Emergence of bistable states and phase diagrams of traffic flow at an unsignalized intersection

• The phase diagrams with complex topology structure are constructed.
• There exist bistable phases in some regions of the phase diagrams.
• The flow formulas in all regions in the phase diagram are derived.
• The deterministic Nagel and Schreckenberg model is adopted.
• Parallel update rules and yield dynamics are employed.

This paper studies phase diagrams of traffic states induced by the bottleneck of an unsignalized intersection which consists of two perpendicular one-lane roads. Parallel updates rules are employed for both roads. At the crossing point, in order to avoid colliding, the consideration of yield dynamics may be suitable herein. Different from previous studies, the deterministic Nagel and Schreckenberg model is adopted in this work. Based on theoretical analysis and computer simulations, the phase diagrams of traffic flow have been presented and the flow formulas in all regions have been derived in the phase diagram. The results of theoretical analysis are in good agreement with computer simulation ones. One finds an interesting phenomenon: there exist bistable states in some regions of the phase diagrams.