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Contribution à la modélisation, l'analyse et la commande des systèmes à événements discrets par les réseaux de Petri et l'algèbre (max, plus) : Application aux systèmes de transport

Abstract : The work presented in this thesis contributes to the modelling, the analysis and the control of public transportation systems by the adaptation of Petri Nets (PN) and dioid algebra. We study in particular the optimised management of passengers connections by planning bus timetables. Then we develop models able to solve problems of performance evaluation and improve the quality of service of bus networks. These issues are addressed by minimising both passengers waiting times and number of used vehicles. Our study is carried out by taking into account the working of buses at the connection stops where the passengers exchanges are made possible. On the one hand, we use timed event graphs (TEG) and stationary linear (max, +) models to describe the synchronised working. On the other hand, we use a dynamic timed event graph with withdrawal of tokens (DTEGWT) model for the non-synchronised working. As the DTEGWT graphical model is subject to structural conflicts, its associated state representation in (max, +) algebra is linear and non-stationary. In order to solve this state model, we consider a resolution policy of the structural conflicts. We propose then, to solve these conflicts, a routing policy determined a priori according to the system characteristics. This policy enables us to first to solve and arbitrate these conflicts on the graphical model, and second to solve the mathematical model. By analysing the obtained solutions and the eigenvectors of characteristic matrix of (max, +) model, we evaluate the various passengers waiting times and we estimate a performances of studied system. Concerned by the amount of time spent during connections and also by the quality of service, we study a control policy. In this phase, we propose two control approaches: the first one enables to synthesise a control based on the residuation theory in dioid algebra. The second relies on the simulation results that enable to obtain a control from the objectives functions optima. The results are validated on a part of Montbéliard city‘s transportation network.
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Contributor : Ahmed Nait Sidi Moh <>
Submitted on : Friday, March 26, 2010 - 8:10:10 PM
Last modification on : Friday, March 26, 2010 - 8:59:39 PM
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Ahmed Nait-Sidi-Moh. Contribution à la modélisation, l'analyse et la commande des systèmes à événements discrets par les réseaux de Petri et l'algèbre (max, plus) : Application aux systèmes de transport. Mathématiques [math]. Université de Technologie de Belfort-Montbeliard, 2003. Français. ⟨tel-00467580⟩

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