New Theoretical Studies and Optimal Cluster-Population Determination for Hierarchical Networks

In order to decrease the overhead of the dynamic routing mechanisms in large networks, the hierarchical routing protocols have been proposed in the early 80´s. The routing complexity and the routing table size are the two most important functional blocks in a dynamic route guidance system. Although various algorithms exist for finding the best routing policy on a hierarchical network, hardly exists any work in studying and evaluating the aforementioned measures of routing complexity and routing table size for a hierarchical network. In this paper, by applying the random geometry theory, we can generalize the mathematical framework from the previous work which discussed the worst-case deterministic models. Our proposed new framework can carry out the averages of the routing complexity and the routing table size, which can be specified as the functions of the hierarchical network parameters such as the number of the hierarchical levels and the subscriber densities (cluster-population) for each hierarchical level. After establishing the relationship between the structure of a hierarchical network and these two crucial network performance measures (routing complexity and routing table size), we present a novel cluster-population optimization method for hierarchical networks and the associated statistical analysis.