Tractable Pathfinding for the Stochastic On-Time Arrival Problem

TL;DR

This paper introduces a new efficient pathfinding algorithm for the stochastic on-time arrival problem, significantly improving computation speed by leveraging policy-based solutions as heuristics and extending preprocessing techniques.

Contribution

The paper presents a novel pathfinding algorithm that uses policy-based solutions as heuristics and extends preprocessing methods for the SOTA problem, enhancing efficiency.

Findings

The new algorithm solves path-based SOTA as quickly as policy-based SOTA.

Extension of policy-based preprocessing to path-based preprocessing.

Introduction of Arc-Potentials for efficient SOTA computation.

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 pseudo-polynomial-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 policy-based 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.