Stochastic Performance Evaluation of Hierarchical Routing for Large Networks

Abstract In its present form, distributed routing extracts a prohibitive price when used in large networks because of the processing time, nodal storage and line capacity required to update, store and exchange routing information among network nodes. In an earlier paper we have shown that hierarchical routing schemes with optimally selected clustering structures yield enormous reductions in routing table length and hence in routing cost, at the price of an increase in network path length. That increase was shown to be negligible in the limit of very large networks. In this paper, we evaluate the tradeoff between the reduction in routing table length and the increase in network path length in terms of the more meaningful network performance measures of delay and throughput. Extended queueing models are developed to exhibit the interrelationships which exist between network variables such as delay, throughput, channel capacity, nodal storage, network path length, routing table length, etc. These models are an extension of the classic model for networks in that they account for line overhead and storage requirements due to routing. The models demonstrate the enormous efficiency of optimized hierarchical routing for a class of large networks.