A queueing theory approach for a multi-speed exclusion process
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.
Cite
@article{arxiv.1109.1756,
title = {A queueing theory approach for a multi-speed exclusion process},
author = {Cyril Furtlehner and Jean-Marc Lasgouttes},
journal= {arXiv preprint arXiv:1109.1756},
year = {2011}
}
Comments
11 pages, 6 figures, in Proceedings of Traffic and granular flow 2007