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On the shortest alpha-reliable path problem

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Akhavan-Tabatabaei, Raha (2021) On the shortest alpha-reliable path problem. Top, 29 (1). pp. 287-318. ISSN 1134-5764 (Print) 1863-8279 (Online)

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Official URL: http://dx.doi.org/10.1007/s11750-021-00592-3

Abstract

In this variant of the constrained shortest path problem, the time of traversing an arc is given by a non-negative continuous random variable. The problem is to find a minimum cost path from an origin to a destination, ensuring that the probability of reaching the destination within a time limit meets a certain reliability threshold. To solve this problem, we extend the pulse algorithm, a solution framework for short- est path problems with side constraints. To allow arbitrary non-negative continuous travel-time distributions, we model the random variables of the travel times using Phase-type distributions and Monte Carlo simulation. We conducted a set of experi- ments over small- and medium-size stochastic transportation networks with and without spatially-correlated travel times. As an alternative to handling correlations, we present a scenario-based approach in which the distributions of the arc travel times are conditioned to a given scenario (e.g., variable weather conditions). Our methodology and experiments highlight the relevance of considering on-time arrival probabilities and correlations when solving shortest path problems over stochastic transportation networks.

Item Type:Article
Uncontrolled Keywords:constrained shortest path problem, pulse algorithm, stochastic shortest path, phase-type distributions, spatial correlation, chance constraints
Subjects:Q Science > QA Mathematics > QA273-280 Probabilities. Mathematical statistics
ID Code:41739
Deposited By:Raha Tabatabaei
Deposited On:22 Aug 2021 17:04
Last Modified:22 Aug 2021 17:04

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