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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received 16 September 2002 / Received in final form 4 November 2002 Published online 31 December 2002
Rights and permissions
About this article
Cite this article
Namazi, A., Eissfeldt, N., Wagner, P. et al. Boundary-induced phase transitions in a space-continuous traffic model with non-unique flow-density relation. Eur. Phys. J. B 30, 559–570 (2002). https://doi.org/10.1140/epjb/e2002-00414-4
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2002-00414-4