Dynamic Multiline Vehicle Dispatching Strategy in Transit Operations

Providing regularity in buses' operation in high-frequency services is essential to offer a good quality of service to users. If buses are not dispatched at regular headways from the terminal, headway irregularity will gradually increase along the line. In this work, we study a vehicle dispatching problem in which multiple lines start their operations from a common terminal where buses can interchange between lines. The model simultaneously decides the ideal dispatching headway for each line and assigns the following arriving buses to the terminal its line to operate and its corresponding dispatching time. The objective is to minimize the dispatching interval's deviation from an ideal headway that is dynamically updated based on the system's status. We formulate our problem as a Mixed-integer quadratic problem and adopt a rolling horizon policy to cope with the dynamic and stochastic environment of public transit systems. We prove that a bus assignment that satisfies the FIFO discipline is an optimal solution for the proposed problem. We evaluate our model in a simulation environment under different operational conditions and study the incremental benefits of allowing different flexibility schemes. Our results show that a full flexibility scheme where buses can freely interchange between lines reduces the coefficient of variation of dispatch headways and improves frequency compliance by nearly 20% when compared with the case where buses are restricted to operate in a single line. It also outperforms a myopic heuristic that adopts a a priori target headway. Computational times are compatible with real-time applications.