The statistical information according to the leaving nodes at the current node is available in an online manner, where the arc costs are assumed to be online parameters of a network. Some online decision criterions are considered and their competitive analyses are presented. Two formulas of the online expected stochastic shortest path lengths are computed with respect to the distribution probabilities of the arc costs and the path lengths. Then, they are applied as online optimality indices in the selection processes of the proposed online algorithms. So, the competitive analyses of the methods are presented. However, cycles in the networks hit the competitive ratio and the formulas will be equivalent in the large cyclic networks.
