A predictive headway-based bus-holding strategy with dynamic control point selection: a cooperative game theory approach

Bus holding is a widely used control method to regularize bus headways and reduce bus bunching. The method works in such a way by delaying buses at control points if their departure times or headways deviate from the planned ones. However, it may result in reduced bus commercial speeds and increased passenger onboard travel time. To avoid this problem, researchers have suggested that control points be spaced cautiously along the route such that only a few are needed. This study proposes a predictive headway-based bus holding strategy with dynamic control point importance ranking and selection based on the cooperative game theory. The framework considers not only individual control points’ impact but also the collective group control effects. Specifically, the proposed framework consists of two components: a performance model and a cooperative game model. The performance model predicts headway performances of all running buses when different control point combinations are in effect. Dynamic bus running times and passenger demands are reflected in the model. Then, these headway performances are passed to the cooperative game model with control points being players and improvements in headway performances compared with that under no holding control being the utility function. The game is solved by Myerson value, a concept that extends Shapley value used for the normal cooperative game and considers the cooperation structure and potential worth of coalitions. We use Myerson value to rank the importance of control points on regularizing headways, as it measures the average marginal utility contribution of a control point to all possible coalitions that exclude that point. We prove that Myerson value lies in the Ω-core of the game and thus satisfies allocation efficiency, individual and coalition rationality. The proposed framework is applied to target headway control and two-way-looking self-equalizing headway control. Simulation results show that the framework can significantly reduce passenger waiting time and bus headway variation.