Dynamic Programming: Stochastic Shortest Path Problems

The shortest path problem is considered to be one of the classical and most important combinatorial optimization problems. Given a directed graph and a length α _ij for each arc (i, j), the problem is to find a path of minimum length that leads from any node i to a node t, called the destination node. So, for each node i, we need to optimally identify a successor node u(i) so as to reach the destination at the minimum sum of arc lengths over all paths that start at i and terminate at t. Of particular relevance is, in the area of distributed computation, the problem of data routing within a computer communication network. In such a case, the cost associated with a particular link (i, j) is related to an average delay. The stochastic shortest path problem is a generalization whereby for each node i we must select a probability distribution over all possible successor nodes j out of a given set of probability distributions p _ij (u), parameterized by a control u ∈ U(i). Clearly, the path...