Influence of synchronized traffic light on the states of bus operating system

•The paper investigates the bus operating system under the control of traffic light.•The analytical equations for the critical passenger arrival rate and average velocity agree with the simulation results well.•The average velocity in the free-flow and bunching state oscillates with the increase of T.•The exact condition for the two states called lag and catch (LC) and variant LC state is presented.•A monotonic decreasing curve instead of oscillation was observed under nonsynchronous traffic light.

This paper investigates the bus operating system under the synchronized traffic light control strategies with cellular automation. Besides the insufficient capacity, the sufficient capacity is observed in the free-flow state of the phase diagram. An analytical equation for the critical passenger arrival rate is developed. The average velocity of free-flow and bunching state oscillates with the increase of signal period. With the increase of the ratio of green phase time, the oscillation amplitude of average velocity decreases while the oscillation frequency increases. At the same time, the critical passenger arrival rate and each region of the phase diagram also vary synchronously. An analytical equation for the average velocity is developed, which shows good agreement with the simulation results. Two states called lag and catch (LC) and variant LC state are observed. The exact condition for the LC state is presented. Finally, a monotonic decreasing curve instead of oscillation was observed under nonsynchronous traffic light. The results indicate that a proper signal period could improve the efficiency of bus system.