Alleviating bus bunching via modular vehicles

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.