Traffic Jams : Cluster Formation in Low-Dimensional Cellular Automata Models for Highway and City Traffic
Cellular automata (CA) models are quite popular in the field of traffic flow. They allow an effective implementation of real-time traffic computer-simulations. Therefore, various approaches based on CA models have been suggested in recent years. The first part of this thesis focuses on the so-called VDR (velocity-dependent randomization) model which is a modified version of the well known Nagel-Schreckenberg (NaSch) CA model. This choice is motivated by the fact that wide phase separated jams occur in the model. On the basis of random walk theory an analytical approach to the dynamics of these separated jam clusters is given. The predictions are in good agreement with the results of computer simulations and provide a deeper insight into the dynamics of wide jams which seem to be generic for CA approaches and are therefore of special interest. Furthermore, the impact of a localized defect in a periodic system is analyzed in the VDR model. It turns out that depending on the magnitude of the defect stop-and-go traffic can occur which can not be found in the VDR model without lattice defects. Finally, the VDR model is studied with open boundaries. The phase diagrams, obtained by Monte-Carlo simulations, reveal two jam phases with a stripped microscopic structure and for finite systems the existence of a new high-flow phase is shown. The second part of this thesis concentrates on CA models for city traffic with the focus on the Chowdhury-Schadschneider (ChSch) model. In the context of jam clusters the model reveals interesting features since two factors exert influence on the jamming behavior. On the one hand, jams are induced at crossings due to the traffic lights, i.e., cars are forced to stop at a ``red light', and, on the other hand, the dynamics of such induced jams is governed by the NaSch model rules. One part of the investigations covers global (fixed) traffic light strategies. These are found to lead to strong oscillations in the global flow except for the case of randomly switching lights. Furthermore, the impact of adaptive (local) traffic light control is analyzed. It is found that the autonomous strategies can nearly match the global optimum of the ChSch model. In order to provide a more realistic vehicle distribution, the ChSch model is enhanced by a stochastic turning of vehicles and by inhomogeneous densities. Here, the autonomous strategies can outperform the global ones in some cases.