Joint optimization of scheduling and capacity for mixed traffic with autonomous and human-driven buses: A dynamic programming approach

Document Type

Journal Article

Publication Date


Subject Area

mode - bus, economics - operating costs, operations - capacity, operations - scheduling, ridership - behaviour, ridership - demand, planning - service improvement, planning - methods


schedule, autonomous bus, capacity, operating cost, passenger demand


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.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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