The online shortest path problem is defined where the whole information of the network is not available. The arc costs are assumed to be online parameters of an acyclic network and decisions should be made while the costs of arcs are not known. The online made decisions cannot be changed or rejected. The permitted nodes and arcs are generally defined according to the departure nodes and arcs of the last traversed node. However, statistical information of the online parameters helps us to improve decision making process. The distribution probabilities of the arc costs and the path lengths are the available statistical information of the network. formula of the expected stochastic online shortest path length is computed according to the distribution probabilities of the arc costs and the path lengths. Then, it is used as the online optimality index in online decision process. So, the competitive analysis of the proposed
