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.
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Furtlehner, C., Lasgouttes, JM. (2009). A Queueing Theory Approach for a Multi-Speed Exclusion Process. In: Appert-Rolland, C., Chevoir, F., Gondret, P., Lassarre, S., Lebacque, JP., Schreckenberg, M. (eds) Traffic and Granular Flow ’07. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77074-9_11
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DOI: https://doi.org/10.1007/978-3-540-77074-9_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77073-2
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