Thomas Bourdeaud'huy

Mathematical programming approach to the Petri nets reachability problem

This paper focuses on the resolution of the reachability problem in Petri nets, using the mathematical programming paradigm. The proposed approach is based on an implicit traversal of the Petri net reachability graph. This is done by constructing a unique sequence of Steps that represents exactly the total behaviour of the net. We propose several formulations based on integer and/or binary linear programming, and the corresponding sets of adjustments to the particular class of problem considered. Our models are validated on a set of benchmarks and compared with standard approaches from IA and Petri nets community.

Performance Analysis of IEEE 802.11b Wireless Networks with Object Oriented Petri Nets

Communication protocols are often investigated using simulation. This paper presents a performance study of the distributed coordination function of 802.11 networks. Firstly, our study illustrates the different classes of Petri Nets used for modeling network protocols and their robustness in modeling based on formal methods. Next we propose a detailed 802.11b model based on Object-oriented Petri Nets that precises backoff procedure and time synchronization. Then, performance analyses are evaluated by simulation for a dense wireless network and compared with other measurements approaches. Our main goal is to propose a modular model that will enable to evaluate the impact of network performances on the performances of distributed discrete event systems.

A MATHEMATICAL MODEL FOR CYCLIC SCHEDULING WITH WORK-IN-PROGRESS MINIMIZATION

Abstract In this paper, we focus on the cyclic scheduling problem. This kind of schedule is well fitted to medium and large production demand, since it allows to avoid the scheduling of the whole tasks and to handle the combinatorial explosion of the problem by considering only a small pattern (cycle). The reduction of combinatorial complexity do not necessarily reduce the overall complexity since new constraints are introduced (scheduling of operations in a temporal window of fixed size). Thus, we propose a formal study of this problem and a linear mathematical model allowing its exact resolution.

Efficient reachability analysis of bounded Petri nets using constraint programming

In this paper, we consider the Petri net (PNs) reachability problem, which consists of finding transition firing sequences leading to a given target marking. We focus on bounded Petri nets for which we develop a correct and complete algorithm using the logical abstraction technique proposed by Benasser and Yim. We define for that the PN sequential depth parameter, which corresponds to the maximal number of transitions to fire in order to reach any marking of the reachability graph.

A Component Modular Modeling Approach Based on Object Oriented Petri Nets for the Performance Analysis of Distributed Discrete Event Systems

Distributed Discrete Event Systems (Distributed DES) are increasing with the development of networks. A major problem of these systems is the evaluation of their performance at the design stage. We are particularly interested in assessing the impact of computer networking protocols on the control of manufacturing systems. In our design methodology, these systems are modeled using Petri nets. In this context, we propose an approach to modeling network protocols based on Oriented Object Petri Nets. Our ultimate objective is to assess by means of simulations the performances of such a system when one distributes their control models on an operational architecture. In this study, we are implementing a component based approach designed to encourage reuse when modeling new network protocols. To illustrate our approach and its reuse capabilities, we will implement it to model the link layer protocols of the norms IEEE 802.11b and IEEE 802.3.

Network protocol modeling: A Time Petri Net modular approach

Communication services are surrounding our daily life; internet, mail, cellular phones... These services are managed by several protocols. In this paper we propose a generic model for the Ethernet protocol based on time Petri nets. A complete modular service-protocol model can help in better managing services and protocols and to easily change a system element without affecting the other elements. Also it can help us to study different properties of the system such as performance, functionality, validation and any qualitative or quantitative property.

Analysis of Reconfiguration Strategies Based On Petri Nets Models and Optimization Techniques

The concept of flexible manufacturing system (FMS) has been initially introduced to enable the production of different types of parts at the same time. But dependable requirements and especially the necessity to continue to produce in spite of the breakdown of a plant component lead to exploit the flexibility to reconfigure the plant. Nowadays, the challenge for researchers and industrials is thus to build reconfigurable manufacturing systems (RMS). A RMS must be able to adapt its configuration in real-time depending on production objectives and available resources. In this paper, we introduce the concept of reconfiguration process that defines the different steps to determine the actions needed to put the system in a state compatible with production resumption. Our approach expresses the reconfiguration process as a Petri net reachability problem instance. Our proposition consists in reusing the initial models developed for control purposes and to adapt them to model the potential reconfiguration actions (alternatives routes, start and stop of resources, feasible operating sequences). We define then a target marking - not necessarily entirely known - corresponding to the specification of a family of desired system states. Then we search for the firing sequences that bring the system from an initial marking to the desired objective marking. This problem is solved using mathematical programming techniques, allowing to optimize criteria corresponding to the relevance of the reconfiguration

Transient inter-production scheduling based on Petri nets and constraint programming

In this article, we focus on the transient inter-production scheduling problem between two cyclic productions in the framework of flexible manufacturing systems. This problem is first formulated as a reachability problem in timed Petri nets (TPN), then solved using a methodology based on constraint programming. Our work is based on the controlled executions proposed by Chretienne to model the sequence of transition firing dates. Our methodology is based on a preliminary resolution of the state equation between initial and final states in the underlying non-TPN. Then, we choose a duration T max corresponding to the maximal duration time of the scheduling. For each solution S of the state equation, we build a controlled execution from the sequence of firings in S. After the propagation of firing date constraints and reachability constraints in the TPN, we use constraint programming to enumerate the set of feasible controlled executions.

A PETRI-NET BASED APPROACH FOR THE RECONFIGURATION OF FLEXIBLE MANUFACTURING SYSTEMS USING OPTIMIZATION TECHNIQUES

Abstract In the framework of dependable systems, we propose a mathematical programming approach for the reconfiguration of flexible manufacturing systems (FMS). This kind of procedure is used when unexpected events (called failures ) occur – or in order to start a new production –, to determine the actions needed to put the system in a state compatible with production resumption. We propose to express the reconfiguration process as a Petri net reachability problem instance. We start from a Petri net representing the initial production, and we introduce additional nodes and tokens in order to model the potential reconfiguration actions (alternative routes, flexibilities, start and stop of machines, etc). We define then a target marking – not necessarily entirely known –, corresponding to the specification of a family of desired system states. A search for firing sequences leading to the desired marking from the initial one is then made. This problem is finally solved using mathematical programming techniques, allowing to optimize criteria corresponding to the relevance of the reconfiguration.

A Heuristic for the Container Stacking Problem in Automated Maritime Ports

Abstract In this paper, we are interested in finding efficient practical approaches to solve the Container Stacking Problem in Maritime Ports. Given container arrivals in a container port terminal, the objective is to assign a slot to each one in a storage area at least cost with respect to pre-defined constraints. The cost is expressed in term of number of expected relocation movements. The constraints to respect are stack height, stack number, and departure dates. We propose to improve a previous heuristic model proposed by Mark B. Duinkerken and Ottjes (2001) based on the computation of an indactor called the “remaining stack capacity“.