Metastability of Traffic Flow in Zero-Range Model

Jevgenijs Kaupužs (), Reinhard Mahnke () and Rosemary J. Harris ()
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Jevgenijs Kaupužs: University of Latvia, Institute of Mathematics and Computer Science
Reinhard Mahnke: Universität Rostock, Institut für Physik
Rosemary J. Harris: Forschungszentrum Jülich, Institut für Festkörperforschung

A chapter in Traffic and Granular Flow’05, 2007, pp 461-466 from Springer

Abstract: Abstract The development of traffic jams in vehicular flow is an everyday example of the occurence of phase separation in low-dimensional driven systems, a topic which has attracted much recent interest [1–4]. In [5] the existence of phase separation is related to the size-dependence of domain currents and a quantitative criterion is obtained by considering the zero-range process (ZRP) as a generic model for domain dynamics. We use zero-range picture to study the phase separation in traffic flow in the spirit of the probabilistic (master equation) description of transportation [6]. Significantly, we find [7] that prior to condensation studied in previous works [8, 9] the system can exist in a homogeneous metastable state and we provide estimates of critical cluster size and mean nucleation time. Finally, we calculate the fundamental flux-density diagram which includes a metastable branch. Metastability and hysteresis effects have been observed in real traffic [10, 11]. For previous work focusing on the description of jam formation as a nucleation process, see [12, 13].

Keywords: Metastable State; Master Equation; Grand Canonical Ensemble; Nucleation Time; Fundamental Diagram (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/978-3-540-47641-2_42

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