One-Dimensional Particle Processes with Acceleration/Braking Asymmetry
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The slow-to-start mechanism is known to play an important role in the particular shape of the Fundamental Diagram of traffic and to be associated to hysteresis effects of traffic flow. We study this question in the context of exclusion and queueing processes, by including an asymmetry between deceleration and acceleration in the formulation of these processes. For exclusions processes, this corresponds to a multi-class process with transition asymmetry between different speed levels, while for queueing processes we consider non-reversible stochastic dependency of the service rate w.r.t. the number of clients. The relationship between these 2 families of models is analyzed on the ring geometry, along with their steady state properties. Spatial condensation phenomena and metastability are observed, depending on the level of the aforementioned asymmetry. In addition, we provide a large deviation formulation of the fundamental diagram which includes the level of fluctuations, in the canonical ensemble when the stationary state is expressed as a product form of such generalized queues.
KeywordsExclusion processes Zero range processes Fundamental diagram of traffic Spatial condensation
We thank Guy Fayolle for useful discussions. We also thank referees for fruitful comments and references. This work was supported by the French National Research Agency (ANR) grant No ANR-08-SYSC-017.
- 10.Furtlehner, C., Lasgouttes, J.: A queueing theory approach for a multi-speed exclusion process. In: Traffic and Granular Flow ’07, pp. 129–138 (2007) Google Scholar
- 17.Kerner, B.: The Physics of Traffic. Springer, Berlin (2005) Google Scholar
- 18.Kipnis, C., Landim, C.: Scaling Limits of Interacting Particles Systems. Springer, Berlin (1999) Google Scholar
- 23.Samsonov, M., Furtlehner, C., Lasgouttes, J.: Exactly solvable stochastic processes for traffic modelling. Tech. Rep. 7278, INRIA (2010) Google Scholar