A shortest path problem in a stochastic network with exponential travel time

摘要

A shortest path problem in a stochastic network is studied in this paper. Assuming travel times between the nodes in the network as exponential random variables, a chance constrained programming formulation of the problem is obtained. Then the deterministic separable convex programming formulation of the problem is derived by using a proposed upper bound technique. The expected length and probability of the shortest path are obtained by solving the converted problem. Finally, the results obtained from the proposed approach are compared with Kulkarni's (1986) method as well as Peer and Sharma's (2007) method for a network of a practical application under consideration with exponential random variables.