Phase diagrams on an unsignalized intersection for the cases of different maximum velocities of vehicles

Using the cellular automaton traffic flow model, we investigate an unsignalized intersection which consists of two perpendicular one-lane roads. Both the roads cross at a point and the intersecting roads are cyclic. Each vehicle may pass or occupy the intersection where all the vehicles on both roads are not allowed to turn. Different from Ishibashi and Fukui’s studies in which the update is carried out for both roads in turn, the parallel update is proposed and its detailed rules are presented in our model. In this work, the cases of different maximum vehicle velocities on both roads are considered. Based on simulation results and the principle for constructing phase diagrams, phase diagrams are mapped out and their specific flow formulas for all the regions in the phase diagrams are obtained for various vehicle densities, which are seldom done in previous studies. One also finds that the topology of phase diagrams depends on the update rules of eastbound and northbound roads and their maximum velocities of vehicles.