The most reliable data path transmission

We examine the problem of transmitting a units of data in the most reliable manner along an (s,t) path of a network N=(V,E,c,d,r,s,t). Each edge of a network is assigned a capacity, a delay and a reliability value. In contrast to the similarly defined shortest path problem, it is shown that for this more complex routing problem the subpaths of an optimal path are not necessarily optimal. However, an optimal polynomial is presented. On acyclic networks with interconnections that operate with the same reliability probability, we present a polynomial time algorithm that computes the best route for each value of σ. This is a very useful precomputation when different amount of data need to be transmitted at different time periods