Analytical modeling of a stop-less modular bus line: Optimization, feasibility, and economies of scale

Abstract

Conventional bus services often struggle with inefficiencies including prolonged dwell times at heavily used stops, especially for through passengers. A stop-less autonomous modular bus service (SLAM) has been proposed to reduce dwell times by decoupling the front pod to serve stops and then coupling it to the next bus. However, the optimal service design and feasibility region remain underexplored, despite their importance for planning and deployment. We propose an analytical optimization model that characterizes the optimal design, feasibility conditions, and sources of scale economies. Three novel constraints distinguish SLAM from conventional bus services: (i) a minimum headway to ensure sufficient time for decoupling, alighting, boarding, and coupling operations, (ii) a maximum headway to guarantee all passengers arriving within a headway fit in the standby pod, and (iii) a minimum bus length constraint, requiring at least two pods per bus to run in a SLAM manner. As ridership grows, the optimal design evolves through several regimes, in which headway constraints alternate between slack and binding states, while capacity constraints shift from one active form to another. Our analysis indicates that, compared with conventional services, SLAM is most suitable at intermediate demand levels: at low demand, the fixed costs of standby pods and the minimum two-pod configuration outweigh the time-saving benefits, whereas at high demand, non-stopping operation becomes infeasible. We further decompose the sources of scale economies into four components: the Mohring effect, through-capacity economies, boarding-capacity economies, and standby-pod costs, identifying under which conditions each of them is present. The numerical results validate the theoretical analysis.