Metastability of Traffic Flow in Zero-Range Model

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].