Impact of the Aggregated Data Sizes on the Optimality of Multi-level Clustering

Multi-level clustering offers the scalability that is essential to large-scale ad hoc and sensor networks in addition to supporting energy-efficient strategies for gathering data. The optimality of a multi-level network largely depends on two design variables: 1) The number of levels, and 2) The number of nodes operating at each level. We characterize these variables within a multi-hop, multi-level hierarchical network of variable size that gathers and aggregates data at each level. Our network communication cost model (EEHC-VA) is parameterized by the size of the data forwarded at each level, which depends on the application and aggregation strategy in place. We minimize the communication cost to obtain the optimal probabilities of distributed and independent selection of level-(n+1) nodes from level-n nodes. Interestingly, we have identified intervals-based on the number of nodes and aggregated data sizes-within which single- or two-level hierarchies are optimal. The results have been numerically verified for a wide range of parameters and validated with network simulations.