The probability of the stochastic shortest path length is defined as the arrival probability to a given sink node from a given source node. Discrete distribution probabilities of arcs existence are known and the arrival probability is computed by establishment of a discrete time Markov chain stochastic process. Two conditions at any node are assumed toward the sink node, departing from current state to a new state when a larger labeled node is visited, or waiting in the current state with expecting better conditions. The uncertainty of the network topology causes several unstable connections between nodes, a network has unstable topology if there are some facilities in the network but it is not possible to use them. However, the original network topology determines possible connections between pairs of nodes. Numerical results show efficiency of proposed method to obtain the arrival probability, the limiting probability and the critical node in the networks with stochastic topologies.
