hal-00175628, version 1
A queueing theory approach for a multi-speed exclusion process.
Cyril Furtlehner
1Jean-Marc Lasgouttes
2
Traffic and Granular Flow '07 (2007) unknown yet
Résumé : We consider a one-dimensional stochastic reaction-diffusion generalizing the totally asymmetric simple exclusion process, and aiming at describing single lane roads with vehicles that can change speed. To each particle is associated a jump rate, and the particular dynamics that we choose (based on 3-sites patterns) ensures that clusters of occupied sites are of uniform jump rate. When this model is set on a circle or an infinite line, classical arguments allow to map it to a linear network of queues (a zero-range process in theoretical physics parlance) with exponential service times, but with a twist: the service rate remains constant during a busy period, but can change at renewal events. We use the tools of queueing theory to compute the fundamental diagram of the traffic, and show the effects of a condensation mechanism.
- 1 : TAO (INRIA Futurs)
- INRIA – CNRS : UMR8623 – Université Paris XI - Paris Sud
- 2 : IMARA (INRIA Rocquencourt)
- INRIA
- Domaine : Physique/Matière Condensée/Mécanique statistique
- Mots-clés : stochastic processes – phase transition – transportation
- Commentaire : 10 pages – 6 figures
- hal-00175628, version 1
- http://hal.inria.fr/hal-00175628
- oai:hal.inria.fr:hal-00175628
- Contributeur : Cyril Furtlehner
- Soumis le : Vendredi 28 Septembre 2007, 19:37:20
- Dernière modification le : Lundi 8 Octobre 2007, 13:06:15






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