  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.
