Synthesis of single-product networks

mode. It is typical of this mode that at each instant information exchange takes place pray between two ne~%vork nodes. These nodes can be commutated with each other only for a relatively short time since another pair must exchange information in the next time interval. ~'hile reducing the effectiveness of information exchange between two nodes in genera[, the time sharing mode makes it possible to use in the network communication channels which are more economical (have lower transmission capacity) than in the mode in which any node can exchange information with any other mode at any instant to which corresponds the multiproduct network mode[. Here we consider the synthesis of an optima[ single-product network and certain algorithms are proposed for the design of suboptimal networks. Problem Formulation. Assume that the desired network has N nodes A i and that there are given N(N- i)/ 2 numbers Rij which represent the demands on the magnitude of flows between A i and Aj (i = I, N; j = I, N). We have to find the network topology and transmission capacities Bij of the communication channels (i, j) such that flows can be transmitted between the nodes A i and Aj, and that the total transmission capacity of the channels is minimal: