Strategic Optimization of Bus Systems with Stochastic Ridership

In global metropolitan areas, public transport benefits from bus systems. Bus design widely applies theoretical models, which typically assume static ridership. However, ridership randomness exists, and lack of attention to it might lead to wrong design decisions. Moving beyond static ridership, we extend the traditional single-line model with stochastic ridership. Further, to optimize the bus system under various ridership randomness, we introduce a hybrid model that combines conventional buses (CBs) and flexible buses (FBs). In both models, we apply a continuous approximation approach and find that: 1) Bus capacity increases with ridership randomness in the extended single-line model; 2) The hybrid model exhibits a binary state: either CBs serve the ridership with rejections under low ridership randomness, or CBs serve the majority while FBs serve the minority with rejections under high ridership randomness. Our findings establish a link between bus system design and ridership randomness, contributing to a more adaptive and efficient public transport framework.