Stochastic networks

The authors consider here a state and action universe, assuming that the effect of any action which may be launched from a given state is not completely determined and depends on some probability distribution. Then, when some initial state x0 and some final state y0 are given, they try to determine a strategy which allows to go from x0 to y0 the fastest (in a probabilistic sense) or the most surely possible. The authors provide a mathematical framework for this problem through the concept of stochastic network and prove that the classical shortest path algorithms (Dijkstra, Dantzig, Bellman, A*) can be rewritten in this context.