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A Queueing Theory Approach for a Multi-Speed Exclusion Process

In: Traffic and Granular Flow ’07

Author

Listed:
  • Cyril Furtlehner

    (Université Paris-Sud, INRIA Futurs, Project Team TAO)

  • Jean-Marc Lasgouttes

    (INRIA Paris-Rocquencourt, Project Team IMARA)

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.

Suggested Citation

  • Cyril Furtlehner & Jean-Marc Lasgouttes, 2009. "A Queueing Theory Approach for a Multi-Speed Exclusion Process," Springer Books, in: Cécile Appert-Rolland & François Chevoir & Philippe Gondret & Sylvain Lassarre & Jean-Patrick Lebacq (ed.), Traffic and Granular Flow ’07, pages 129-138, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-77074-9_11
    DOI: 10.1007/978-3-540-77074-9_11
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