Stochastic on-time arrival problem in transit networks

•We address the stochastic on-time arrival problem (SOTA) in transit networks, where the travel time and waiting time for transit services are both stochastic.•We design a dynamic programming based solution approach with time complexity that is pseudo-polynomial in the number of transit stations and the travel time budget.•We define the notation of transit line dominance, and provide techniques to both identify such dominance and exploit it to reduce computation time.•Numerical experiments show a computation time reduction of up to 90%.•Extensive numerical experiments are conducted on both a synthetic network and the Chicago transit (bus) network. This article considers the stochastic on-time arrival problem in transit networks where both the travel time and the waiting time for transit services are stochastic. A specific challenge of this problem is the combinatorial solution space due to the unknown ordering of transit line arrivals. We propose a network structure appropriate to the online decision-making of a passenger, including boarding, waiting and transferring. In this framework, we design a dynamic programming algorithm that is pseudo-polynomial in the number of transit stations and travel time budget, and exponential in the number of transit lines at a station, which is a small number in practice. To reduce the search space, we propose a definition of transit line dominance, and techniques to identify dominance, which decrease the computation time by up to 90% in numerical experiments. Extensive numerical experiments are conducted on both a synthetic network and the Chicago transit network.