Bus Holding of Electric Buses With Scheduled Charging Times

In high-frequency electric bus services, bus operators strive to increase the service regularity by minimizing the deviation between the planned and actual headways. In this pursue, bus operators apply corrective control strategies, such as bus holding(s) at control point stops. This study expands the traditional headway-based, bus holding models to cater for the planned arrival times of electric buses at the respective charging points. To this end, this study models - for the first time - the bus holding problem for electric buses considering the scheduled charging times in the objective function. Additionally, it introduces an analytic solution that can return an optimal holding decision in real-time. Our approach is tested using realistic data from bus line 15 in Amsterdam demonstrating a significant reduction of charging delays with only a marginal increase of the average passenger waiting times when compared to existing holding strategies. Its closed-form expression is suitable for real-time holding control and can be applied to obtain a reliable solution or perform stochastic optimization in the case of travel time uncertainty.