It is a common practice for transit lines with fluctuating passenger demands to use demand-driven bus scheduling to reduce passenger waiting time and avoid bus overcrowding. However, current literature on the demand-driven bus scheduling generally assumes fixed bus capacity and exclusively optimizes bus dispatch headways. With the advent of connected and autonomous vehicle technology and the introduction of autonomous minibus/shuttle, the joint design of bus capacity and dispatch headway holds promises to further improving the system efficiency while reducing operating and passenger costs. This paper formulates this problem as an integer nonlinear programming model for transit systems operating with mixed human-driven and autonomous buses. In such mixed operating environment, the model simultaneously considers: (1) dynamic capacity design of autonomous bus, i.e., autonomous buses with varying capacity can be obtained by assembling and/or dissembling multiple autonomous minibuses; (2) trajectory control of autonomous bus, i.e., autonomous bus can dynamically adjust its running time as a function of its forward and backward headways; and (3) stop-level passenger boarding and alighting behavior. The objective of the model is designed to balance the trade-off between the operating costs of dispatching different types of bus and the costs of increased passenger waiting time due to inadequate bus dispatching. The model is solved using a dynamic programming approach. We show that the proposed model is effective in reducing passenger waiting time and total operating cost. Sensitivity analysis is further conducted to explore the impact of miscellaneous factors on optimal dispatching decisions, such as penetration rate of autonomous bus, bus running time variation, and passenger demand level.

对于乘客需求波动的公交线路，使用按需求驱动的公交时刻表来减少乘客的等待时间并避免公交拥挤是一种常见的做法。但是，当前有关需求驱动的公交车调度的文献通常假定公交车容量固定，并且专门优化公交车的调度进度。随着联网和自动驾驶汽车技术的出现以及自动小巴/班车的引入，公交车容量和调度进度的联合设计有望进一步提高系统效率，同时降低运营和乘客成本。本文将这个问题表述为用于混合人类驱动和自主公交的公交系统的整数非线性规划模型。在这种混合操作环境中，模型同时考虑：（1）自主公交的动态容量设计，即通过组装和/或拆卸多条自主小客车，可以获得容量可变的自主公交；（2）自主公交的轨迹控制，即自主公交可以根据其前进和后退的车头动态地调整其运行时间；（3）站级旅客的上下车行为。该模型的目的是在分配不同类型公交车的运营成本与由于公交车分配不足而增加的乘客等待时间的成本之间取得平衡。该模型使用动态编程方法求解。我们表明，提出的模型可有效减少乘客的等候时间和总运营成本。