stations to dumping stations, through a designed shared road network. At pickup stations, shovels are continuously digging during a shift according to a pre-assigned mining production plan. Trucks are moving in a cyclical manner between shovels (pickup stations), and dumping areas (delivery stations). A truck cycle time is defined as the time spent by a truck to accomplish an affected mission that consists of travelling to a specific shovel, being serviced by the shovel and hauling material to a specific dumping area. Alarie and Gamache [25] state that mine productivity is very sensitive to truck dispatching decisions which are closely related to the truck cycle time. Thus several papers have studied and proposed algorithms and software to resolve this problematic issue. In fact, this critical decision consists of finding, according to the real environment, to which best shovel a truck must be affected. Such decision has to be generated continuously during a shift, whenever a truck finished dumping at a delivery station. Despite the several proposed dispatching software, recent articles by Jaoua et al. [26] and Krzyzanowska [7] formally criticize the simplistic assumption behind those software which tend to provide dispatching decisions with the objective to optimize a truck cycle times previously calculated. Generally speaking, those softwares based the optimization process on the past period collected data of trucks cycle times and assume that for the next period trucks will spend on average the same time to accomplish missions. But in the reality of mining operation, the duration of truck travel time appears to be very sensitive to the variable traffic state and road conditions. Burt and Caccetta

120 101 [6] and Krzyzanowska [7], point out the unresolved problematic of truck bunching and platoon formation in mining road network which apparently induce lower productivity. In the last decade, similarly to material transportation in mining operation, several papers (Ioannou [27], Vis [28] and Cortes et al. [29]) have provided methods for improving container terminal complex operations. In such applications, three types of handling operations are defined: vessel operations, receiving/delivery operations and container handling and storage operations in the stack yards. As we are interested by internal transportation systems, our review concerns the papers dealing with the container handling and storage operations in the stack yards. Generally speaking, vessels bring inbound containers to be picked up by internal trucks and distributed to the respective stocks in the yard. Once discharged, vessels have to leave with on board outbound containers which also are delivered by internal trucks from the storage yard. For this purpose, trucks are moving through a terminal internal road network. In order to decrease the vessel turnaround time, which is the most important performance measure of container terminals, it is important to perform those operations as quickly as possible. In fact according to Maurizio et al. [30], this movement of containers between quay sides and storage yards appears to greatly affect the productivity of containership s journey. Vis and Koster [28] gives an extended review of numerous research papers, providing algorithms to solve this complex routing and scheduling problem. They criticize the lack of consistency of the simplistic assumptions made to solve the proposed models within the real-world highly stochastic environment. The ignored traffic situation in the complex seaport internal transportation network is strongly criticized in recent papers [2], [3] and [5]. For example, in Maurizio et al. [30], a travel time of a container internal truck is modelled as a static mean time of travel, based on the distance and the truck average speed. Duinkerken et al. [31], put a uniform distribution between zero and 30% of the nominal travel time formulation, aiming to assimilate the complexity of traffic. More accurate work to solve this issue is the one provided recently by Lau and Lee [32]. They integrate a traffic model to the internal service model and reported the effectiveness of this integration which allows analysing

121 102 the tractor traffic flow in a port container terminal. Conscious about the critical problem of congestion in the road network inside a terminal, Katta et al. [5] have developed a quantitative measure of congestion to be added as a controllable decision variable. For this purpose, they considered the road system inside the terminal as a directed network and they measured flows on arcs in units of trucks travelling per unit time. Those two last works appear as providing the leader approach in term of consideration of congestion and traffic in container terminals; however, their approach is ultimately macroscopic. As we have lately discussed, even if this macroscopic approach allows analysing the traffic behavior, the highly detailed microscopic model is more efficient for an effective real-time traffic monitoring and control. Through this literature review, we demonstrated the need for more accurate models to be able to control traffic and to alleviate congestion in those internal and outdoors transportation systems. Subsequently, the following section deals with the specification phase of such new models. 4.3 Specification of the proposed conceptual model In the Journal of the Operation Research society, Hollocks [33] asserted that discrete-event simulation is now considered as the most popular modelling techniques. For example, in container terminal operations, in the two recent and extended reviews by Steenken et al. [8] and Ioannou [27], it is explained that despite the huge number of papers providing analytical models for managing operations, discrete event simulation remains the most used approach when it comes to resolve real operational problems and consider the real system stochasticity. Even though simulation modelling appears to lead to more realistic results, some researchers remain sceptical in regard to the lack of specifications of the provided simulation models. In fact, the majority of the research papers on simulation modelling does not provide any specification of the conceptual model and only discusses the computer model. Recent books, by Page et al. [9] and Robinson [34], dealt with this

122 103 important issue and provided fundamental insight conceptual modelling of discrete event systems. Thus, in our present work, we apply the methodology based on object-oriented specification with UML proposed by Page et al. [9]. For the conceptual modelling of the static system structure, we used the UML class diagrams. The Statechart formalism is used in modelling the dynamic behavior of the transportation system. For more insight UML concepts, reader could consult Pender et al [35]. In the present work, we choose the transportation system in surface mining environment as a prototype application. However, it is very easy to translate it to other types of applications, for example the truck could be replaced by other type of vehicles such as internal tractors in container terminal, the loading area are the pickup stations, the unloading area as : crushers, stockpiles and waste dumps are delivery stations, etc. Furthermore, our proposed static system structure depicted using the UML class diagram has already been provided by Jaoua et al. [26], then the following section mainly discuss the conceptual difference between our modelling approach versus the classical one, generally used for this type of internal transportation systems The conceptual difference in modelling system static structure Since the earlier dedicated book to discrete-event simulation provided by Pritsker [36] till recently in Page et al. [9], we found that internal transportation systems are modelled by representing the internal road network as a resource serving transporters during a specified time. This processing time is generally referred to as processing delay time or service time. Thus, the vehicle travelling between stations is an activity conducted during this specified processing delay time. In fact, this system view goes back to the earliest works done in discrete-event simulation modelling. In simulation books (see Banks [37] and Chung [38]), the purpose was to demonstrate how real-life systems could be viewed as a customer-teller bank system; and then modelled as a network with basically three components: entity, queue and resource.

123 104 In this example, customers are viewed as entities entering the system and waiting in a queue node to be serviced by the resource, the teller. When the teller is free, a customer is removed from the queue and a service activity is initiated to be processed during the specified delay time. In order to fit this mould of the classical network model as a banking system, in internal transportation systems, very often, entities are viewed as trucks and the transportation network is considered as the resource which serves the trucks. Subsequently, after the specified time delay, modellers assume that the entity, i.e. the truck, has reached its destination and liberates the resource. The corresponding conceptual model, to this internal transporters activity representation logic, is showed in the following graph extracted from the UML class diagram, see Fig. 1. This diagram is related to the Object-Oriented model, provided by Knaak and Page [45], for a gravel pit system. The same logic is also founded in the Object-Oriented model developed by Maurizio et al. [30], for internal transport in container terminal system. Figure 4.1 Example of a UML class diagram from (Knapp and Page [45]). In the model, Fig. 1, a generator process denoted TruckArrival, creates Truck objects at a specified arrival rate and inserts them into a Queue object. Thus, the main logic consists on, aggregating the movement and interaction of trucks in the transportation network under a specified delay time. This time, is then expressed in term of arrival rate. This modelling logic could be sufficient to address earlier strategic planning and design problems, such as the haulage network layout or equipment selection, but it presents

124 105 limitation when it comes to solve real-time truck routing and dispatching problem. In fact, this problem of dynamic fleet management in shared transportation network is very sensitive to the traffic state. Thus, the required model must reproduce this traffic by accurately emulating the truck interactions in the network. In this context we propose a more realistic modelling approach depicted in the following class diagram, see Fig. 2, for vehicle-based internal transport systems. Occupay Affected to Assign Truck Respect Unload Control Figure 4.2 UML class diagram of a surface mine model, provided by Jaoua et al. [26]. It is obvious, from the class model specification, that our approach is different from the former one. The principle is that we go beyond the concept of a passive truck entity, which only recognizes server states such as idle or busy, to an autonomous object which initiates action by itself and in parallel with other trucks. Actually, to control the transportation system, it is essential to define each truck as an autonomous object. Kemper et al. [39] define an autonomous object as an active object which can initiate responses to environmental changes. Thus, in our model, each truck is capable of

125 106 perceiving stimuli, i.e. routing and dispatching orders, and reacting according to a behavioural map. This behavioural map is based on concepts borrowed from traffic engineering for modelling microscopic traffic simulator. For this purpose, Gartner et al. [11], define three main aspects to be modelled: environment, vehicle and driving. Modelling the environment consists of reproducing the characteristics of the internal haulage road network. Thus, we define the following four classes: HaulroadNetwork, Section, Node, and Cell. Herein, Section is composed of two one-way lanes. The mine haul roads geometry and layout are reproduced by the mean of class attributes. For example, Section has a speed attribute representing aspects of reality such speed variation in uphill/downhill section or a speed limitation in narrow curve. Node represents physical intersection on the road. For this class, attributes such as right of way are defined to represent traffic priorities. Others attributes could be added signalized or unsignalized intersections, speed limits, etc. The Cell class allows an accurate tracking of the vehicle current position. The definition of a cell length is related to the dimensions of the trucks. Generally speaking a judicious choice would be to define the length of a cell as the average length of a single truck. In some cases where different vehicle sizes are used, such as in container terminal with multi-trailer system, the number of associated cell could be greater than one. Later in this work, the importance of this Cell class in settling the congestion indicator will be exposed. The vehicle modelling is used to define the truck class. Truck is characterized as an autonomous object. Attributes such as truck physical dimension, nominal velocity, acceleration, and deceleration, are also defined. The following subsection presents the model of the dynamic driving behavior Modelling dynamic system behavior A fundamental component when defining the behavioural map of the Truck object consists on building the driving model. Driving in internal road network could be done under two types of traffic flow: free flow and following flow. In free flow, the truck

126 107 driver is not constrained by a predecessor and is free to choose its proper speed. Under this unconstrained traffic mode, speed regulation is assumed to follow a Gaussian distribution. The mathematical fundament behind this assumption is provided by Liu et al. [41]. Authors prove that driving behavior is inconsistent due to many stochastic factors, and this statement allows taking into account this variability. In following flow, the vehicle is constrained by a predecessor and must adjust its speed depending upon speed changes of the preceding vehicle. In order to reproduce this longitudinal interaction many car-following models are provided. Developing models to represent the reaction of a driver to the changes in the relative positions of the vehicle ahead, constitutes a large and active research field in traffic engineer, named the carfollowing theories. An extended description of those car-following models is provided in Mathew [40]. The basic philosophy of the herein used model is similar to the General Motors' model. According to Mathew [40], the principle of this widely used model is that each vehicle-driver regulates its speed according to the surrounding traffic conditions by accelerating or decelerating the vehicle. The motion of individual vehicle is funded based on Newtonian equations of motion. For capturing this dynamic system behavior we use the capability of the UML Statechart diagram. The following Statechart diagram, presented in Fig. 3, shows the lifecycle of trucks in the internal transportation system.

127 108 Figure 4.3 Statechart diagram. From this Statechart, the fundamental difference between our modelling approach and the classical one becomes more perceptible. In the former Statechart, such the one provided in [9], truck travelling is modelled as a transition triggered by a time event from a state, named On the Road. The specified instant at which this transition occurs, i.e. the truck terminates travelling, is set equal to the travel duration. In our model, the truck travel is a more complex state. Thus, we use the notion of composite state. The state, DrivingToLoadStation, is a superstate aggregating a set of specialized states called substates, shown Fig. 3. Then the motion of truck is regulated according to those substates elements of the composite Statechart diagram. Depending on the path s cells status, speed is computed according to the discussed flow models. In this section, based on the UML specification, we have demonstrated that our model is conceptually different from the classical one. This difference was elucidated through, the static system structure modelling as well as the dynamic behavior

128 109 modelling. After studying the conceptual model, the next section deals with the computer model implementation. 4.4 Implementation and validation of the transportation model The purpose of this section is mainly to elucidate implementation issues, related to the traffic behaviour modelling. The implementation details of the classes (see Fig. 2), related to the mine transportation system such as Dispatcher, are not depicted in this work. However, interested reader could consult Jaoua et al. [26]. The second subsection deals with the validation study. This study is conducted to test the capability of the simulator to reproduce the longitudinal interactions between vehicles, under constrained traffic conditions Implementation of the proposed internal transportation model For the implementation of this transportation model, we opt for the Siman/Arena simulation language, see Kelton et al. [24] Kesen and Baykoc [46]. This choice is mainly motivated by the advantage in term of speed in model building comparatively to the case when general purpose programming language is used, [34]. In other hands, Hunter [22] and Radwan [23] have recognized the potential improvement when such general-purpose simulation languages are used for developing traffic simulator. Authors explain that, this method is the most effective way to counter the inflexibility and the black box problem of commercial traffic simulation packages. However, when Hunter [22] developed an open architecture for transportation system based on the Siman/Arena, his model fails to reproduce the important longitudinal interaction. Thus, he deduced that, despite their advantages, general-purpose simulation language, primarily used in manufacturing industry, are unable to track important traffic behavior. In this section, we provide how the longitudinal interactions could indeed be captured, but with the SIMAN lower-level language.

129 110 SIMAN s CAPTURE and RELINQUISH blocks are essential to manage the different types of flow through the system. When under the classical modelling approach the flow of transported material (container, ore, etc.) is aggregated with the flow of transporters (truck, vehicle, etc.), in our approach those two flows are separated. An advantage of this modelling approach is that we deal with more readily measured variables. An example of a variable is the truck nominal velocity along specific road segment. When this data could easily be settled from the real-word system, the widely used truck travel time in the classical transportation model need more examination. This issue has been criticized by Banks [37] under a more general context. He states that, very often, in the developed simulation model, the dynamic of the real system is ignored and the modeller has to provide a probabilistic distribution for a phenomenon that represents the interaction of several random variables. This aggregation processes merely amplifies the stochasticity of the real-word systems. Another important issue when coding the SIMAN model is to use the TRANSPORT block instead of the ROUTE block. This ROUTE block lets the system assume that the truck object is a virtual entity moving through modules. This infers the problem of unrealistic vertical queuing as encountered and criticized by Hunter [22] in his transportation model. He found that the vertical queue allows for vehicles to enter virtually a place when actually this vehicle may be physically trapped in another area. The problem is that the vertical queue could not reproduce the longitudinal vehicle interaction along the road segment, and then the model could not capture a fundamental source of platoons formation and the resulting congestion propagation. The proposed solution in our work is to firstly use the CAPTURE block to allocate physical space through the system network; and then to embed the flow models in the TRANSPORT block to move the truck in the network.

130 Validation of the model behavior under constrained traffic The purpose of this subsection is to analyse a traffic pattern and to validate the microscopic behavior of the trucks under constrained traffic. It is important to understand this critical issue of capturing longitudinal interaction; with such capability our model will be able to provide a reliable and effective traffic state measurement for future tracking and control of congestion. In this experimentation, we use a 2000 meter one-way road section. We choose also two types of trucks effectively operating in hauling material at surface mine, the Liebherr T262 and the Liebherr T282. Table 1 presents the performance of each truck model. Those characteristics are retrieved from Brown and Koellner [42]. The driving under free flow condition is modelled using the Gaussian distribution. The mean of this distribution is put equal to the corresponding propel speed from Table 1, and a standard deviation of 5% is imposed. Table 4.1 Truck performance Liebherr T262 Liebherr T282 Nominal payload (tons) Propel Speed (Km/h) Acceleration (m/s2) Deceleration (m/s2) The diagram in Fig. 4a presents the simulated trajectories of the trucks in the road section according to our developed model. The diagram in Fig. 4b shows the simulated trajectories of the seven trucks, using the classical model in which the truck interaction along the road is not captured. In those simulations, trucks enter the road section according to the following sequence: the first truck is the Liebherr T282, followed by the Liebherr T262, followed by the rest of the five trucks from Liebherr s T282 model. In those graphs, the dotted line reproduces the motion of the T262 truck; the bold lines denote the trajectories of the six trucks T282.

131 112 (a) Our modelling approach (b) Classical modelling approach Figure 4.4 Time-distance diagrams. In Fig. 4a, the first truck entering the section is not faced by a predecessor thus it drives unconstrained under the free flow regime. Even if the second truck has a predecessor, since the T282 is faster than the T262, then we observe that this second truck also drive with the free flow regime. The distance between those two trucks never drops under the headway, then the second truck is never constrained by its predecessor. An interesting region to observe in this time-distance diagram is the one bounded by the line denoting the motion of the slow T262 truck. In fact, it is easy to detect from slopes observation how speed regulation is performed under constrained traffic conditions. As the second truck T262 is moving slowly, trucks 3 to 7 slow down in order to avoid collision and adjust their speed to this leader slow truck. Those last five trucks are then moving according to the following flow regime which induces platoon formation. This platoon is formed by the leader truck T262 driving unconstrained and followed by the five trucks T282 driving constrained as they get stuck behind this T262 slow truck. Eventually, the five last trucks T282 are trapped in the platoon until the leaving of the slow moving truck. Once this slow truck departs from this section we notice from slopes variation that those trucks tend to recover their original speed. The longitudinal interaction along this road section is then well reproduced by our model. In fact, the

132 113 curves forms in this graph, see Fig. 4a, are analogous to the curves in the original graph reproducing realistic vehicles trajectories forming a jam presented in Tampere [17]. When analysing the results delivered by simulation of a transportation model in which truck s interaction is ignored, it is obvious from Fig. 4b that each truck move according to the free flow regime and when a slower truck is encountered no speed regulation is performed. In Fig. 4b the lines denoting the motion of trucks 3-5 intersect the line of the second slow truck motion. Those trucks are moving without being trapped behind the leader slow truck T262. This behavior induces the formally criticized vertical queuing. With this model, the platoon formation is not reproduced in the simulation; and then the model is unable to capture congestion formation and propagation under constrained traffic patterns. Another inconsistency with this last model is in the arrival time obtained from the outcome of the simulation in Fig. 4b. As the congestion is not reproduced the resulted delay is not taken into account. When the simulation outcome of the fourth truck trajectory indicates its arrival to the end of section at time t=4.426 minutes in the realistic first simulation model outcome, see Fig. 4a, this truck reaches the end of section at time t= The magnitude of this time error could be considered as not relevant for applications in urban transportation, but in internal transportation systems, where the mission time is relatively small (5 to 20 minutes), such error propagation induces a substantial gap between the simulated and the real results. From this validation study, we deduce that our developed simulation model realistically reproduces traffic behavior under constrained as well as unconstrained conditions. Then, this model is capable of tracking congestion apparition and propagation on the network of internal transportation systems. The next experimentation section, investigate the potential of this simulator as a predictor and an observer modules in a formerly developed simulation-based control architecture.

133 Experimentation and analysis of the real-time truck routing For this experimentation phase a control scheme is used. The purpose of this control system, see Fig. 5, in surface mine transportation environment, is to find and implement a control law, i.e. truck dispatching orders that minimize the deviation of the system output from the reference trajectory. This reference input is the target production plan of each shovel and is computed off-line according to strategic constraints. The searching processing is conducted according to the simulation-based optimization technique. In the optimization module, we embedded a simulated annealing metaheuristic. The control law must be specified under short term control horizon within the range of few minutes. In this control architecture, our simulation model plays a fundamental role, since it is embedded in the predictor and the observer modules. Figure 4.5 Our simulation-based control scheme. In the following experimentations, this control scheme is used to conduct two different studies. The objective of the first study is to analyse the effect of roads blockage on a medium scaled simulated mine; and to investigate the capability of the predictor module to find new routing and dispatching orders under such upset

134 115 occurrences. The second study concerns the problem of congestion. For this purpose, a larger transportation network with highly traffic volume is used. The objective is to investigate the potential of the observer module for tracking real-time congestion state and delivering feedback for truck rerouting control actions Real-time truck routing under road blockage upset In a mining environment, the complexity of the pit layout induces poor geometric design of the transportation road network. Krzyzanowska [7], reports that often during the shift some segment of haul roads must be closed for reparation due to the frequent deterioration of the ground condition. Thus for maintaining safe driving conditions traffic is restricted on those roads until they are fixed. Such situation is, for example, due to the very frequent spillage problem or rocks fallen from the face. Trucks will then bunch and wait until the road is repaired. With our control system we propose to integrate a routing decision and to test the potential of rerouting flexibility. For the experimentation, we use a medium-scale simulated mine, see Fig. 6, with a fleet of 15 trucks. This mine is composed of three shovels affected to the pickup stations (S 1, S 2, S 3 ); and two delivery stations called Crusher (C) and Waste Dump (WD). The associated haulage network is formed of 13 sections and 12 nodes. The corresponding road segment distances are expressed in kilometre as section length.

135 116 x : Section length (Km) n4 S2 0,1 n3 2 C, WD: Delivery Stations Si: Pickup Station D: Depart Station n6 S3 0,1 n5 3 n2 0,1 n1 C n12 0,1 n11 S1 WD n8 0,1 n7 2 n9 n10 0,1 D Figure 4.6 Abstract graph of the medium scale mine. The original truck dispatching problem consists of finding an allocation set for every delivery station at each control horizon. An example of an allocation set related to the Crusher delivery station, is C={S 1,S 3,S 3 }. This set indicates that the first truck leaving the Crusher, in the next control horizon of 10 minutes will be assigned to the Shovel 1, the second truck to Shovel 3 and so on. The purpose herein is to use our control architecture and to include a routing order to the original dispatching control law. Then, we add another dimension to the previously defined allocation set named the path set. For every delivery station two sets are then maintained: the allocation and the path sets. The simulated scenario at this first study supposes that during the shift the deterioration of the driving condition on two roads (n 2 n 3 and n 9 n 12 ) imposes to close those segments for a reparation period of 20 minutes. For route assignation, the following path table is defined, see Table 2. This table maintains the various possible routes between pickup and delivery stations. Those paths are classified gradually from the shortest path (path 1) to the longest path (path 3). The closed road segments n 2 n 3 and n 9 n 12 are showed in bold. For example, when a truck at the crusher is assigned to the Shovel 3, this truck will take the shortest path (3200 meters). This path consists of the following sequence: node 1 node 2 node n 5 node 6. If the road segment n 2 n 5 must be avoided the second shortest

136 117 path, named path 2 is 4200 meters long, could be used. This path is defined as node 1 node 2 node 3 node 5 node 6. Table 4.2 Path table Crusher (C) Shovel 1 (S 1 ) Shovel 2 (S 2 ) Shovel 3 (S 3 ) Path 1 n 1, n 2, n 12, n 11 n 1, n 2, n 3, n 4 n 1, n 2, n 5, n 6 Path 2 n 1, n 2, n 5, n 7, n 9, n 12, n 11 n 1, n 2, n 5, n 3, n 4 n 1, n 2, n 3, n 5, n 6 Path 3 n 1, n 2, n 3, n 5, n 7, n 9, n 12, n 11 n 1, n 2, n 12, n 9, n 7, n 5, n 3, n 4 n 1, n 2, n 12, n 9, n 7, n 5, n 6 WasteDump (WD) Shovel 1 (S 1 ) Shovel 2 (S 2 ) Shovel 3 (S 3 ) Path 1 n 8, n 7, n 9, n 12, n 11 n 8, n 7, n 5, n 3, n 4 n 8, n 7, n 5, n 6 Path 2 n 8, n 7, n 5, n 2, n 12, n 11 n 8, n 7, n 5, n 2, n 3, n 4 n 8, n 7, n 9, n 12, n 2, n 5, n 6 Path 3 n 8, n 7, n 5, n 3, n 2, n 12, n 11 n 8, n 7, n 9, n 12, n 2, n 3, n 4 n 8, n 7, n 9, n 12, n 2, n 3, n 5, n 6 In order to respond to this upset of traffic restriction the following three control decisions are possible: D1: send trucks even if the associated shortest path contains the closed road segment, trucks have to wait at the entering of the section until the road is repaired. D2: maintain the affectation decision and switch to the next feasible path, from the path table (Table 2), for trucks rerouting. D3: use the simulation-based control system for generating a new control law i.e. routing and dispatching orders, according to the new, perturbed, mine state. For this case we assume that the original decision for the next control horizon of 20 minutes was the following: C= { S 1,S 1,S 3,S 2,S 3 }, C path = {P 1, P 1,P 1, P 1,P 1 }, WD= {S 2,S 1,S 1,S 3,S 1,S 2,S 1 }, WD path = { P 1, P 1,P 1, P 1,P 1, P 1,P 1 } The simulation results for this study are presented in the following graph, Fig. 7.

137 118 Production under different control decision 8325 Production (tonnes) No Blockage D1 D2 D3 Control Decision Figure 4.7 Simulation output according Decision. From the graph presented in Fig. 7, we deduce that the decision D 3 induces the least decrease of production rates. In fact comparatively to the normal case where no blockage occurs, the D 1 mode induces a loss of 13%, the D 2 mode a loss of 10% and the D 3 mode a loss of only 5%. The following Table 3 reports the generated control law under the different decisions D i. Table 4.3 Generated control law Decision Dispatching Routing D 1 C S 1,S 1,S 3,S 2,S 3 P 1, P 1,P 1, P 1,P 1 WD S 2,S 1,S 1,S 3,S 1,S 2,S 1 P 1, P 1,P 1, P 1,P 1, P 1,P 1 D 2 C S 1,S 1,S 3,S 2,S 3 P 1, P 1,P 1, P 2,P 1 WD S 2,S 1,S 1,S 3,S 1,S 2,S 1 P 1, P 2,P 2, P 1,P 2, P 1,P 2 D 3 C S 1,S 3,S 3,S 1,S 3 P 1, P 1,P 1, P 1,P 1 WD S 1,S 2,S 1,S 2,S 2,S 2,S 2 P 2, P 1,P 2, P 1,P 1, P 1,P 1 From those results, we found that the difference between D 1 and D 2 is not substantial. In fact under D 2 the truck from crusher to Shovel 2 will be rerouted to path 2, the cost of this route deviation is 3 km. Also, the dispatching decision consists on sending four trucks from Waste dump (WD) to shovel 1, those trucks will be rerouted to take path 2

138 119 and this deviation cost is equal to 24 km. Thus the total cost of rerouting is 27 km. Then for this haulage road network layout and for a road reparation time estimation of 20 minutes, it may be interesting to opt for the first decision of stopping trucks at the entering of the closed roads. Obviously this decision is related to the estimation of the required time for the route maintenance. A more interesting solution under those circumstances is computed by using our simulation model as a predictor module in the optimization searching process. The closed-loop control system takes the real-time state of the simulated mine and find new dispatching and routing decisions. The delivered solution, see Table 3, consists of furthering affecting trucks from crusher to only Shovel 1 and 3, while Shovel 2 will be mainly served by trucks from waste dump. This new shovels and routes reassignment ultimately decreases the loss of production. In fact, the embedded simulated annealing as an optimizer tries to find new affectations with the feasible routes while decreasing the gap of production. The founded new control law keeps production running and decrease the loss to only 5%. It is important to understand that this delivered solution is computed under a time constraints of 2 minutes. Then at this stage we are not discussing the optimality neither the superiority of this metaheuristic. Our objective is to find a good solution in term of production loss alleviation under real-time constraints Real-time rerouting from highly congested roads For this study, we choose a large-scale mine that is presented in Fig. 8. This mine is composed of 10 shovels affected to the pickup stations (S i, i=1,..,10) and three delivery stations i.e. a crusher (C), a waste dump (WD) and a stockpile (SP). The fleet is composed of 60 trucks which cause the high traffic volumes in the internal transportation shared network. This network is composed of 33 sections and 28 nodes.

139 120 5,1 Figure 4.8 Abstract graph of the large-scale mine As it has been reported lately in this work, the complexity of congestion is that it is a context-specific notion and it must exceed a threshold in order to be recognized as a problematic issue. Our simulator, as an observer module, is capable of reproducing the traffic state; but in order to monitor and control this traffic, we need to define an effective measurement of the congestion state to identify this threshold. Thus, we opt to embed the recently introduced concept of measuring traffic congestion, by Bham and Benekohal [15], with the space occupancy. This space occupancy indicator, named (S oc ), delivers an accurate measure of the congestion magnitude and it appears very efficient for real-time control of network traffic. The S oc is calculated as the percentage length of section occupied by vehicles to the total length of the considered section. More insight into the effectiveness and formulation of this indicator could be found in [43]. Once this measure is settled, the next step is to conduct tests to identify the critical occupancy level threshold. This value will be considered as an upper bound to allow the rerouting of trucks during the execution phase. This rerouting order consists on sending

140 121 trucks to a new longer but less congested path. Those tests are similar to the one provided by Chen et al. [44] to identify critical occupancy level for preventing congestion on highways. For the studied internal transportation network, see Fig. 8, a problem of congestion is easily detected at the section n 2 n 5 due to the highly demand for the delivery station C. Then, an interesting solution to alleviate this congestion is to reroute dispatched trucks from WD to S 9 toward a longer and less occupied path. This second possible path contains the section n 11 n 13, which is also at the entering of the delivery station SP. Thus we conduct tests to analyse the state of those two road sections. First, the tests presented in Fig. 9a, consist in using our simulator to analyse S oc on section n 2 n 5 within three levels of service: high, medium and low. The tests presented in Fig. 9b, concern the S oc on section n 11 n 13 under the three levels of service. (a) Section n 2 n 5 (b) Section n 11 n 13 Figure 4.9 Space occupancy on road sections Graphs in Fig. 9a indicate the increasing tendency of the S oc on the road section n 2 n 5. This increase is founded under the three levels of the road service. Thus we conclude that for the next 100 minutes, sending trucks through this section will ultimately intensify the congested state by enlarging the bunching and queuing time. However, from graphs in Fig. 9b, we detect that the behavior of the third graph corresponding to

141 122 the highest level of service is different from those obtained with the medium and the low levels of service. In fact, the space occupancy under the highest level of the road service has not an increasing tendency as it may be observed with the other levels. This indicates that if the S oc could be maintained below a threshold value of 12% in this section n 11 n 13, the problematic congestion state will be prevented. Once such critical value is detected, we could use it as a stimulus, from the observer to the controller, for real-time trucks rerouting actions. In the following experimentations two scenarios are conducted, under fixed and flexible routing. In the first one, the controller ignores the stimulus and continues to send trucks from WD to S 9 according to the second path. In the second scenario, when the space occupancy reaches threshold value of 12%, the controller send a new path set to reroute trucks to the third feasible path (through section n 19 n 17 ). Simulation results are exposed in the following Fig. 10. Figure 4.10 Transported tonnage under fixed versus flexible routing Obviously, from Fig. 10, providing routing flexibility in real-time operation could greatly enhance the system productivity. In fact, trucks rerouting to less congested path,

142 123 not only decreases the unproductive queuing and bunching time, but also alleviates the traffic congestion in the whole network. From those experimentations, we deduce that an effective closed-loop control, for dynamic vehicle fleet management in the internal transport system, could be achieved by using our highly detailed simulation model. Furthermore, we demonstrate that our developed simulator is an accurate traffic state observer. 4.6 Conclusion This paper presented an efficient simulation modelling framework for resolving realtime fleet management problems in internal transport systems. The provided model has been embedded into a simulation-based control architecture to demonstrate the substantial production improvement, in a surface mine transportation application. Our experimentations confirmed the expectations on the reachable benefit when trucks are rerouted from highly congested path in internal road network. In fact when under static condition the best path should be the shortest one; in real life operations rerouting vehicles to less congested but longer path may greatly enhance the whole system performance. For the proposed simulation model, we have provided the conceptual model, based on the strong object-oriented formalism, in order to allow its reusability and to elucidate important issue in traffic dynamic behavior modelling. Our simulation modelling approach could then easily be adapted to other applications, as for the internal transport of containers. We have also elucidated the conceptual difference between our model and the widely classical approach. When those models used to be sufficient to solve earlier design problems, we criticize their limitation for real-time fleet management problems. In fact, for an effective routing and dispatching of trucks, the real network traffic state as well as the physical position of transporters is essential. Thus, our model explicitly

143 124 integrates the microscopic traffic approach when solving the dynamic fleet management problems in internal transport systems. For future real implementation of our model, calibration study must be carried out. This calibration phase, of the highly detailed traffic models has been identified as a problematic issue in urban road networks. Due to the lack of data, modellers need to use probe vehicle to collect on-road traffic state. However, for internal transportation application, the used transporters are generally equipped with on-board positioning system. Thus, each truck is already a probe vehicle and the calibration would be straightforward. REFERENCES [1] R. Van der Meer, Operational Control of Internal Transport, Ph.D. thesis, The Netherlands TRAIL Research School, [2] T. L. Anh, Intelligent control of vehicle-based internal transport systems, Ph.D. thesis, Erasmus Universiteit Rotterdam, The Netherlands, [3] M. Grunow, H. O. Gunther, M. Lehmann, Strategies for dispatching AGVs at automated seaport container terminals, OR Spectrum, 28 (2006) [4] I. F. A. Vis, Survey of research in the design and control of automated guided vehicle systems, European Journal of Operational Research 170 (2006) [5] K. G. Murty, J. Liu, Y.-W. Wan, R. Linn, A decision support system for operations in a container terminal, Decision Support Systems, 39 (2005) [6] C. N. Burt, L. Caccetta, Match factor for heterogeneous truck and loader fleets, International Journal of Mining, Reclamation and Environment 21 (2007) [7] J. Krzyzanowska, The impact of mixed fleet hauling on mining operations at Venetia mine, Journal of The South African Institute of Mining and Metallurgy, 107 (2007) [8] D. Steenken, S. Voss, R. Stahlbock, Container terminal operation and operations research-a classification and literature review, OR Spectrum 26 (2004) [9] B. Page, W. Kreutzer, B. Gehlsen, The Java simulation handbook : simulating discrete event systems with UML and Java, [10] A. Jaoua, M. Gamache, D. Riopel, Comparaison d approches de modélisation de problèmes tests pour le pilotage du transport, 7ème Conférence Internationale de Modélisation, Optimisation et Simulation des Systèmes MOSIM 08,France 2008, 10 p.

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147 128 CHAPITRE 5 DISCUSSION GÉNÉRALE Notre objectif ici n est pas de rediscuter les conclusions établies dans les différents articles. Ce chapitre porte principalement sur la revue de littérature présentée au chapitre 1. Nous discuterons, dans un premier temps, de la pertinence du recours aux modèles de simulation. Ensuite, nous revoyons l intérêt de la cartographie réalisée, pour situer notre application du transport minier dans le processus global d exploitation minière. Dans la première partie de la revue de littérature, nous avons décelé les deux types de modèles utilisés pour les systèmes complexes à événements discrets : les modèles analytiques et les modèles de simulation. Bien que dans nos travaux, nous avons opté pour les modèles de simulation; nous n adhérons pas à l idée de délaisser l approche analytique pour le pilotage et le contrôle de la classe émergente des systèmes dynamiques complexes. En effet, nous décelons dans plusieurs travaux récents que la faiblesse des modèles mathématiques jugés statiques face aux environnements réels stochastiques, mène certains chercheurs et surtout les industriels à délaisser complètement l approche analytique et de se tourner ultimement vers la simulation. Ainsi, avec l abondance des logiciels de simulation, l écart entre les praticiens et les théoriciens se trouve plus élargi. Quand les théoriciens en recherche opérationnelle restent sceptiques vis-à-vis de cette méthode de simulation qui, pour eux, manque de fondement mathématique, les industriels et praticiens optent formellement pour ces modèles informatiques réalistes et ergonomiques de simulation. Il est vrai que, grâce à la simulation, nous avons pu développer un modèle d une grande fidélité, permettant de reproduire finement le comportement dynamique des systèmes de transport minier. Cependant, le fondement sur lequel repose notre structure de commande prédictive est d imposer des lois de commande permettant d assurer la poursuite d une trajectoire de référence en sortie. Cette trajectoire est ainsi supposée

148 129 connue à l avance. Ceci ramène à résoudre un problème d optimisation classique en hors-ligne. Durant des décennies, la communauté de recherche opérationnelle a proposé des approches basées sur la modélisation analytique et permettant de résoudre de façon exacte ces problèmes d optimisation en boucle ouverte. Dans ce contexte, il nous semble alors judicieux d opter pour ces méthodes afin de définir la trajectoire de référence pour notre structure de commande. Une fois une trajectoire cible est définie par une technique analytique, notre structure de commande à base de modèle de simulation agit durant la phase opérationnelle de sorte que la trajectoire du système contrôlé suive cette cible. Nos travaux viennent alors affirmer la vision de Habchi (2001) sur le potentiel éventuel de combiner les modèles de simulation et analytiques pour faire face aux exigences en agilité, flexibilité et robustesse. La seconde partie de cette discussion porte sur l importance d élaborer une analyse structurée pour situer les processus à améliorer avant de les étudier spécifiquement. Grâce à la cartographie réalisée, nous avons pu identifier les différents processus ainsi que leurs interconnexions lors de l exploitation des mines à ciel ouvert. Cette structuration nous a permis de déceler plusieurs aspects largement ignorés lors de l étude du processus de chargement et de transport. Par exemple, nous avons repéré la forte dépendance entre le cycle de transport et l état des routes. La vérification et l entretien des pistes de roulage paraissaient comme partie intégrante du processus de chargement et de transport. En effet, dans les mines, les fosses sont creusées en gradins concentriques reliés par des routes aménagées en spirale. Dans un tel réseau de circulation, le nombre de pentes et de rampes est considérable, ce qui engendre très souvent des déversements à cause de ces conditions de roulage ardus. La compréhension de la fréquence de telles interventions nous a permis de les considérer comme étant des processus s exécutant en parallèle avec le chargement et le transport. Une telle logique de fonctionnement requiert des modèles différents des autres qui considèrent seulement les camions, les pelle et le système répartiteur comme intervenant dans le processus de transport et de chargement minier. Les limitations d un tel niveau d abstraction pour la

149 130 commande effective du transport ont été démontrées dans nos travaux. Notre cartographie a contribué à situer des phénomènes caractérisant l environnement réel minier, mais jusqu à lors ignorés ou encore catégorisés comme étant des dysfonctionnements qui causent un arrêt global du système de transport.

150 131 CONCLUSION ET RECOMMANDATIONS Conclusion La présente thèse a proposé une nouvelle architecture permettant la commande en temps réel des systèmes complexes à événements discrets. Cette architecture de commande a été élaborée graduellement avec les analyses et les travaux des différents articles. Ces travaux nous ont permis de dégager des résultats et des conclusions relatives aux problèmes de commande durant la phase opérationnelle des systèmes. Nous avons ainsi décelé différents nouveaux enjeux propres à cette phase de commande à court terme. Dans ce contexte, nous avons montré l importance de la granularité des modèles développés pour la résolution des problèmes de commande. En effet, à ce stade, la fidélité des modèles dans la reproduction du comportement du système à commander devient critique. Dans ce prototype du système de transport, nous avons ainsi souligné l importance de disposer d un modèle capable de positionner chaque camion dans le réseau, afin de générer une loi de commande efficiente à appliquer durant le prochain horizon de contrôle. L approche classique qui assimile les camions comme des entités virtuelles et modélise leurs mouvements dans le réseau par une distribution temporelle est alors inefficace pour la commande en temps réel de ces systèmes de transport. Le recours à une approche structurée et orientée objet nous a ainsi permis de développer un modèle spécifique pour la commande. La principale caractéristique d un tel modèle est qu on doit être capable de l initialiser à tout instant à l état du système physique renvoyé par les capteurs. Un autre problème traité dans nos travaux concerne la spécification des systèmes de commande en temps réel. Un tel système doit être capable de générer les lois de commande appropriées de façon robuste et agile. Ainsi, la réponse d un système de commande doit non seulement être correcte mais elle doit aussi être générée à temps.

151 132 Cet aspect temporel est fondamental pour parvenir à implanter un système de commande dans les applications complexes manufacturières ou de transport. Pour nos travaux, nous avons alors adopté une méthodologie objet basée sur le langage UML et développée pour la spécification des applications temps-réel. La robustesse de cette méthodologie nous a permis d aboutir à un système performant de commande temps-réel. L adaptation de ce standard de formalisme nous a aussi mené à concevoir un système répondant aux besoins de qualités intrinsèques : généralité, extensibilité et réutilisabilité. Dans nos travaux, le problème relatif à la commande des systèmes de transport interne a été abordé. Nous avons montré que la prise en compte du trafic est nécessaire pour une résolution effective des problèmes de gestion de flotte en temps réel. En effet, plusieurs travaux antérieurs ont rapporté la faiblesse des systèmes de réparation face à l environnement dynamique du transport. Contrairement aux méthodes classiques de résolutions des problèmes de répartition, notre approche considère le trafic comme étant une composante inhérente des systèmes de transport. Pour cette fin, nous avons introduit un modèle de trafic dans un modèle classique de transport interne. Cette intégration a permis de réaliser le routage en temps réel des camions ainsi que de contrôler le trafic afin de réduire la congestion. Ce couplage entre le modèle de trafic et le modèle de gestion de flotte de transport constitue l une des originalités de nos travaux. Nous avons constaté que les problèmes de gestion de flotte ont principalement été abordés par la communauté de recherche opérationnelle. Parallèlement en génie civil, des chercheurs ont proposé des modèles de trafic pour résoudre d autre type de problèmes comme la gestion de feux de carrefour, la conception de route et de bretelles, etc. Ainsi dans nos travaux, nous nous sommes inspirés des avancées faites en théorie du trafic et avons proposé un modèle générique intégrant le trafic aux modèles classiques de transport.

152 133 Recommandations L objectif principal de nos travaux de recherche était de proposer une architecture générique pour la commande en temps réel des systèmes complexes à événements discrets. Bien que nos travaux portent sur une application prototype du problème de transport, la méthodologie utilisée lors de la phase de spécification permet une adaptation aisée de cette architecture de commande. Ainsi, suite à nos travaux, plusieurs domaines d application peuvent s ouvrir vers la commande en temps réel. Ce type de commande pourrait être d un grand apport en termes d optimisation de performances et d augmentation de profits dans les environnements manufacturier, hospitalier, etc. Cependant pour une commercialisation éventuelle du système de commande pour l industrie minière l utilisation d un langage unique pour le code source serait préférable. En effet, plusieurs langages ont été utilisés dans nos travaux à cause de contraintes techniques et de temps. Une autre avenue de recherche concerne l analyse des performances des métaheuristiques pour la génération intelligente de lois de commande en temps réel. Dans nos travaux, nous avons prouvé la faisabilité de l utilisation du recuit simulé dans une architecture de commande basée sur un modèle de simulation. Étant donné que plusieurs autres métaheuristiques ont été aussi jugées très performantes pour résoudre des problèmes de gestion hors-ligne, une voie de recherche future serait d intégrer ces métaheuristiques et d étudier leurs performances pour l optimisation «on-line». Finalement une étape importante qui permettrait l implantation de notre structure de commande dans un système réel de transport minier, reste celle de la calibration du simulateur. En ingénierie du trafic, la calibration des simulateurs microscopiques parait comme l un des inconvénients majeurs de cette approche micro, vu la complexité de collecte de données dans les réseaux de trafic urbain. Cependant, étant donné que nous adressons le problème de transport dans un réseau fermé, où tous les camions sont équipés de systèmes de positionnement, la complexité de cette étape sera réduite. De

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171 152 ANNEXE A La référence de cet article est : A. Jaoua, M. Gamache et D. Riopel, " Comparaison d approches de modélisation de problèmes tests pour le pilotage du transport : application aux mines à ciel ouvert", 7éme Conférence Internationale de MOdélisation et SIMulation, MOSIM Éditions Tec&Doc Lavoisier ISBN :

172 COMPARAISON D APPROCHES DE MODELISATION DE PROBLEMES TESTS POUR LE PILOTAGE DU TRANSPORT : APPLICATION AUX MINES A CIEL OUVERT A. JAOUA, M. GAMACHE GERAD, GERAD École Polytechnique de Montréal C.P. 6079, Succ. Centre-ville, Montréal, Québec, Canada, H3C 3A7 [email protected], [email protected] D. RIOPEL GERAD École Polytechnique de Montréal C.P. 6079, Succ. Centre-ville, Montréal, Québec, Canada, H3C 3A7 [email protected] RESUME : Cet article vise l analyse du type de modélisation des problèmes tests utilisés par les chercheurs pour valider leurs stratégies de pilotage des systèmes de transport. Pour la gestion du trafic, deux principaux types de modélisation sont utilisés : macroscopique et microscopique. Tandis que pour la gestion dynamique des flottes de véhicules, la majorité des problèmes tests sont modélisés uniquement selon une composante macroscopique. Nous démontrons que la modélisation macroscopique peut biaiser les résultats obtenus par simulation et causer ainsi un large écart de performance entre les résultats simulés et réels. Cet écart est aujourd hui critiqué par les responsables dans les entreprises du transport qui pensent que les chercheurs avancent des résultats utopiques. Nous montrons l écart de performance entre ces deux types de modélisation sur un problème test typique des systèmes de transport minier. Ce problème test est utilisé dans la validation des algorithmes de gestion dynamique de flotte de camions. Nous décrivons aussi le modèle orienté objet que nous avons développé afin d implanter un simulateur microscopique de pilotage de système de transport minier. Cette approche objet permet la réutilisabilité de ce simulateur microscopique pour d autres problèmes tests. MOTS-CLES : pilotage du transport, répartition, camions, modélisation microscopique, modélisation macroscopique 1. INTRODUCTION Il existe plusieurs variantes du pilotage des systèmes de transport qui dépendent du domaine d application : transport aérien, transport ferroviaire, transport routier, transport minier, etc. Dans le présent travail, on s intéresse au pilotage des systèmes de transport routier et du transport minier. Pour le transport routier, on distingue principalement deux catégories de problématiques largement étudiés dans la littérature. La première porte sur la gestion du trafic et la seconde sur la gestion de flottes de véhicules. Bien que ces deux volets ont suscité l intérêt de plusieurs chercheurs depuis des décennies, rares sont les travaux qui les étudient conjointement. Pour la problématique reliée à la gestion du trafic, qui est de nature dynamique, on trouve dans la littérature différentes approches de modélisation pour la reconstitution des états du réseau de trafic routier. Ces modèles permettent principalement de tester et d évaluer les stratégies de régulation (Lebacque et Khoshyaran, 1998). Bourrel (Bourrel, 2003) précise que ces modèles peuvent être scindés en deux grandes catégories : les modèles macroscopiques et les modèles microscopiques. Les modèles macroscopiques consistent à décrire le trafic comme un flux continu et unidimensionnel, par analogie avec la mécanique des fluides. Alors que les modèles microscopiques s intéressent à une description détaillée des trajectoires et de la dynamique des véhicules individualisés. Quant à la problématique reliée à la gestion de flottes de véhicules, on discerne dans la littérature plusieurs stratégies de répartition en temps réel basées sur des algorithmes d optimisation (Laporte et Osman, 1995; Gendreau et al., 1999). Bien que l application

173 154 de ces algorithmes sur des problèmes tests semble performante, Burckert et al. (2000) critiquent le large écart entre les résultats attendus (simulés sur des problèmes tests) et ceux générés par l implantation réelle de ces algorithmes. Ils concluent à l inadéquation de ces méthodes pour un pilotage en temps réel robuste des systèmes de transport actuels. Pour comprendre les raisons de ce large écart de performance, nous avons étudié les modèles des problèmes tests utilisés pour la validation de ces algorithmes. Nous avons ainsi décelé que la majorité des problèmes tests utilisés pour la validation de ces stratégies dynamiques de pilotage (Godfrey et Powell, 2002; Rousseau, 2003; Larsen et al., 2004 et Ichoua et al., 2006) sont modélisés uniquement selon une composante macroscopique. Les performances de ces algorithmes stochastiques de pilotage sont ainsi testées sur des graphes dans lesquels des temps de parcours sont associés aux arcs en ignorant alors la dynamique engendrée par les interactions sur le réseau physique. L idée du présent article est de mesurer, sur un problème test typique de pilotage des systèmes de transport minier, l éventuelle différence de performance entre une modélisation macroscopique et une modélisation microscopique. Cette différence pourrait expliquer le large écart entre les résultats théoriques (simulés) et réels de ces algorithmes. Dans cet article on s intéresse au pilotage en temps réel d une flotte de camions évoluant dans un système de transport minier. Cette application s apparente avec la problématique de gestion en temps réel d une flotte de camions routiers. En effet, dans une mine à ciel ouvert, il faut piloter une flotte constituée de camions et de pelles. Sur un réseau de transport minier, les camions transportent soit le minerai détaché du front de taille par les pelles (points de collecte) vers le lieu de traitement soit le stérile vers un lieu d entreposage (points de livraison). Une fois que le camion a déversé sa charge, il faut l affecter à une pelle (génération d une requête) de façon à satisfaire plusieurs contraintes dynamiques (état de la pelle, niveau du mélange du minerai acheminé au concasseur, plan de production, etc.). Comme pour les algorithmes de pilotage d une flotte de véhicules routiers, plusieurs travaux critiquent l écart entre les résultats simulés et réels de l implantation des algorithmes stochastiques de répartition de flotte de camions miniers (Dunbar et al., 2003; Chung et al. 2005). Dans le domaine minier, la modélisation des problèmes tests utilisés se base uniquement sur l approche macroscopique. Ces modèles ne reproduisent pas l aspect dynamique engendré par les interactions physiques sur le réseau de transport d une mine. Afin de pouvoir mener une analyse comparative sur les types de modélisation des problèmes tests, nous proposons, dans un premier temps, un modèle générique orienté objet que nous avons développé afin d implanter un modèle microscopique de simulation de pilotage de système de transport minier. Nous présentons, en second lieu, les résultats comparatifs entre la modélisation macroscopique et notre modélisation microscopique des systèmes de transport minier. Cette évaluation porte sur un problème test largement utilisé dans l évaluation des algorithmes d optimisation de routage et d ordonnancement de la flotte de camions miniers. 2. REVUE DE LITTÉRATURE 2.1. Modélisation des problèmes tests pour le pilotage des systèmes de transport routier En s intéressant au pilotage des systèmes de transport routier, on trouve que les travaux dans ce domaine sont scindés selon deux axes de recherche. Le premier axe traite des problèmes de gestion de trafic routier, tandis que le deuxième concerne la gestion de flottes de véhicules de transport Problèmes de gestion de trafic routier Les objectifs de gestion de trafic routier sont présentés par Bourrel (2003) comme regroupant - la définition des stratégies d action pour répartir et contrôler les flux de trafic et éviter l'apparition des perturbations ou d'en atténuer les effets; - la mise en place d actions préventives comme la proposition des itinéraires non congestionnés; - le traitement en temps réel des flux de trafic pour la réduction des effets des perturbations à travers des stratégies de gestion des zones de goulot et des intersections comme les barrières de péage, les feux, etc. Afin d évaluer et de valider les performances des méthodes de gestion de trafic à implanter, les chercheurs ont recours à la modélisation de problèmes tests leur permettant de reproduire les états du trafic. Dans la littérature, on

174 155 discerne principalement deux grandes catégories de modélisation en vue d implantation des problèmes tests pour l évaluation des stratégies de gestion de trafic routier : la modélisation macroscopique et la modélisation microscopique. Avec la modélisation suivant une composante macroscopique le déplacement de l entité unique n est pas représenté mais seul compte le fonctionnement à un niveau agrégé. La propagation des véhicules est décrite à travers des variables globales : le débit, la concentration (nombre de véhicules par unité d espace) ou bien la vitesse du flot (vitesse moyenne des véhicules), (Cohen, 1990). À l opposé, la modélisation microscopique tente de s approcher le plus possible du comportement réel des véhicules en définissant selon l application le niveau de granularité désiré : il peut s'agir du comportement du conducteur et de celui de son véhicule ou bien encore du comportement du couple conducteurvéhicule. Cette approche microscopique vise l analyse des composants du réseau de transport. Elle s appuie sur des notions d entités (tronçon, intersection, conducteur, véhicule, signalisation, etc.), chacune caractérisée par des attributs, pour modéliser leurs interactions (Krauß, 1997). Plusieurs travaux proposent une synthèse et une revue détaillée sur ces modèles, le lecteur pourra se reporter à la thèse de Bourrel (2003). De même, Herviou (2006) présente une revue détaillée dans laquelle il rajoute la définition de modèles hybrides appelés modèles mésocopiques. Lebacque et Khoshyaran (1998) précisent que chaque type de modélisation est orienté vers des applications qui correspondent à une taille de réseau donné. Les modèles macroscopiques sont mieux adaptés pour la régulation, la prévision et la planification du trafic sur les grands réseaux routiers caractérisés par des phénomènes d écoulement homogène, par exemple une autoroute à quatre voies. Herviou (2006) définit l approche microscopique comme étant la mieux adaptée pour la prise en compte et l analyse robuste du trafic et des phénomènes d interaction principalement présents dans un système de transport routier urbain. Cependant, étant donné la complexité du développement des modèles microscopiques et les quantités importantes de calcul qui peuvent en résulter, il faudra choisir le niveau de description du comportement que l'on souhaite simuler en fonction de l application Problèmes de gestion de flottes de véhicules Les problèmes de gestion de flottes de véhicules peuvent être de nature statique ou dynamique. Dans le cas statique, plusieurs algorithmes ont été proposés pour identifier, dans un cadre invariant, un ensemble de routes minimisant une fonction de coût prédéfinie. Mais ces algorithmes ne peuvent pas gérer l aspect dynamique du monde réel comme l arrivée de requêtes inattendues (Laporte et Osman, 1995). En s intéressant alors à l aspect dynamique de la gestion de la flotte, on discerne dans la littérature de nombreux modèles de répartition en temps réel de la flotte de véhicules (Laporte et Osman, 1995; Gendreau et al., 1999). Ichoua (2001) classifie, selon le type de l application et le degré de dynamisme, les problèmes de répartition des véhicules en temps réel. Parmi ces applications, on distingue entre autres les problèmes de camionnage, les problèmes de transport sur demande, les problèmes de service de courrier rapide, les problèmes de réparateur, les problèmes de services d urgence. Pour chaque type de problèmes, on trouve dans la littérature plusieurs modèles, certains étant basés sur la programmation linéaire en nombres entiers d autres, plus récents, sont basés sur la programmation stochastique. Bien que l application de ces algorithmes sur des problèmes tests semble performante, Burckert et al. (2000) critiquent le large écart entre les résultats attendus (simulés sur des problèmes tests) et ceux générés par l implantation réelle de ces algorithmes. Ainsi, en analysant les modèles des problèmes tests utilisés pour la validation des méthodes dynamiques de gestion de flottes de véhicules dans les travaux de (Laporte et Osman, 1995; Gendreau et al., 1999; Godfrey et Powell, 2002; Rousseau, 2003; Larsen, 2004 et Ichoua et al., 2006) nous avons décelé un recours commun à la modélisation macroscopique des problèmes tests. En effet, ces travaux ont principalement recours à des variantes des problèmes tests euclidiens créés par (Solomon, 1987). Les performances de ces méthodes dynamiques de pilotage sont alors testées sur des graphes pour lesquels des poids (dépendant principalement des distances) sont associés aux arcs, en ignorant ainsi la dynamique engendrée par les interactions du trafic routier sur le réseau physique. Ce recours à la modélisation macroscopique peut s expliquer par la simplicité et rapidité du développement de ces modèles. La complexité de l approche

175 156 microscopique réside dans la spécification des intervenants et dans la délimitation du niveau de granularité Modélisation des problèmes tests pour le pilotage des systèmes de transport minier Pilotage des systèmes de transport minier Les systèmes de transport des mines à ciel ouvert ont largement suscité l intérêt de plusieurs travaux de recherche et ils représentent jusqu'à l heure actuelle une problématique pour les responsables miniers (Chung et al., 2005). En effet, les chercheurs estiment que l optimisation de ce processus de transport minier peut affecter jusqu'à 50% des coûts opératoires (Alarie et Gamache, 2002; Wang et al., 2006). Ce problème de pilotage d une flotte de camions peut être classé comme étant un problème de camionnage routier (selon la classification d Ichoua (2001)) où les points de collecte sont les pelles et ceux de livraison sont les sites de culbutage. La différence est que dans les problèmes de camionnage routier, le degré de dynamisme est plus faible que dans une mine où les délais des requêtes se quantifient en minutes et les attributs du problème (temps de parcours, qualité du mélange, etc.) sont confrontés à plusieurs variations stochastiques. La répartition des camions dans une mine présente aussi des ressemblances avec la classe des problèmes de services d urgence, caractérisée par la fréquence de l apparition de nouvelles requêtes (il faut atteindre un niveau de production donné pour chaque pelle), mais la différence principale avec cette classe se situe dans la connaissance du point de déclenchement des requêtes (les camions sont envoyés à des pelles placées dans des endroits fixes durant le quart de travail). Ainsi, le problème de gestion de flotte de camions dans une mine présente un degré plus élevé de dynamisme rattaché à la plus grande fréquence d apparition de requêtes (par rapport aux problèmes de camionnage routier) et à la forte composante stochastique des attributs de chaque nouvelle requête (temps de début de service, temps de parcours, etc. ). L approche la plus commune pour la résolution de ce type de problème consiste à implanter un module de pilotage multiniveau (voir figure 1). Figure 1. Module de pilotage multiniveau Ce module se base sur un noyau de résolution qui propose de résoudre au niveau supérieur le problème d allocation par des modèles de programmation mathématique. Quand au niveau inférieur, il s agit de résoudre le problème de répartition en temps réel via des heuristiques. Pour le niveau supérieur, plusieurs chercheurs proposent des programmes linéaires, (Gamache, 2007; Bissiri, 2002; White et al., 1993). Chung et al. (2005) ont recours à la programmation stochastique, Temeng et al.(1997) proposent la résolution d un modèle de programmation par objectifs (goal programming) et Elbrond et Soumis (1987) résolvent un modèle de programmation non linéaire. Au niveau inférieur, on cherche à minimiser les déviations par rapport aux cibles de production des pelles obtenues au niveau supérieur. Munirathinam et al. (1994) présentent une revue de littérature sur les heuristiques de type glouton utilisées pour cette étape de résolution. Plus récemment, Dunbar et al. (2003) proposent une méthode basée sur l'optimisation par colonie de fourmis Modélisation des problèmes tests Chung et al. (2005), Bissiri (2000), Temeng et al. (1997), White et al. (1991) et Elbrond et Soumis (1987) prouvent par simulation sur des problèmes tests que leurs algorithmes de pilotage sont performants. Mais Clayton (2005) rapporte l insatisfaction des responsables miniers des modules de répartition qui sont très peu robustes et sont affectés par un simple retard d un camion. De même, Wang et al. (2006) critiquent le large écart entre les performances simulées de ces modules et leurs performances réelles en mine. Ainsi comme pour les systèmes de transport routier, notre intérêt se concentre sur l étude de la modélisation des problèmes tests utilisés pour

176 157 la validation de ces algorithmes de pilotage du transport minier. Nous constatons que les modèles utilisés sont des modèles macroscopiques. Ces modèles considèrent la propagation des camions à travers des variables globales (la densité du trafic, la vitesse du flux) et définissent ainsi le temps moyen de parcours. Ces modèles des problèmes tests (voir figure 2) considèrent que la mine est constituée d une flotte de N camions, d un ensemble de sites de culbutage (Ci), et d un ensemble de sites d extraction (Ej). Les camions attendent leur affectation dans les sites Ci. À partir d un site Ci, il est généralement possible d envoyer un camion vers tous les sites Ej. Tandis qu à partir d un site Ej il faut le diriger vers des sites Ci spécifiques (c'est-à-dire si le site E 1 extrait du stérile, il faut le diriger vers un site de culbutage Ci de stérile et non pas le diriger vers un concasseur). Suite à la définition des parcours admissibles, un coût noté Ĉ Ci,Ej est associé à chaque vecteur. Ce coût dépend principalement du temps moyen de parcours entre le couple (Ci,Ej) en tenant compte du sens du vecteur correspondant. En effet, la charge d un camion minier peut atteindre 360 tonnes et cette charge exerce une influence sur sa vitesse, il faut alors faire la distinction entre le coût d un parcours en charge et le coût d un parcours à vide. À chaque site de culbutage Ci et d extraction Ej est associé un temps t s de service dépendant des paramètres techniques de la ressource. Une file d attente est ainsi créée en amont des sites. Ĉ C1,E2 Ĉ E2,C1 Ĉ C1,E4 Ĉ C2,E4 Ĉ E4,C2 Ĉ E5,C2 Ĉ C2,E5 recours aux modèles macroscopiques peut s expliquer par la simplicité de leur développement, mais ce manque de réalisme dans la reproduction de l environnement réel de l application pourrait être un des facteurs élargissant l écart entre les résultats réels et ceux simulés par ces modèles. Ainsi, tout comme pour la gestion dynamique de flottes en transport routier, les modules de répartition de flottes dans les mines sont validés sur des modèles macroscopiques. Afin de mener une étude comparative de l impact de ce choix de modélisation macroscopique des problèmes tests, nous proposons dans la section suivante de développer un modèle générique pour l implantation d un modèle microscopique de simulation de pilotage de systèmes de transport minier. 3. MÉTHODOLOGIE Afin que notre simulateur puisse répondre aux besoins de réutilisabilité et d extensibilité, nous avons opté lors de sa conception pour une approche orientée-objet. En effet, Perret (Perret, 2003) définit la structuration objet comme une réponse adaptée aux besoins d extensibilité, de réutilisabilité et de qualité logicielle. Grâce à cette approche, nous offrons une plateforme de simulation microscopique permettant une implantation simplifiée de problèmes tests de pilotage des systèmes de transport minier. Ainsi, à l aide du digramme de classe UML (Unified Modeling Language), nous formalisons les classes impliquées dans le système. En effet, le langage UML est considéré comme un standard de modélisation objet (Muller et Gaertner, 2000). La seconde étape consiste à implanter ce modèle avec le langage de simulation à événements discrets SIMAN développé par SYSTEM MODELING (Pedgan, 1995) et largement utilisé dans les travaux de recherche actuels (Cardin et Castagna, 2006). Ĉ E3,C1 Ĉ C1,E3 Figure 2. Exemple typique d une représentation macroscopique de système de transport minier Ce type de modélisation ignore alors les phénomènes d interaction dans le circuit fermé du réseau de transport minier. Il est vrai que le 3.1. Modélisation UML Le diagramme de classe UML représente l'architecture conceptuelle du système. Il décrit les classes que le système utilise en spécifiant les intervenants, ainsi que leurs liens. Dans ce diagramme, les différents types d association permettent de représenter les relations structurelles qui existent entre les objets de différentes classes. Parmi ces relations, la relation de composition qui est une forme d agrégation forte. Cette relation décrit une

177 158 contenance structurelle entre instances. Elle suppose que la partie composante appartient exclusivement à la partie composée et entraine des contraintes sur l existence du composant par rapport au composé. Pour plus de détails concernant ces diagrammes le lecteur peut se référer aux travaux de Muller et Gaertner (2000). Le diagramme de classe UML (voir figure 3) représente les classes qui sont implémentées dans notre système. Classe Site d extraction : admet deux classes dérivées, Extraction de stérile et Extraction de minerai. Dans une mine à ciel ouvert, on retrouve généralement ces deux types de site d extraction, mais il est possible que pour un quart de travail un seul type soit fonctionnel. Classe Equipement : est associée par une relation de composition avec les deux classes composites, Pelle et Camion. Le processus de transport dans une mine à ciel ouvert est basé principalement sur ces deux types d équipements. Classe Site de culbutage : de même que pour la classe Site d extraction, admet deux classes dérivées, Concasseur et Halde de stérile. Classe Réseau de transport : associée par une relation de composition avec les deux classes composites Section et Nœud. Ces classes permettent de décrire la topologie du circuit. Ainsi, la définition précise des tronçons permet de modéliser de façon microscopique les phénomènes d interaction sur le réseau physique de transport minier. Classe Répartiteur : est le noyau décideur dans notre système de pilotage. Les classes sont principalement reliées par des associations binaires, sauf pour la génération de missions qui nécessite une relation ternaire faisant intervenir les classes Répartiteur, Réseau de transport et Camion. Figure 3. Diagramme de classes 3.2. Implantation du modèle avec SIMAN Le système de pilotage que nous modélisons est complexe, de plus la difficulté s amplifie lorsqu on cherche à le modéliser de façon microscopique. Ainsi, l utilisation des composants de haut niveau d ARENA ne permet pas de reproduire finement le comportement des camions sur le réseau de trafic minier. Le recours au langage SIMAN est nécessaire pour ce type de modélisation. L utilisation d ARENA se limite à la couche supérieure d environnement d édition et de visualisation graphique. On a implanté sur SIMAN le modèle de classe présenté précédemment en trois principales étapes. La première étape consiste en l implantation de la classe Réseau de transport. Cette classe permet de définir la topographie du circuit dans la mine à travers les objets 'Intersections', 'Links' et 'Networks' du langage SIMAN. La deuxième étape est d introduire les classes : Site d extraction, Site de culbutage et

178 159 Équipement. Ces trois classes correspondent aux ressources de notre système. Les ressources comme les pelles et les concasseurs sont supposée fixes pour un quart de travail, mais les camions sont des ressources mobiles. On a représenté les camions par analogie aux transporteurs autoguidés définis par SIMAN; ceci a permis de travailler avec les algorithmes de graphes pour la résolution des problèmes du plus court chemin. La dernière étape est d implanter le module logique du pilotage de la classe Répartiteur. Paramètres Valeurs en physiques minutes Coût des parcours Ĉ C1,E1 Tri(9,10,11) Ĉ C1,E2 Tri(4,5,6) Ĉ E1,C1 Tri(10,11,12) Ĉ E2,C1 Tri(5,6,7) Temps de service La figure 4 montre l implantation du réseau de t E1 Constant : 3 min transport minier, où: t E2 Constant : 3 min i i et l j représentent, respectivement les nœuds et t C1 Constant : 2 min sections du réseau Tableau 1. Valeurs des paramètres du modèle n Ci capacité de la pelle i. macroscopique n Ej capacité du centre de culbutage j. L objectif du plan de production est d avoir un d Ci,Ej distance entre le site de culbutage Ci et le site d extraction Ej. Figure 4. Configuration de base sur SIMAN d un réseau de transport minier 4. SIMULATION DU PROBLEME TEST 4.1. Implantation du modèle macroscopique du problème test Le problème test étudié se caractérise par un site unique de culbutage (C 1 ) et deux sites d extraction (E 1 et E 2 ). Cette configuration est utilisée pour la validation des modèles stochastiques de répartition en temps réel proposés par Chung et al. (2005), ainsi que pour la validation du modèle agent présenté par Dunbar et al. (2003). Dans le problème test utilisé par Dunbar, le coût associé aux différents parcours est un temps moyen exprimé en minutes et distribué selon une loi triangulaire alors que les temps de service dans les sites sont supposés constants (tableau 1). nombre égal de camions chargés à partir de chaque pelle au bout d une période de 12 heures de travail. En se basant sur les temps moyens du tableau 1, Dunbar et al. définissent les temps de cycle à partir de chaque site d extraction : TcycE 1 =26 min et TcycE 2 =16 min. Ces temps de cycle permettent aux décideurs de déterminer le nombre de camions qu il faut affecter à chaque pelle pour satisfaire le niveau de production désiré. Étant donné que le temps de production d une pelle est de 3 minutes l objectif est de 20 chargements/heure. Le nombre de camions nécessaire est de 8 pour la pelle au centre d extraction E 1 et 5 camions pour la pelle au centre E 2. Le niveau de production voulu est alors calculé en terme de nombre de camions chargés, il est égal à 446 camions soit 221 camions à partir de E 1 et 225 camions à partir de E 2. En implantant avec ARENA le modèle macroscopique correspondant à ce problème test on retrouve les résultats du modèle de Dunbar et al. La figure 6 montre l évolution du nombre de chargements de camion en fonction du temps. En effet, le nombre de camions chargés est retenu comme mesure de performance du système étudié. Un léger décalage de nombre de chargements existe entre la valeur calculée théoriquement et celle retrouvée par simulation, ce décalage est dû à la file d attente en amont du site de culbutage. Le temps moyen d attente dans cette file est de 4,5 minutes.

179 Implantation du modèle microscopique du problème test Afin de comparer les deux approches de modélisation des problèmes tests (macroscopique et microscopique) nous avons implanté le problème test de Dunbar et al. (2003) dans notre simulateur microscopique. Le tableau 2 présente les différents paramètres utilisés. Paramètres Valeurs en physiques minutes Distances d C1,E m d C1,E m Temps de service t E1 Constant : 3 min t E2 Constant : 3 min t C1 Constant : 2 min Tableau 2. Valeurs des paramètres du modèle microscopique La figure 5 montre l implantation topographique du réseau de transport minier de ce problème test. Avec cette première configuration, pour déverser la charge extraite à partir des sites E 1 et E 2, les camions utilisent des tronçons de routes disjointes (l angle Φ>0). E2 Tronçons C1E 1 C 1E 2 E1C 1 E 2C 1 et et Loi de distribution de la vitesse Normale (7,1) Normale (6,0.8) Tableau 3. Lois de distributions des vitesses Pour la validation de notre modèle de simulation, nous estimons le nombre de réplications nécessaires à n=10 garantissant ainsi un intervalle de confiance de 95%. Ainsi, les résultats de simulation du modèle microscopique sont présentés à la figure 6. C h a rg e m en ts Temps Macroscopique Microscopique Figure 6. Évolution du nombre de chargements E1 C1 La figure 6 montre l évolution du nombre de camions chargés en fonction du temps. On peut dès lors remarquer un léger écart entre les résultats générés par le modèle macroscopique et ceux générés par le modèle microscopique. Une analyse plus pointue de cet écart est présentée à la section suivante. Figure 5. Implantation topographique En posant comme hypothèse que la flotte de camions est homogène (même caractéristiques techniques), le comportement sur chaque section de réseau, du couple camion-conducteur est décrit comme suivant une loi gaussienne. Pour plus de clarifications sur ce type d hypothèses; les lecteurs peuvent consulter les travaux de Liu et al. (2005). Ainsi, les vitesses suivent la loi de distribution suivante Tableau 3 : 5. ANALYSE DES RESULTATS 5.1. Évaluation de l écart de performance Pour évaluer l écart entre le modèle macroscopique et le modèle microscopique du problème test étudié dans la section précédente, nous avons introduit une variable (écart) qui représente l évolution de la différence des temps en fonction du nombre de chargements effectués. Ainsi, pour un nombre (n t ) de chargements on associe la valeur : écart (n t ) = t Micro(n t ) t Macro (n t ) (c est-à-dire pour n t =107 chargements, on a t Micro (107) = 227,10 minutes et t Macro (107) = 215,69 minutes). La figure

180 161 suivante (figure 7) présente l évolution de cette variable écart en fonction du nombre de chargements. 60, Deuxième configuration (Φ=0) 50,00 Écarts 50 40, Première configuration (Φ>0) Écart 30,00 20, Chargements Figure 8. Comparaison des écarts 10,00 0, ,00 Figure 7. Évolution de la variable écart La pente positive de la courbe indique un élargissement de l écart. Ainsi plus on avance dans le temps plus le résultat généré par la modélisation macroscopique diffère de celui généré par la modélisation microscopique. En calculant le pourcentage de cet écart, pour cette configuration du problème test, on trouve qu il ne dépasse pas 7%. Dans la partie suivante l effet d un changement topographique sur la valeur de l écart est comparé entre une modélisation macroscopique et une modélisation microscopique Effet d un changement topographique de la mine Dans la partie précédente, le réseau de transport minier est constitué de deux tronçons indépendants (figure 5). On suppose maintenant que la configuration de la mine change et que les pelles deviennent placées de sorte que le tronçon entre le site de culbutage C 1 et le site d extraction E 2 devient un tronçon commun à tous les camions (angle Φ=0 dans la configuration de la figure 5). Nous avons alors implanté cette nouvelle topographie du réseau de transport minier dans notre simulateur microscopique. Comme pour le cas précédent nous avons calculé l écart entre le modèle macroscopique et cette nouvelle implantation du modèle microscopique. La figure 8 regroupe les deux représentations de l évolution de la variable écart en fonction du nombre de chargements. On remarque qu avec ce changement topographique l écart s élargit considérablement. Cet écart s explique par le fait que la congestion engendrée sur le tronçon commun ainsi que les interactions qui en découlent (décélérations et accélérations) ont été ignorés par le modèle macroscopique. Ainsi, on constate que l existence d un tronçon commun peut affecter jusqu'à 13% les résultats générés par la modélisation macroscopique. Chargements 5.3. Évaluation des heuristiques d assignation Dans la littérature, plusieurs travaux de recherche ont recours à la modélisation macroscopique des systèmes de transport des mines à ciel ouvert pour la détermination de la meilleure heuristique à implanter au niveau inférieur de leur noyau de résolution. Ainsi, ces travaux ne considèrent pas que dans une mine, la flotte de camions est généralement hétérogène ce qui engendre une variabilité élevée des vitesses dépendantes des caractéristiques techniques des camions. Pour évaluer l effet de l hétérogénéité de la flotte sur les performances du système de pilotage, on a rajouté un autre site de culbutage d où un autre point de répartition où on implante une heuristique d assignation. Le modèle comporte alors un nouveau site de culbutage C 2, en supposant que du site d extraction E1 on ne déverse que dans C 1 et du site E2 on ne déverse que dans C2 (E1 est site d extraction de minerai et C 1 est un concasseur, alors que E 2 est un site d extraction de stérile et C 2 est une halde de stérile). À partir des sites de culbutages il est possible d envoyer les camions vers E 1 ou E 2. Pour comparer l effet d une flotte hétérogène, on considère deux règles d assignation : assignation fixe (FA, fixed truck assignment) et assignation tournante (RA, Rounding truck

181 162 assignment). En assignation fixe, on suppose que pour le parcours entre C 1 et E 1 des camions identiques sont affectés de même entre C 2 et E 2. La deuxième règle consiste à envoyer le camion vers le prochain site d extraction et non pas vers le site qu il vient de quitter, ainsi des camions hétérogènes vont se croiser sur les tronçons du réseau. Les résultats sont reproduits à la figure 9. Chargements RA (flotte hétérogène) FA (flotte hétérogène) RA (flotte homogène) FA (flotte homogène) Figure 9. Évaluation des stratégies Minerai Stérile Stratégies On constate alors que lorsque la flotte de camions est considérée homogène, les deux règles de répartition résultent en moyenne à un nombre de chargements identique. Cependant quand l hétérogénéité de la flotte est prise en compte, on voit qu en optant pour l assignation fixe la réponse de notre système est améliorée jusqu'à 8%. En effet, avec l assignation tournante étant donné que les voies de circulation dans une mine sont étroites (c est-àdire sans possibilité de dépassement) les camions lents vont alors gênés les camions rapides ce qui conduit à la formation de pelotons. Ce phénomène est ignoré lorsqu on considère que la flotte est homogène. En conclusion, l utilisation d un modèle macroscopique pour l évaluation des performances des heuristiques d assignation a induit des résultats erronés. Ces résultats montrent que les deux règles d assignation sont équivalentes lorsque la flotte est considérée homogène, alors que lorsqu on a pris en compte les interactions résultantes de l hétérogénéité de la flotte nous avons trouvé un écart significatif de performance entre ces deux règles d assignation. 6. CONCLUSION Cet article montre que, dans le contexte fortement dynamique des systèmes de transport, le recours à la modélisation macroscopique des problèmes tests pour la validation des stratégies de gestion de flotte peut biaiser significativement les résultats générés par les simulations. Nous avons montré que cet écart entre la modélisation macroscopique et la modélisation microscopique augmente considérablement avec l augmentation dans le réseau du nombre de tronçons communs. En effet, le recours à la modélisation microscopique du système de transport minier a permis de tenir compte de la dynamique engendrée par les interactions des différentes entités dans le réseau. Ce travail présente le modèle générique orienté objet que nous avons développé afin d implanter un modèle microscopique de simulation de pilotage de système de transport minier. Ce modèle générique extensible et réutilisable permet alors de faciliter l implantation de simulateur microscopique des problèmes tests de transport minier. Étant donné que plusieurs travaux de recherches récents traitent la potentialité de la simulation proactive (Bensaoud et al., 2005; Cardin, 2006), l une des perspectives de ce travail sera d utiliser ce simulateur pour la conduite en ligne des systèmes de transport minier. REFERENCES Alarie, S. et M. Gamache, Overview of Solution Strategies Used in Truck Dispatching Systems for Open Pit Mines. International Journal of Surface Mining Reclamation and Environment. 16, 59. Bensaoud S., A. Jaoua and N.Bensaoud, Efficient Simulator Based on Metaheuristic for FMS and AGV Systems Design and Control. Journal of Computer Science, Bissiri Y., Application of Agent-Based modelling to truck-shovel dispatching systems in open pit mines. Thèse de Doctorat, University of british Columbia, Canada. Bourrel, E., Modélisation dynamique de l écoulement du trafic routier : du macroscopique au microscopique. Thèse de Doctorat, l Institut National des Sciences Appliquées de Lyon, France. Burckert, H.J., K. Fischer and G. Vierke, Holonic transport scheduling with TELETRUCK. Applied Artificial Intelligence, Cardin O., P. Castagna, 2006, Utilisation de la simulation proactive une aide au pilotage des systémes de production. Proceedings of

182 163 the 6e Conférence Francophone de MOdélisation et SIMulation, MOSIM 06, Rabat, Maroc. Chung, T., J.V. Kresta, J.F. Forbes and H.J. Marquez, A stochastic optimization approach to mine truck allocation. Journal of Surface Mining Reclamation and Environment. Vol. 19, No. 3, Clayton C., More clearer faster: it's all about information technology. CIM Bulletin. 98, Cohen, S., Ingénierie du trafic routier éléments de théorie du trafic et applications. Paris : Presses de l'école nationale des ponts et chaussées Dunbar, W.S., Y. Bissiri and J.V. Kresta, Let the Ants do the Dispatching. CAMI, Calgary, Canada. Elbrond J. and F. Soumis, Towards Integrated Production Planning and Truck Dispatching in Open Pit Mines. International Journal of Surface Mining. 1, 1-6. Gamache, M., Overview of Dispatching Systems and Challenges for the Future. Laurentian University, Canada. Gendreau, M., F. Guertin, J.-Y. Potvin, and E. Taillard, Parallel Tabu Search for Real-Time Vehicle Routing and Dispatching. Transportation Science 33, Godfrey, G.A. and W.B. Powell, An adaptive dynamic programming algorithm for dynamic fleet management, II: Multiperiod travel times. Transportation Science 36, Herviou, D., La perception visuelle des entités autonomes en réalité virtuelle : Application à la simulation de trafic routier. Thèse de Doctorat, l'université de Bretagne Occidentale. Ichoua, S., Problèmes de gestion flottes de véhicules en temps réel. Thèse de Doctorat, Université de Montréal, Canada. Ichoua, S., M. Gendreau and J.-Y. Potvin, Exploiting knowledge about future demands for real-time vehicle dispatching. Transportation Science 40, Krauß, S., Microscopic Traffic Simulation: Ro bustness of a Simple Approach. Proceeding of Traf fic and Granular Flow. Laporte, G. and I. H. Osman, 1995.Routing problems: A bibliography. Freight transportation Annals of operations research. Amsterdam: Baltzer Science Publishers, Larsen, A., B.G., Madsen and M. Solomon, The A priori dynamic traveling salesman problem with time windows. Transportation Science 38, Lebacque, J.P. et M.M. Khoshyaran, First order macroscopic traffic flow models for networks in the context of dynamic assignment. EURO, WGT. Muller P.A, N. Gaertner, Modélisation objet avec UML. 2e éd. Paris : Eyrolles. Munirathinam, M. and J.C. Yingling, 1994: A Review of Computer-Based Truck Dispatching Strategies for Surface Mining Operations. International Journal of Surface Mining, Reclamation and Environments. 8,1 15. Pegden C., R. Shannon, and R. Sadowski, Introduction to Simulation Using SIMAN, McGraw-Hill, 2nd edition. Perret J., Intégration des Réseaux de Petri Différentiels à Objets dans une plateforme de simulation dynamique hybride : application aux procédés industriels, Thèse de Doctorat, INP, Toulouse, France Rousseau, L.M, Gestion de flotte avec fenêtres horaires : approches de résolution mixtes utilisant la programmation par contraintes. Thèse de Doctorat, Université de Montréal, Canada. Solomon M.M., Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints. Operations Research 35, Temeng V.A., F.O. Otuonye and J.O. Frendewey, Real-Time Truck Dispatching Using a Transportation Algorithm. Int. J. of Surface Mining, Reclamation and Environment. 11, Wang, Q., Y. Zhang, C.Chen and W.Xu, Open-Pit Mine Truck Real-time Dispatching Principle under Macroscopic Control. Proceedings of the First International Conference on Innovative Computing, Information and Control. 1, White,J.W., J.P., Olson and S.I. Vohnout, On Improving Truck/Shovels Productivity in Open Pit Mines. CIM Bull. 86, 43 49

183 164 ANNEXE B Diagrammes de Processus : mesure en teneur; abattage; terrassement; chargement et transport.

184 165 Aide-Boutefeu Boutefeu Méthode et Planification Conducteur de Carotteur Entretien Méthode et Planification

185 166 Terrassement Entretenir et nettoyer les pistes de roulage, les tirs et les verses Front ou verses pollués ou débordant Vérifier la propreté pour le travail du pelliste ou préposé aux verses Conforme? Oui Informer le central Lancement des opérations de production Plan de production Court terme Porion Piste de roulage impraticable Sols trop humides Vérifier l état des pistes de roulage Vérifier l écoulement des eaux Non Préparer plan de nettoyage ou d assainissement Plan de nettoyage ou d assainissement Registre de contrôle des pressions des terrains Fichier central Opérateurs Manœuvre de mine Nettoyer l endroit, enlever résidus et poussiére Gros résidus de roches Oui Non Activer l assainissement par pompage Plan topographiqu e de la mine Conducteur de bouteur Pousser les matériaux pour dégager endroit de travail Normes de sécurité chargement et transport Fichier central état des verses Conducteur de niveleuse Régler la surface des pistes (Enlever les couches de glaces ou de neiges) Conditions climatiques Chargement et transport Charger et transporter les matériaux du front de taille vers les lieux de déversements Camionneur Aiguilleur Répartiteur Pelliste Entretien Planification Plan d action de Matériaux ébranlés chargement et de au front de taille Préparer le Plan transport d action Vérifier états des équipement des routes et des lieux Conduire la pelle Déplacer les gros Gros fragments Oui vers lieu de fragments pour un de roche chargement abattage Non Affecter le camion a la pelle selon Oui plan d action Vérifier l adéquation Adéquation? du planning avec l environnement réel Non Oui Stérile? Non Conduire le camion vers la pelle Réaliser des manœuvres de Saisir les positionnement caractéristiques du pour le chargement matériau chargé Attente Charger le camion sans contrôle de sélectivité Rediriger le camion Contrôler la sélectivité Transporter la charge vers lieu de déversement Charger le camion selon l ordre de l aiguilleur Mettre à jours le plan de production Donner les ordres de chargements Déverser charge selon instruction pour éviter contamination Minerai dans Mettre à jours le concasseur et central stérile dans les piles Intervention d entretien Signaler au Non camionneur la fin Autre mission? de chargement Oui Camion dans lieux Vérifier l état des de déversement verses Mettre à jours le central Informer le Mettre à jours le camionneur de central l état Non Autre mission? Oui Plan de production Court terme Fichier central cubage Fichier central Équipements Fichier central Opérateurs Plan topographiqu e de la mine Normes de sécurité chargement et transport Fichier central état des verses