Phase transition at an on-ramp in the Nagel–Schreckenberg traffic flow model

Recent empirical observations show that traffic flow is related to various phase transitions, especially at bottlenecks. This paper studies traffic flow induced by an on-ramp in the Nagel–Schreckenberg model. It is shown that when considering the situation that vehicles on main road and on-ramp interact in a relatively long road section, first-order phase transition from free flow to congested flow occurs. In contrast, it is second-order phase transition from free flow to congested flow if the interaction road section is short. We have investigated the reason why first-order phase transition occurs. The interaction of vehicles may be viewed as a kind of cooperation behavior of drivers. Therefore, our results indicate that in future traffic flow research, investigation on cooperation behavior should be carried out.