Optimal clustering structures for hierarchical topological design of large computer networks

Abstract

AbstractLarge packet switching computer networks on the order of hundreds or thousands of nodes will soon emerge to handle the fast‐growing demands in data communication and resource sharing among various information processing systems around the world. The network topology design problem has long been recognized as extremely complex and very quickly becomes unmanageable as the size of the network increases. Existing heuristic design procedures are quite efficient for the design of small to moderate‐sized networks (25–75 nodes); however, they become very costly and even prohibitive when dealing with large networks. A design methodology based on the hierarchical clustering of the network nodes is presented in this paper in order to alleviate the computational cost involved in the design. More specifically, the emphasis is on the determination of a clustering structure which minimizes the computational cost of the design. Such a cost is assumed to have a polynomial growth with the number of nodes in the subnet to be designed. We present optimum results both for the number of clusters, number of superclusters, etc., and for the number of hierarchical levels. An expression for the average delay of a message in such a hierarchical network is also provided in terms of the average delays in the subnets composing the network. This decomposition leads to the design of smaller subnetworks for which we can utilize present design strategies.