Continuum Approximation Model for Transit Service Design with Stochastic Demand

Travel demand is commonly predefined as a constant during the planning period in transit service design, but it varies daily with many factors, for example, weather, vacation, and social activity. Under the uncertain demand, the transit system operates in two states, that is, unsaturation and saturation, distinguished by whether or not the capacity of transit vehicle satisfies the possible demand. Thus, we propose a continuum approximation (CA) model for transit service design, including headway and station location, to account for the effects of the stochastic demand via a penalty cost, a service-reliability constraint, and equilibrium. The penalty cost is utilized to describe the saturation state. The service-reliability constraint is applied to ensure the robustness of the transit system. The equilibrium is introduced to allocate the household location where trip demand is generated in a corridor. Furthermore, we build a bilevel framework to find the solutions to the proposed model. In the numerical experiment, the proposed model is applied in the impact analyses of the service-reliability constraint, as well as the sensitivity analyses of the household numbers and value of time. The impact analyses indicate that the transit service design integrated with the effect of housing location choice is necessary under the stochastic demand. The sensitivity analyses show that the number of households and the value of time play a significant role in the performance of transit systems accounting for service reliability. The proposed model and findings serve to improve the design of the transit system under stochastic demand.