Application of Norton's theorem on queueing networks with finite capacities

Abstract

A method is developed which allows the application of Norton's theorem on queuing networks with finite capacities. A node is arbitrarily selected and the subnetwork containing all remaining nodes is replaced by a composite node with infinite capacity; thus the entire network is reduced to a two-node network having the node of interest and the composite node. Although blocking causes interdependencies between nodes in the network, the selected node is totally isolated from the rest of the network by constructing phases in the server which reflect the blocking events. An algorithm is given to compute the parameters of the phases. Several examples are discussed to demonstrate the efficiency and generality of the technique. Comparisons with simulation results show that the proposed technique provides accurate results for throughput values.<>