The notorious phenomenon of bus bunching prevailing in uncontrolled bus systems produces irregular headways and downgrades the level of service by increasing passengers’ expected waiting time. Modular autonomous vehicles (MAVs), due to their ability to split and merge en route, have the potential to help both late and early buses recover from schedule deviation while providing continuous service. In this paper, we propose a novel bus bunching alleviation strategy for MAV-aided transit systems. We first consider a soft vehicle capacity constraint and establish a continuum approximation (CA) model (Model I) to capture the system dynamics intertwined with the MAV splitting and merging operations, and then establish an infinite-horizon stochastic optimization model to determine the optimal splitting and merging strategy. To capture the reality that passengers may fail to board an overcrowded bus, we propose a second model (Model II) by extending Model I to accommodate a hard vehicle capacity constraint. Based on the characteristics of the problem, we develop a customized deep Q-network (DQN) algorithm with multiple relay buffers and a penalized ruin state applicable for both models to optimize the strategy for each MAV. Numerical results show that the strategy obtained via the DQN algorithm is an effective bunch-proof strategy and has a better performance than the myopic strategy for MAV-aided systems and the two-way-looking strategy for conventional bus systems. Sensitivity analyses are also conducted to examine the effectiveness and benefits of the proposed strategy across different operation scenarios.

中文翻译：

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通过模块化车辆缓解公交车聚集


在不受控制的公交系统中普遍存在的臭名昭著的公交车聚集现象会产生不规则的车距，并通过增加乘客的预期等待时间来降低服务水平。模块化自动驾驶汽车 （MAV） 由于能够在途中拆分和合并，因此有可能帮助晚点和早点的公交车从时间表偏差中恢复过来，同时提供持续的服务。在本文中，我们提出了一种用于 MAV 辅助交通系统的新型公交车聚集缓解策略。我们首先考虑软车辆容量约束，并建立连续体近似 （CA） 模型（模型 I）来捕捉与 MAV 拆分和合并操作交织在一起的系统动力学，然后建立无限水平随机优化模型来确定最佳拆分和合并策略。为了捕捉乘客可能无法登上过度拥挤的公交车的现实，我们提出了第二种模型（模型 II），通过扩展模型 I 以适应硬性车辆容量限制。根据问题的特点，我们开发了一种定制的深度 Q 网络 （DQN） 算法，该算法具有多个中继缓冲区和适用于两种模型的惩罚废墟状态，以优化每个 MAV 的策略。数值结果表明，通过 DQN 算法获得的策略是一种有效的防束策略，并且比 MAV 辅助系统的短视策略和传统总线系统的双向查找策略具有更好的性能。还进行了敏感性分析，以检查所提出的策略在不同操作场景中的有效性和益处。