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 the lengths of some arcs have stochastic characteristics and meanwhile some have uncertain characteristics. In order to investigate paths in these networks, this paper introduces the chance distribution of minimum length from source node to destination node, based on which the shortest path of uncertain random networks is defined. To obtain the chance distribution of minimum length, an algorithm derived from the Dijkstra Algorithm is proposed. It also designs an algorithm to find the shortest path in uncertain random networks. Finally, numerical examples are given to illustrate the effectiveness of the algorithms.