Shortest path problem of uncertain random network

The shortest path problem is one of the most fundamental problems in network optimization. This paper is concerned with shortest path problems in non-deterministic environment, in which some arcs have stochastic lengths and meanwhile some have uncertain lengths. In order to deal with path problems in such network, this paper introduces the chance theory and uses uncertain random variable to describe non-deterministic lengths, based on which two types of shortest path in uncertain random networks are defined. To obtain the shortest paths, an algorithm derived from the Dijkstra Algorithm is proposed. Finally, numerical examples are given to illustrate the effectiveness of the algorithms.