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A queueing theory approach for a multi-speed exclusion process

By Cyril Furtlehner and Jean-Marc Lasgouttes

Abstract

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.Comment: 11 pages, 6 figures, in Proceedings of Traffic and granular flow 200

Topics: Condensed Matter - Statistical Mechanics
Year: 2011
OAI identifier: oai:arXiv.org:1109.1756

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