Keywords: traffic flow, cellular automaton, traffic light, signal strategy, critical density, green wave.

In this paper, a cellular automaton model is proposed to describe the urban traffic flow with the consideration of traffic light effects and driving behaviour. Unlike most models used to describe evolution of traffic flow controlled by traffic lights [1,2,3], in which the traffic lights only affect the leading vehicle and have no direct influence on others, the anticipation effect is taken into account in this new cellular automaton model, which reflects drivers' behaviour facing the changing traffic lights in detail and considers the influence of varying traffic lights on all vehicles in this proposed model.

Based on this model, the characteristics of the urban traffic flow on a single-lane road are studied under three different strategies, i.e., the synchronized, the green wave and the random strategies. The numerical simulation is performed and the results under different strategies are compared with each other. The fundamental diagrams and time-space patterns of the traffic flows are provided for these strategies respectively. It is found that the saturation of flow exists in a density range and the dynamical transition to the congested flow appears when the vehicle density is higher than a critical level. The simulation results indicate that the saturated flow does not depend on the cycle time and the strategies of the traffic light control, while the critical density varies with the cycle time and the strategies. The green wave strategy is proved to be the most effective one among the three strategies, which would allow a cluster of vehicles to pass through the intersections without interruption. In order to generate green wave effects, it is suggested that the adjacent traffic lights should have appropriate delays in urban traffic. When the density increased furthermore, a traffic jam is inevitable and there is no need to adjust the traffic strategy to improve the traffic flow and reduce the emission.

1

K. Nagel and M. Schreckenberg, "A cellular automaton model for freeway traffic", J. Phys. I France, 2, 2221-2233, 1992. doi:10.1051/jp1:1992277

2

D. Chowdhury and A. Schadschneider, "Self-organization of traffic jams in cities: Effects of stochastic dynamics and signal periods", Phys. Rev. E, 59, R1311-R1314, 1999. doi:10.1103/PhysRevE.59.R1311

3

E. Brockfeld, R. Barlovic, A. Schadschneider, and M. Schreckenberg, "Optimizing traffic lights in a cellular automaton model for city traffic", Phys. Rev. E, 64, 056132:1-12, 2001. doi:10.1103/PhysRevE.64.056132

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