Boundary-induced phase transitions in a space-continuous traffic model with non-unique flow-density relation

TL;DR

This paper studies boundary-induced phase transitions in a continuous-space traffic model, revealing stable high flow states and extending the extremal principle to open systems with non-unique flow-density relations.

Contribution

It demonstrates that the Krauss-model's phase diagram under open boundaries can be fully characterized by the fundamental diagram using an extremal principle, and introduces boundary strategies for exploring the model's state space.

Findings

High flow states are stable, not metastable.

The phase diagram is determined by the fundamental diagram via an extremal principle.

Boundary strategies enable exploration of the full state space.

Abstract

The Krauss-model is a stochastic model for traffic flow which is continuous in space. For periodic boundary conditions it is well understood and known to display a non-unique flow-density relation (fundamental diagram) for certain densities. In many applications, however, the behaviour under open boundary conditions plays a crucial role.In contrast to all models investigated so far, the high flow states of the Krauss-model are not metastable, but also stable. Nevertheless we find that the current in open systems obeys an extremal principle introduced for the case of simpler discrete models. The phase diagram of the open system will be completely determined by the fundamental diagram of the periodic system through this principle. In order to allow the investigation of the whole state space of the Krauss-model, appropriate strategies for the injection of cars into the system are needed.Two methods solving this problem are discussed and the boundary-induced phase transitions for both methods are studied.We also suggest a supplementary rule for the extremal principle to account for cases where not all the possible bulk states are generated by the chosen boundary conditions.