Title: Finding shortest path in a combined exponential-gamma probability distribution arc length

Authors: Mohammad Hessam Olya

Addresses: Department of Industrial Engineering, Mazandaran University of Science and Technology, Sardaran 12 Street, Babol, Iran

Abstract: We propose a dynamic programme to find the shortest path in a network having exponential and gamma probability distributions as arc lengths. Two operators of sum and comparison need to be adapted for the proposed dynamic programme. Convolution approach is used to sum any two probability distributions being employed in the dynamic programme. Generally, stochastic shortest path problems are treated using expected values of the arc probabilities, but in the proposed method using distributed observed past data as arc lengths, an integrated value is obtained as the shortest path length. The objective of this paper is to extend the shortest path problem in dynamic and stochastic networks where link travel times are defined as gamma or exponential probability distributions.

Keywords: shortest path; dynamic programming; convolution; arc length; network paths; exponential probability; gamma probability; stochastic networks; dynamic networks.

DOI: 10.1504/IJOR.2014.064020

International Journal of Operational Research, 2014 Vol.21 No.1, pp.25 - 37

Received: 06 Nov 2012
Accepted: 08 Jan 2013

Published online: 30 Aug 2014 *

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