Showing papers by "Andreas Schadschneider published in 1998"
TL;DR: It is shown that this model exhibits metastable states, thus sheding some light on the prerequisites for the occurance of hysteresis effects in the flow-density relation, and proposes a simple generalization of the NaSch model by introducing a velocity-dependent randomization.
Abstract: Measurements on real traffic have revealed the existence of metastable states with very high flow. Such states have not been observed in the Nagel-Schreckenberg (NaSch) model which is the basic cellular automaton for the description of traffic. Here we propose a simple generalization of the NaSch model by introducing a velocity-dependent randomization. We investigate a special case which belongs to the so-called slow-to-start rules. It is shown that this model exhibits metastable states, thus sheding some light on the prerequisites for the occurance of hysteresis effects in the flow-density relation.
520 citations
TL;DR: In this article, the authors study the asymmetric exclusion process (ASEP) for different types of updates, namely random-sequential, sequential, sublattice-parallel, and parallel.
Abstract: The asymmetric exclusion process (ASEP) has attracted a lot of interest not only because of its many applications, e.g., in the context of the kinetics of biopolymerization and traffic flow theory, but also because it is a paradigmatic model for nonequilibrium systems. Here we study the ASEP for different types of updates, namely random-sequential, sequential, sublattice-parallel, and parallel. In order to compare the effects of the different update procedures on the properties of the stationary state, we use large-scale Monte Carlo simulations and analytical methods, especially the so-called matrix-product Ansatz (MPA). We present in detail the exact solution for the model with sublattice-parallel and sequential updates using the MPA. For the case of parallel update, which is important for applications like traffic flow theory, we determine the phase diagram, the current, and density profiles based on Monte Carlo simulations. We furthermore suggest an MPA for that case and derive the corresponding matrix algebra.
278 citations
TL;DR: Numerical simulations suggest the absence of critical behavior in the cellular automaton model for traffic flow, which exhibits a jamming transition from a free-flow phase to a congested phase.
Abstract: The cellular automaton model for traffic flow exhibits a jamming transition from a free-flow phase to a congested phase In the deterministic case this transition corresponds to a critical point with diverging correlation length In the presence of noise, however, no consistent picture has emerged up to now We present data from numerical simulations that suggest the absence of critical behavior The transition of the deterministic case is smeared out and one only observes the remnants of the critical point
83 citations
TL;DR: In this article, the authors investigated the allowed configurations in the stationary state of the cellular automaton model for single-lane traffic and found that certain states in the configuration space cannot be reached if one uses parallel dynamics.
Abstract: We investigate the allowed configurations in the stationary state of the cellular automaton model for single-lane traffic. It is found that certain states in the configuration space cannot be reached if one uses parallel dynamics. These so-called Garden of Eden (GoE) states do not exist for random-sequential dynamics and are responsible for the strong short-ranged correlations found in parallel dynamics. By eliminating the GoE states we obtain a simple and effective approximative description of the model. For the exact solution is recovered. For this elimination leads to much higher values of the flux compared to the mean-field result which are in good agreement with Monte Carlo simulations.
46 citations
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TL;DR: In this article, the authors investigated the allowed configurations in the stationary state of the cellular automaton model for single-lane traffic and found that certain states in the configuration space can not be reached if one uses parallel dynamics.
Abstract: We investigate the allowed configurations in the stationary state of the cellular automaton model for single-lane traffic. It is found that certain states in the configuration space can not be reached if one uses parallel dynamics. These so-called Garden of Eden (GoE) states do not exist for random-sequential dynamics and are responsible for the strong short-ranged correlations found in parallel dynamics. By eliminating the GoE states we obtain a simple and effective approximative description of the model. For $v_{max}=1$ the exact solution is recovered. For $v_{max}=2$ this elimination leads to much higher values of the flux compared to the mean-field result which are in good agreement with Monte Carlo simulations.
40 citations
15 Dec 1998
TL;DR: A simulation tool for an urban road network based on real-time traffic data and a cellular automaton model for traffic flow is presented and the quality of the reproduced traffic states is investigated.
Abstract: The modelling and prediction of traffic flow is one of the future challenges for science. We present a simulation tool for an urban road network based on real-time traffic data and a cellular automaton model for traffic flow. This tool has been applied to the inner city of Duisburg. The quality of the reproduced traffic states is investigated with regard to vehicle densities and typical features of urban traffic.
3 citations