Effect of slow-to-start in the extended BML model with four-directional traffic

In this paper, an extended Biham-Middleton-Levine (BML) model is proposed to simulate complex characteristics of four-directional traffic flow by considering the effect of slow-to-start. The simulation results show that the system does not exhibit a sharp transition from moving phase to jamming phase, which is consistent with the results of the latest studies about the original BML model. Differently from the structure geometric patterns in previous studies, a new phase separation phenomenon, i.e., the coexistence of multiple free flow stripes and multi-local jams, can be observed. The formation mechanisms of typical dynamic patterns are also explored. Furthermore, a mean field analysis for the maximum velocity in the moving phase is obtained, which is in good accordance with simulation results. In addition, an interesting feature is found that this new coexistence phenomenon of two phases is determined only by the effect of slow-to-start and is completely independent of traffic light (only considering red light and green light) period.