Dynamic Programming of Optimum Flows in Lossy Communication Nets

This paper deals with assignments of optimum flows in lossy communication nets. In a lossy communication net, each edge has an edge efficiency factor as well as an edge capacity . If edge is an edge from node to node , then the flow entering into node is not only limited by the edge capacity but also suffers a loss of in passing through , consequently, emerges from at node . A flow with the sending flow value at the source and the receiving flow value at the sink is said to be optimum if there is no flow which has less sending flow value value than while having the same receiving value . Necessary and sufficient conditions are described for the optimality of flows in Theorem 1 and Theorem 2. Based on these characterizations, dynamic programming of optimum flows in a lossy communication net is devised and demonstrated by an example.