Tractable Pathfinding for the Stochastic On-Time Arrival Problem

Abstract

Abstract. We present a new and more efficient technique for computing the route that maximizes the probability of on-time arrival in stochastic networks, also known as the path-based stochastic on-time arrival (SOTA) problem. Our primary contribution is a pathfinding algorithm that uses the solution to the policy-based SOTA problem-which is of pseudopolynomial-time complexity in the time budget of the journey-as a search heuristic for the optimal path. In particular, we show that this heuristic can be exceptionally efficient in practice, effectively making it possible to solve the path-based SOTA problem as quickly as the policybased SOTA problem. Our secondary contribution is the extension of policy-based preprocessing to path-based preprocessing for the SOTA problem. In the process, we also introduce Arc-Potentials, a more efficient generalization of Stochastic Arc-Flags that can be used for both policy-and path-based SOTA. After developing the pathfinding and preprocessing algorithms, we evaluate their performance on two different real-world networks. To the best of our knowledge, these techniques provide the most efficient computation strategy for the path-based SOTA problem for general probability distributions, both with and without preprocessing.

A New Formulation of The Shortest Path Problem with On-Time Arrival Reliability

“…Uncertain Road Network Modeling: The edge-centric uncertain road network model has been applied extensively in stochastic routing [4], [5], [7]- [16]. In the edge-centric model, each edge is associated with an uncertain travel time and different edges' uncertain travel times are independent.…”

“…Stochastic shortest path finding: There exist two categories of stochastic shortest path finding-the Shortest path with on-time arrival reliability problem (SPOTAR) and the Stochastic on time arrival problem (SOTA) [4], [5]. SPOTAR identifies an a-priori path that maximizes the on time arrival reliability of reaching a destination within a pre-defined time budget.…”

“…We maintain an uncertain travel time for each edge. The edge-centric model is considered as the de-facto model in stochastic routing [4]- [9], [16].…”

“…Although the SPOTAR problem has been studied in the literature [4], [5], they all consider a classical uncertain road network modeling, where uncertain travel times are assigned to only edges, and the uncertain travel times on different edges are independent. We call the classical model the edge-centric model.…”

Stochastic on-time arrival problem in transit networks

“…To further reduce the computation time, Sabran et al (2014) modify two deterministic shortest path preprocessing techniques: reach (Gutman 2004) and arc-flags (Bauer andDelling 2009, Hilger et al 2009), and apply them to the SOTA problem. Other studies (Nikolova et al 2006, Nie and Wu 2009, Parmentier and Meunier 2014, Niknami and Samaranayake 2016) explore computationally efficient solution strategies for providing reliability guarantees in stochastic shortest path problems, where a fixed route (as opposed to a policy) is desired.…”