On the existence of a variational principle for deterministic cellular automaton models of highway traffic flow

It is shown that a variety of deterministic cellular automaton models of highway traffic flow obey a variational principle which states that, for a given car density, the average car flow is a non-decreasing function of time. This result is established for systems whose configurations exhibits local jams of a given structure. If local jams have a different structure, it is shown that either the variational principle may still apply to systems evolving according to some particular rules, or it could apply under a weaker form to systems whose asymptotic average car flow is a well-defined function of car density. To establish these results it has been necessary to characterize among all number-conserving cellular automaton rules which ones may reasonably be considered as acceptable traffic rules. Various notions such as free-moving phase, perfect and defective tiles, and local jam play an important role in the discussion. Many illustrative examples are given.Comment: 19 pages, 4 figure

Car-oriented mean-field theory for traffic flow models

We present a new analytical description of the cellular automaton model for single-lane traffic. In contrast to previous approaches we do not use the occupation number of sites as dynamical variable but rather the distance between consecutive cars. Therefore certain longer-ranged correlations are taken into account and even a mean-field approach yields non-trivial results. In fact for the model with $v_{max}=1$ the exact solution is reproduced. For $v_{max}=2$ the fundamental diagram shows a good agreement with results from simulations.Comment: LaTex, 10 pages, 2 postscript figure

Quantitative analysis of pedestrian counterflow in a cellular automaton model

Pedestrian dynamics exhibits various collective phenomena. Here we study bidirectional pedestrian flow in a floor field cellular automaton model. Under certain conditions, lane formation is observed. Although it has often been studied qualitatively, e.g., as a test for the realism of a model, there are almost no quantitative results, neither empirically nor theoretically. As basis for a quantitative analysis we introduce an order parameter which is adopted from the analysis of colloidal suspensions. This allows to determine a phase diagram for the system where four different states (free flow, disorder, lanes, gridlock) can be distinguished. Although the number of lanes formed is fluctuating, lanes are characterized by a typical density. It is found that the basic floor field model overestimates the tendency towards a gridlock compared to experimental bounds. Therefore an anticipation mechanism is introduced which reduces the jamming probability.Comment: 11 pages, 12 figures, accepted for publication in Phys. Rev.

Generalized Centrifugal Force Model for Pedestrian Dynamics

A spatially continuous force-based model for simulating pedestrian dynamics is introduced which includes an elliptical volume exclusion of pedestrians. We discuss the phenomena of oscillations and overlapping which occur for certain choices of the forces. The main intention of this work is the quantitative description of pedestrian movement in several geometries. Measurements of the fundamental diagram in narrow and wide corridors are performed. The results of the proposed model show good agreement with empirical data obtained in controlled experiments.Comment: 10 pages, 14 figures, accepted for publication as a Regular Article in Physical Review E. This version contains minor change

Cluster formation and anomalous fundamental diagram in an ant trail model

A recently proposed stochastic cellular automaton model ({\it J. Phys. A 35, L573 (2002)}), motivated by the motions of ants in a trail, is investigated in detail in this paper. The flux of ants in this model is sensitive to the probability of evaporation of pheromone, and the average speed of the ants varies non-monotonically with their density. This remarkable property is analyzed here using phenomenological and microscopic approximations thereby elucidating the nature of the spatio-temporal organization of the ants. We find that the observations can be understood by the formation of loose clusters, i.e. space regions of enhanced, but not maximal, density.Comment: 11 pages, REVTEX, with 11 embedded EPS file

Disorder Effects in CA-Models for Traffic Flow

We investigate the effect of quenched disorder in the Nagel-Schreckenberg model of traffic flow. Spatial inhomogenities, i.e. lattice sites where the braking probability is enlarged, are considered as well as particle disorder, i.e. cars of a different maximum velocity. Both types of disorder lead to segregated states.Comment: 6 pages, 4 postscript figures, Proceedings of the conference "Traffic and Granular Flow '97", Duisburg, Germany, October 5-8, 199

The asymmetric exclusion process: Comparison of update procedures

The asymmetric exclusion process (ASEP) has attracted a lot of interest not only because 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 a MPA for that case and derive the corresponding matrix algebra.Comment: 47 pages (11 PostScript figures included), LATEX, Two misprints in equations correcte