One-Dimensional Particle Processes with Acceleration/Braking Asymmetry |
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Authors: | Cyril Furtlehner Jean-Marc Lasgouttes Maxim Samsonov |
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Institution: | 1.INRIA Saclay–?le-de-France – LRI, Bat. 490,Université Paris-Sud,Orsay cedex,France;2.INRIA Paris–Rocquencourt – Domaine de Voluceau,Le Chesnay cedex,France |
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Abstract: | 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. |
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