Towards a realistic microscopic description of highway traffic

Abstract

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...

Cellular automata approach to three-phase traffic theory

“…The original NagelSchreckenberg model (NaSch model) as well as all subsequent modifications and refinements of it [22,23,36,37,38,39] belong to the fundamental diagram approach ( Fig. 1 (a)).…”

“…Different explanations of these empirical findings have been proposed by various groups in the last years, but so far they remain controversial (see e.g., [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] and the excellent review by Helbing [1]). …”

Modelling vehicular interactions for heterogeneous traffic flow using cellular automata with position preference

“…This improvement in the model significantly changes the outcome of simulation as shown in subsequent sections. Also, in CA models, lane change rules can be symmetric or asymmetric with respect to lanes or vehicle type [9]. In symmetric models, both lanes are treated equally or all vehicle types have equal probability of acquiring a position on cell lattice.…”

“…The longitudinal movement rules used in the study are similar to those proposed by Mallikarjuna and Rao [12] for heterogeneous conditions but with some modifications. In this model, originally based on Knospe's brake light model [9], the subject vehicle would react to the 'brake light status' of the leader vehicle. If the gap in front is less than the interaction headway, it would adjust itself based on the speed of the leader vehicle.…”

“…Due to the discreteness of this model, it provides an opportunity to simulate large-scale real time microscopic phenomena like platoon formation and the capacity drop at transitions between free and congested flow. Later, others [8][9][10] contributed to the development of the model by adding more rule sets to increase its capability to replicate traffic features seen in multilane and heterogeneous traffic. Matthew et al [11] proposed a modified cell size, randomisation rule and lane-changing rule of CA model for heterogeneous conditions.…”