Stochastic on-time arrival problem in transit networks

TL;DR

This paper addresses the stochastic on-time arrival problem in transit networks by developing a dynamic programming approach that accounts for stochastic travel and waiting times, incorporating dominance techniques to improve computational efficiency.

Contribution

It introduces a network structure suitable for online decision-making and proposes dominance-based methods to significantly reduce computation time in solving the problem.

Findings

Dominance techniques reduce computation time by up to 90%.

The method is effective on both synthetic and real transit networks.

The approach handles stochastic travel and waiting times in transit planning.

Abstract

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.