Optimal solution of total routing table size for hierarchical networks

Hierarchical routing is an effective way to solve the scalability problem in flat networks. The optimal total routing table (RT) size is affected by four parameters: the total number of nodes in a network hierarchy levels, the number of clusters at each level, and cluster size distribution. An optimal solution of total RT size was given in L. Kleinrock et al. (1977). However, the optimal solution was based on a major assumption: all nodes in the network have equal size RTs. It is not clear whether the optimal results stated in L. Kleinrock et al. (1977) still hold without this assumption. We provide the general integer solution of optimal RT sizes without this assumption. In addition, we will show how the total number of nodes, the number of hierarchical levels, and the number of the highest-level clusters affect the total RTsize. Moreover, some important properties of the two-level cluster structure are extensively addressed, namely the impact of the variance of cluster size distribution on intra-cluster update costs and the RTsize.