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The Krauss-model is a stochastic model for traffic flow which is continuousin space. For periodic boundary conditions it is well understood and known todisplay a non-unique flow-density relation (fundamental diagram) for certaindensities. In many applications, however, the behaviour under open boundaryconditions 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 extremalprinciple introduced for the case of simpler discrete models. The phase diagramof the open system will be completely determined by the fundamental diagram ofthe periodic system through this principle. In order to allow the investigationof the whole state space of the Krauss-model, appropriate strategies for theinjection of cars into the system are needed.Two methods solving this problemare discussed and the boundary-induced phase transitions for both methods arestudied.We also suggest a supplementary rule for the extremal principle toaccount for cases where not all the possible bulk states are generated by thechosen boundary conditions.Comment: 12 Pages, 14 figure

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