Random walk theory of jamming in a cellular automaton model for traffic flow

The jamming behavior of a single lane traffic model based on a cellular automaton approach is studied. Our investigations concentrate on the so-called VDR model which is a simple generalization of the well-known Nagel-Schreckenberg model. In the VDR model one finds a separation between a free flow phase and jammed vehicles. This phase separation allows to use random walk like arguments to predict the resolving probabilities and lifetimes of jam clusters or disturbances. These predictions are in good agreement with the results of computer simulations and even become exact for a special case of the model. Our findings allow a deeper insight into the dynamics of wide jams occuring in the model.Comment: 16 pages, 7 figure

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

A Microscopic Model for Packet Transport in the Internet

A microscopic description of packet transport in the Internet by using a simple cellular automaton model is presented. A generalised exclusion process is introduced which allows to study travel times of the particles ('data packets') along a fixed path in the network. Computer simulations reveal the appearance of a free flow and a jammed phase separated by a (critical) transition regime. The power spectra are compared to empirical data for the RTT (Round Trip Time) obtained from measurements in the Internet. We find that the model is able to reproduce the characteristic statistical behaviour in agreement with the empirical data for both phases (free flow and congested). The phases are therefore jamming properties and not related to the structure of the network. Moreover the model shows, as observed in reality, critical behaviour (1/f-noise) for paths with critical load.Comment: 9 pages, 7 figure

Optimizing Traffic Lights in a Cellular Automaton Model for City Traffic

We study the impact of global traffic light control strategies in a recently proposed cellular automaton model for vehicular traffic in city networks. The model combines basic ideas of the Biham-Middleton-Levine model for city traffic and the Nagel-Schreckenberg model for highway traffic. The city network has a simple square lattice geometry. All streets and intersections are treated equally, i.e., there are no dominant streets. Starting from a simple synchronized strategy we show that the capacity of the network strongly depends on the cycle times of the traffic lights. Moreover we point out that the optimal time periods are determined by the geometric characteristics of the network, i.e., the distance between the intersections. In the case of synchronized traffic lights the derivation of the optimal cycle times in the network can be reduced to a simpler problem, the flow optimization of a single street with one traffic light operating as a bottleneck. In order to obtain an enhanced throughput in the model improved global strategies are tested, e.g., green wave and random switching strategies, which lead to surprising results.Comment: 13 pages, 10 figure

Mechanical restriction versus human overreaction triggering congested traffic states

A new cellular automaton (CA) traffic model is presented. The focus is on mechanical restrictions of vehicles realized by limited acceleration and deceleration capabilities. These features are incorporated into the model in order to construct the condition of collision-free movement. The strict collision-free criterion imposed by the mechanical restrictions is softened in certain traffic situations, reflecting human overreaction. It is shown that the present model reliably reproduces most empirical findings including synchronized flow, the so-called {\it pinch effect}, and the time-headway distribution of free flow. The findings suggest that many free flow phenomena can be attributed to the platoon formation of vehicles ({\it platoon effect})Comment: 5 pages, 3 figures, to appear in PR

Optimal traffic states in a cellular automaton for city traffic

The impact of global traffic light control strategies for city networks is analyzed in a recently proposed cellular automaton model. The model combines basic ideas of the Biham-Middleton-Levine model for city traffic and the Nage-Schreckenberg model for highway traffic. The city network has a simple square lattice geometry. All streets and intersections are treated equally, i.e., there are no dominant streets