Effect of Spatial Distribution of Traffic Lights to the Traffic Flow Behaviour

We present some preliminary results of a study that extends the work by D-W Huang and W-N Huang [1]. They proposed a model to describe the traffic from suburb to downtown during the rush hours. The model is a cellular automaton which consists of a 1D open lattice with regularly spaced traffic lights and parking lots and vehicles that enter the lattice at one end and left it at a parking lot or at the other end. The vehicles evolve following the single lane Nagel and Schreckenberg local dynamics [2]. We investigate how changes in traffic lights spacing affects the traffic behaviour. The motivation was the fact that the Nagel and Schreckenberg dynamics exhibits a critical state as the density of vehicles approaches a determined value [3]. In that state, the stream of vehicles self-organizes into a fractal structure that reflects a power law distribution of jam sizes. The initial results indicate that a power law distribution of the traffic lights spacing tends to increase the stream flux no matter the value of traffic lights period and the inflow rate. Nevertheless, in contrast to the regularly arranged traffic lights model, a power law distribution spacing caused a high sensitivity of the stream flux to the inflow rate.\\

[1] Huang, D-W.; Huang, W-N. A model for city traffic in rush hours. Chinese Journal of Physics, Taipei, v. 45, n. 6-II, p. 708-715, dez. 2007.\\

[2] Nagel, K.; Schreckenberg, M. A cellular automaton model for freeway traffic. Journal de Physique I France, Paris, v. 2, n. 12, p. 2221-2229, dez. 1992.\\

[3] Nagel, K.; Paczuski, M. Emergent traffic jams. Physical Review E, New York, v. 51, n. 4, p. 2909-2918, abr. 1995.\\