Designing robust schedule coordination scheme for transit networks with safety control margins

We propose a robust schedule coordination scheme which combines timetable planning with a semi-flexible departure delayed control strategy in case of disruptions. The flexibility is provided by allowing holding for the late incoming bus within a safety control margin (SCM). In this way, the stochastic travel time is addressed by the integration of real-time control and slacks at the planning phase. The schedule coordination problem then jointly optimises the planning headways and slack times in the timetable subject to SCM. Analytical formulations of cost functions are derived for three types of operating modes: uncoordinated operation, departure punctual control and departure delayed control. The problem is formulated as a stochastic mixed integer programming model and solved by a branch-and-bound algorithm. Numerical results provide an insight into the interaction between SCM and slack times, and demonstrate that the proposed model leads to cost saving and higher efficiency when SCM is considered. Compared to the conventional operating modes, the proposed method also presents advantages in transfer reliability and robustness to delay and demand variation.