A Queueing Theory Approach for a Multi-Speed Exclusion Process

Cyril Furtlehner () and Jean-Marc Lasgouttes ()
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Cyril Furtlehner: Université Paris-Sud, INRIA Futurs, Project Team TAO
Jean-Marc Lasgouttes: INRIA Paris-Rocquencourt, Project Team IMARA

A chapter in Traffic and Granular Flow ’07, 2009, pp 129-138 from Springer

Abstract: Summary 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.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-77074-9_11

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DOI: 10.1007/978-3-540-77074-9_11

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