Improving Bus Operations through Integrated Dynamic Holding Control and Schedule Optimization

Bus bunching can lead to unreliable bus services if not controlled properly. Passengers will suffer from the uncertainty of travel time and the excessive waiting time. Existing dynamic holding strategies to address bus bunching have two major limitations. First, existing models often rely on large slack time to ensure the validity of the underlying model. Such large slack time can significantly reduce the bus operation efficiency by increasing the overall route travel times. Second, the existing holding strategies rarely consider the impact on the schedule planning. Undesirable results such as bus overloading issues arise when the bus fleet size is limited. This paper explores analytically the relationship between the slack time and the effect of holding control. The optimal slack time determined based on the derived relationship is found to be ten times smaller than in previous models based on numerical simulation results. An optimization model is developed with passenger-orient objective function in terms of travel cost and constraints such as fleet size limit, layover time at terminals, and other schedule planning factors. The optimal choice of control stops, control parameters, and slack time can be achieved by solving the optimization. The proposed model is validated with a case study established based on field data collected from Chengdu, China. The numerical simulation uses the field passenger demand, bus average travel time, travel time variance of road segments, and signal timings. Results show that the proposed model significantly reduce passengers average travel time compared with existing methods.