Probabilistic Traffic Flow Breakdown In Stochastic Car Following Models

D. Jost, K. Nagel

Dominic Jost and Kai Nagel

Date: 9 November 2003

Abstract:

There is discussion if traffic displays spontaneous breakdown. This paper presents computational evidence that stochastic car following models can have a control parameter that moves the model between displaying and not displaying spontaneous phase separation for some densities. Those phases can be called ``laminar'' and ``jammed''. Models with spontaneous phase separation show three states as a function of density: a first state at low density, where those models are homogeneously laminar; a second state at high density, wherey they are homogeneously jammed; and a third state at intermediate density, where they consist of a mix between the two phases (phase coexistence). This is the same picture as for a gas-liquid transition when volume is the control parameter.

Although the gas-liquid analogy to traffic models has been widely discussed, no traffic-related model so far displayed a completely understood stochastic version of that transition. Having a stochastic model is important to understand the potentially probabilistic nature of the transition. Most importantly, if indeed models with spontaneous phase separation describe certain aspects correctly, then this leads to an understanding of spontaneous breakdown. Alternatively, if models without spontaneous phase separation describe these aspects better, then there is no spontaneous breakdown ($=$ no breakdown without a reason). Interestingly, even models without spontaneous phase separation can still allow for jam formation on small scales, which may give the impression of having a model with spontaneous phase separation.

Keywords: traffic flow theory, car following models, traffic breakdown, traffic simulation, phase transition, phase separation, critical point