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.
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Notes
- 1.
The target objective can in fact be generalized to utility functions other than the probability of on-time arrival [2] with little effect on our algorithms, but for our purposes, we limit our discussion to this scenario.
- 2.
In this article, we only consider time-invariant travel-time distributions. The problem can be extended to incorporate time-varying distributions as discussed in [3].
- 3.
Parmentier and Meunier [13] have concurrently also developed a similar approach concerning stochastic shortest paths with risk measures.
- 4.
It should be noted that the largest network we consider only has approximately 71,000 edges and is still much smaller than networks used to benchmark deterministic shortest path queries, which can have millions of edges [14].
- 5.
As explained later, there is a potential pitfall that must be avoided when the preprocessed policy is to be used as a heuristic for the path.
- 6.
We assume that at most one edge exists between any pair of nodes in each direction.
- 7.
The bounds of this integral can be slightly tightened through inclusion of the minimum travel times, but this has been omitted for simplicity.
- 8.
Recall that we must have \(\varDelta t \le \min _{(i,j)\in E} \delta _{ij}\), which is \(\approx 1\,\mathrm {s}\) for our networks.
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Niknami, M., Samaranayake, S. (2016). Tractable Pathfinding for the Stochastic On-Time Arrival Problem. In: Goldberg, A., Kulikov, A. (eds) Experimental Algorithms. SEA 2016. Lecture Notes in Computer Science(), vol 9685. Springer, Cham. https://doi.org/10.1007/978-3-319-38851-9_16
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