Stationary State Properties of a Microscopic Traffic Flow Model Mixing Stochastic Transport and Car-Following

Sylvain Lassarre (), Michel Roussignol (), Andreas Schadschneider () and Antoine Tordeux ()
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Sylvain Lassarre: IFSTTAR – GRETTIA
Michel Roussignol: Paris-Est University – LAMA
Andreas Schadschneider: Universität zu Köln, Institut für Theoretische Physik
Antoine Tordeux: Paris-Est University – LVMT

A chapter in Traffic and Granular Flow '11, 2013, pp 35-46 from Springer

Abstract: Abstract We study the stationary properties of a microscopic traffic flow model related to a continuous time mass transport process. It is a stochastic collision-free mapping of a classical deterministic first order car-following model calibrated by the targeted speed function and the driver reaction time. The stationary states of the model are analytically treated for vanishing reaction time. Some approximations are calculated, assuming a product form of the invariant measure. When the reaction time is strictly positive, the process is studied by simulation. A relation between the parameters and the propagation of kinematic stop-and-go waves is identified as identical to the well-known stability condition of the car-following model. The results underline a negative impact of the driver reaction time parameter on the homogeneity of the flow in stationary state.

Keywords: Traffic Flow; Beta Distribution; Invariant Distribution; Jump Size; Totally Asymmetric Simple Exclusion Process (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-39669-4_4

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DOI: 10.1007/978-3-642-39669-4_4

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