A queueing theory approach for a multi-speed exclusion process.

Cyril Furtlehner 1 Jean-Marc Lasgouttes 2
1 TANC - Algorithmic number theory for cryptology
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
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.
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Contributor : Cyril Furtlehner <>
Submitted on : Friday, September 28, 2007 - 7:37:20 PM
Last modification on : Wednesday, March 27, 2019 - 4:41:29 PM
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  • HAL Id : hal-00175628, version 1



Cyril Furtlehner, Jean-Marc Lasgouttes. A queueing theory approach for a multi-speed exclusion process.. Traffic and Granular Flow '07, Jun 2007, Orsay, France. pp.unknown yet. ⟨hal-00175628⟩



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