Optimal vehicle capacity and dispatching policy considering crowding in public bus transit services

This study investigates the often overlooked impact of on-board crowding on operational and user costs in public transit systems, specifically within a many-to-many bus transit line with varying demand patterns. While previous research has used mathematical programming for similar problems, this paper employs analytical approaches to offer deeper insights and address fundamental questions. First, we propose an approach to determine optimal bus capacities, factoring in in-vehicle crowding costs, assuming a fixed headway. Second, we explore the optimal dispatching policy for buses with fixed capacities, considering crowding costs. Third, we optimize both headway and vehicle capacity simultaneously. Our findings reveal that optimal vehicle capacity correlates with average passenger trip length and the square root of crowding-discomfort costs, especially when crowding increases linearly with load factor. When both headway and capacity are variable, smaller vehicles with shorter headways are favored, particularly in moderate-demand scenarios, especially with cost-effective staff models like autonomous fleets.