基于合作博弈的公交滞站点优化模型

公交滞站控制是防治公交串车的常用方法. 现有研究主要集中于公交滞站时间的优化，很少关注滞站点优化问题. 本文提出一种基于合作博弈的公交滞站点优化模型. 根据系统当前状态，模型首先预测当控制不同滞站点组合时该滞站点组合对公交串车率的改进；其次，以滞站点为博弈人，以滞站点组合及其对公交串车率的改进量为效用函数，构建合作博弈，分析滞站点的单独和联合控制效果，并用Shapley 值刻画滞站点的相对重要性. 通过在最有效的滞站点实施滞站控制，能够有效防治公交串车. 最后，通过仿真实验对滞站点的数量和位置的确定进行说明，模型能有效降低公交车头时距波动，减少公交串车率，最终减少乘客平均候车时间.

A Cooperative Game-based Holding-point Optimization Model for Bus Bunching

Holding control is a commonly used method for bus bunching prevention. Current study generally focuses on holding time optimization，yet with a little effort being put on holding-point optimization. This study proposes a cooperative game-based holding-point optimization model for bus bunching prevention. First，based on the current system states，the model predicts the improvement in the share of bus bunching when different holding point combinations are in effect. Then，the model constructs a cooperative game to analyze individual and collective control effects between holding points. In the game，holding points are regarded as players，while their collective control effects form the utility function. The cooperative game is solved using Shapley value，which represents the importance of holding-points in reducing bus bunching in this study. Finally，dynamic simulation experiments are conducted to illustrate the control point optimization process. Simulation results suggest that the model reduces headway variance，bus bunching share and passenger waiting time significantly.