مرکز منطقه ای اطلاع رساني علوم و فناوري - Dynamic Programming of Optimum Flows in Lossy Communication Nets

Abstract :

This paper deals with assignments of optimum flows in lossy communication nets. In a lossy communication net, each edge $e$ has an edge efficiency factor $\\alpha _e (0 \\leq \\alpha _e \\leq 1)$ as well as an edge capacity $C_e$ . If edge $e$ is an edge from node $x$ to node $y$ , then the flow $\\psi(e, x)$ entering into node $x$ is not only limited by the edge capacity $(0 \\leq \\psi(e, x) \\leq C_e)$ but also suffers a loss of $(1 - \\alpha _e) \\cdot \\psi(e, x)$ in passing through $e$ , consequently, $\\alpha _e \\cdot \\psi (e, x)$ emerges from $e$ at node $y$ . A flow $\\psi$ with the sending flow value $\\hat{t}$ at the source and the receiving flow value $\\underbrace {t}$ at the sink is said to be optimum if there is no flow which has less sending flow value value than $t$ while having the same receiving value $\\underbrace {t}$ . 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.