Switched max-plus linear-dual inequalities: cycle time analysis and applications

P-time event graphs are discrete event systems suitable for modeling processes in which tasks must be executed in predefined time windows. Their dynamics can be represented by max-plus linear-dual inequalities (LDIs), i.e., systems of linear dynamical inequalities in the primal and dual operations of the max-plus algebra. We define a new class of models called switched LDIs (SLDIs), which allow to switch between different modes of operation, each corresponding to a set of LDIs, according to a sequence of modes called schedule. In this paper, we focus on the analysis of SLDIs when the considered schedule is fixed and either periodic or intermittently periodic. We show that SLDIs can model a wide range of applications including single-robot multi-product processing networks, in which every product has different processing requirements and corresponds to a specific mode of operation. Based on the analysis of SLDIs, we propose algorithms to compute: i. minimum and maximum cycle times for these processes, improving the time complexity of other existing approaches; ii. a complete trajectory of the robot including start-up and shut-down transients.Comment: 49 pages, 17 figures, journal paper, fixed typo in Remark 3, fixed formulas in Remarks 3 and

Foundations of Multi-Paradigm Modelling for Cyber-Physical Systems

This open access book coherently gathers well-founded information on the fundamentals of and formalisms for modelling cyber-physical systems (CPS). Highlighting the cross-disciplinary nature of CPS modelling, it also serves as a bridge for anyone entering CPS from related areas of computer science or engineering. Truly complex, engineered systems—known as cyber-physical systems—that integrate physical, software, and network aspects are now on the rise. However, there is no unifying theory nor systematic design methods, techniques or tools for these systems. Individual (mechanical, electrical, network or software) engineering disciplines only offer partial solutions. A technique known as Multi-Paradigm Modelling has recently emerged suggesting to model every part and aspect of a system explicitly, at the most appropriate level(s) of abstraction, using the most appropriate modelling formalism(s), and then weaving the results together to form a representation of the system. If properly applied, it enables, among other global aspects, performance analysis, exhaustive simulation, and verification. This book is the first systematic attempt to bring together these formalisms for anyone starting in the field of CPS who seeks solid modelling foundations and a comprehensive introduction to the distinct existing techniques that are multi-paradigmatic. Though chiefly intended for master and post-graduate level students in computer science and engineering, it can also be used as a reference text for practitioners

Ordonnancement cyclique robuste appliqué à la gestion des conteneurs dans les ports maritimes de taille moyenne

This PhD thesis is dedicated to propose a robust cyclic scheduling methodology applied to container management of medium sized seaport which faces ever changing terminal conditions and the limited predictability of future events and their timing. The robust cyclic scheduling can be seen not just a predictable scheduling to compute a container transportation schedule, but also a reactive scheduling to eliminate the disturbances in real time. In this work, the automated intelligent vehicles (AIV) are used to transport the containers, and the P-time strongly connected event graph (PTSCEG) is used as a graphical tool to model the container transit procedures. Before the arrival of the container vessel, a cyclic container transit schedule can be given by the mixed integer programming (MIP) method in short time. The robustness margins on the nodes of the system can be computed by robustness algorithms in polynomial computing time. After the stevedoring begins, this robust cyclic schedule is used. When a disturbance is observed in system, it should be compared with the known robustness margin. If the disturbance belongs to the robustness margin, the robustness algorithm is used to eliminate the disturbance in a few cycle times. If not, the MIP method is used to compute a new cyclic schedule in short timeCette thèse présente une méthodologie d’ordonnancement cyclique robuste appliquée à la gestion des conteneurs dans les ports maritimes de taille moyenne. Ces derniers sont sujet constamment à des variations des conditions des terminaux, la visibilité réduite sur des évènements futurs ne permet pas de proposer une planification précise des tâches à accomplir. L’ordonnancement cyclique robuste peut jouer un rôle primordial. Il permettra non seulement de proposer un ordonnancement prédictif pour le transport des conteneurs, mais aussi, il proposera également une planification robuste permettant d’éliminer les perturbations éventuelles en temps réel. Dans ce travail nous utilisons les Véhicules Intelligents Automatisés (AIV) pour transporter les conteneurs et nous modélisons les procédures de transit de ces derniers par des graphes d’évènements P-temporels fortement connexes (PTSCEG). Avant l’arrivée d’un porte conteneur au port, un plan (planning) de transport des conteneurs est proposé en un temps court par la programmation linéaire mixte (MIP). Des algorithmes polynomiaux de calcul de robustesse permettent de calculer sur les différents nœuds du système les marges de robustesse. Une fois le navire à quai, l’ordonnancement cyclique robuste est appliqué. Lorsqu’une perturbation est observée (localisée) dans le système, une comparaison avec la marge de robustesse connue est effectuée. Si cette perturbation est incluse dans la marge de robustesse, l’algorithme robuste est utilisé pour éliminer ces perturbations en quelques cycles. Dans le cas où la perturbation est trop importante, la méthode MIP est utilisée pour calculer un nouvel ordonnancement cyclique en un temps rédui

Scheduling of flexible manufacturing systems integrating petri nets and artificial intelligence methods.

The work undertaken in this thesis is about the integration of two well-known methodologies: Petri net (PN) model Ii ng/analysis of industrial production processes and Artificial Intelligence (AI) optimisation search techniques. The objective of this integration is to demonstrate its potential in solving a difficult and widely studied problem, the scheduling of Flexible Manufacturing Systems (FIVIS). This work builds on existing results that clearly show the convenience of PNs as a modelling tool for FIVIS. It addresses the problem of the integration of PN and Al based search methods. Whilst this is recognised as a potentially important approach to the scheduling of FIVIS there is a lack of any clear evidence that practical systems might be built. This thesis presents a novel scheduling methodology that takes forward the current state of the art in the area by: Firstly presenting a novel modelling procedure based on a new class of PN (cb-NETS) and a language to define the essential features of basic FIVIS, demonstrating that the inclusion of high level FIVIS constraints is straight forward. Secondly, we demonstrate that PN analysis is useful in reducing search complexity and presents two main results: a novel heuristic function based on PN analysis that is more efficient than existing methods and a novel reachability scheme that avoids futile exploration of candidate schedules. Thirdly a novel scheduling algorithm that overcomes the efficiency drawbacks of previous algorithms is presented. This algorithm satisfactorily overcomes the complexity issue while achieving very promising results in terms of optimality. Finally, this thesis presents a novel hybrid scheduler that demonstrates the convenience of the use of PN as a representation paradigm to support hybridisation between traditional OR methods, Al systematic search and stochastic optimisation algorithms. Initial results show that the approach is promising

Discrete-Event Control and Optimization of Container Terminal Operations

This thesis discusses the dynamical modeling of complex container terminal operations. In the current literature, the systems are usually modeled in static way using linear programming techniques. This setting does not completely capture the dynamic aspects in the operations, where information about external factors such as ships and trucks arrivals or departures and also the availability of terminal's equipment can always change. We propose dynamical modeling of container terminal operations using discrete-event systems (DES) modeling framework. The basic framework in this thesis is the DES modeling for berth and quay crane allocation problem (BCAP) where the systems are not only dynamic, but also asynchronous. We propose a novel berth and QC allocation method, namely the model predictive allocation (MPA) which is based on model predictive control principle and rolling horizon implementation. The DES models with asynchronous event transition is mathematically analyzed to show the efficacy of our method. We study an optimal input allocation problem for a class of discrete-event systems with dynamic input sequence (DESDIS). We show that in particular, the control input can be obtained by the minimization/maximization of the present input sequence only. We have shown that the proposed approach performed better than the existing method used in the studied terminal and state-of-the-art methods in the literature

Removing and restoring control flow with the Value State Dependence Graph

This thesis studies the practicality of compiling with only data flow information. Specifically, we focus on the challenges that arise when using the Value State Dependence Graph (VSDG) as an intermediate representation (IR). We perform a detailed survey of IRs in the literature in order to discover trends over time, and we classify them by their features in a taxonomy. We see how the VSDG fits into the IR landscape, and look at the divide between academia and the 'real world' in terms of compiler technology. Since most data flow IRs cannot be constructed for irreducible programs, we perform an empirical study of irreducibility in current versions of open source software, and then compare them with older versions of the same software. We also study machine-generated C code from a variety of different software tools. We show that irreducibility is no longer a problem, and is becoming less so with time. We then address the problem of constructing the VSDG. Since previous approaches in the literature have been poorly documented or ignored altogether, we give our approach to constructing the VSDG from a common IR: the Control Flow Graph. We show how our approach is independent of the source and target language, how it is able to handle unstructured control flow, and how it is able to transform irreducible programs on the fly. Once the VSDG is constructed, we implement Lawrence's proceduralisation algorithm in order to encode an evaluation strategy whilst translating the program into a parallel representation: the Program Dependence Graph. From here, we implement scheduling and then code generation using the LLVM compiler. We compare our compiler framework against several existing compilers, and show how removing control flow with the VSDG and then restoring it later can produce high quality code. We also examine specific situations where the VSDG can put pressure on existing code generators. Our results show that the VSDG represents a radically different, yet practical, approach to compilation