Simple cellular automata models are able to reproduce the basic properties of highway traffic. The comparison with empirical data for microscopic quantities requires a more detailed description of the elementary dynamics. Based on existing cellular automata models we propose an improved discrete model incorporating anticipation effects, reduced acceleration capabilities and an enhanced interaction horizon for braking. The modified model is able to reproduce the three phases (free-flow, synchronized, and stop-and-go) observed in real traffic. Furthermore we find a good agreement with detailed empirical single-vehicle data in all phases.Cellular automata (CA) models for traffic flow [1] allow for a multitude of new applications. Since their introduction it is possible to simulate large realistic traffic networks using a microscopic model faster than real time [2,3]. But also from a theoretical point of view, these kind of models, which belong to the class of one-dimensional driven lattice gases [4], are of particular interest. Driven lattice gases allow us to study generic non-equilibrium phenomena, e.g. boundary-induced phase transitions [5]. Now, almost ten years after the introduction of the first CA models, several theoretical studies and practical applications have improved the understanding of empirical traffic phenomena (for reviews, see e.g. [6][7][8][9][10][11]). CA models have proved to be a realistic description of vehicular traffic, in particular in dense networks [2,3].Already the first CA model of Nagel and Schreckenberg [1] (hereafter cited as NaSch model) leads to a quite realistic flow-density relation (fundamental diagram). Furthermore, spontaneous jam formation has been observed. Thereby the NaSch model is a minimal model in the sense that any further simplification of the model leads to an unrealistic behaviour. In the last few years extended CA models have been proposed which are able to reproduce even more subtle effects, e.g. meta-stable states of highway traffic [12]. Unfortunately, the comparison of simulation results with empirical data on a microscopic level is not that satisfactory. So far the existing models fail to reproduce the microscopic structure observed in measurements of real traffic [13]. But in highway traffic in particular, a correct representation of the microscopic details is necessary because they largely determine the stability of a traffic state and therefore also the collective behaviour of the system. From our point of view a realistic traffic model should satisfy the following criteria. First it should reproduce, on a microscopic level, empirical data sets, and second, a very efficient implementation of the model for large-scale computer simulations should be possible. Efficient implementations are facilitated if a discrete model with local interactions is used.Our approach is based on a driving strategy which comprises four aspects:(i) At large distances the cars move (apart from fluctuations) with their desired velocity v max .(ii) At intermediate distances drivers...

Based on a detailed microscopic test scenario motivated by recent empirical studies of singlevehicle data, several cellular automaton models for traffic flow are compared. We find three levels of agreement with the empirical data: 1) models that do not reproduce even qualitatively the most important empirical observations, 2) models that are on a macroscopic level in reasonable agreement with the empirics, and 3) models that reproduce the empirical data on a microscopic level as well. Our results are not only relevant for applications, but also shed new light on the relevant interactions in traffic flow.

It is shown that the desire for smooth and comfortable driving is directly responsible for the occurrence of complex spatio-temporal structures ("synchronized traffic") in highway traffic. This desire goes beyond the avoidance of accidents which so far has been the main focus of microscopic modeling and which is mainly responsible for the other two phases observed empirically, free flow and wide moving jams. These features have been incorporated into a microscopic model based on stochastic cellular automata and the results of computer simulations are compared with empirical data. The simple structure of the model allows for very fast implementations of realistic networks. The level of agreement with the empirical findings opens new perspectives for reliable traffic forecasts.

For single-lane traffic models it is well known that particle disorder leads to platoon formation at low densities. Here we discuss the effect of slow cars in two-lane systems. Surprisingly, even a small number of slow cars can initiate the formation of platoons at low densities. The robustness of this phenomenon is investigated for different variants of the lane-changing rules as well as for different variants on the single-lane dynamics. It is shown that anticipation of drivers reduces the influence of slow cars drastically.Comment: RevTeX, 22 eps-figures included, 10 page

A two-lane extension of a recently proposed cellular automaton model for traffic flow is discussed. The analysis focuses on the reproduction of the lane usage inversion and the density dependence of the number of lane changes. It is shown that the single-lane dynamics can be extended to the two-lane case without changing the basic properties of the model which are known to be in good agreement with empirical single-vehicle data. Therefore it is possible to reproduce various empirically observed two-lane phenomena, like the synchronization of the lanes, without fine-tuning of the model parameters.