Capacity and Energy-Consumption Optimization for the Cluster-Tree Topology in IEEE 802.15.4

IEEE 802.15.4 proposes to use a cluster-tree hierarchy to organize the transmissions in Wireless Sensor Networks. In this letter, we propose a framework to analyze formally the capacity and the energy consumption of this structure. We derive a Mixed Integer Linear Programming (MILP) formulation to obtain a topology compliant with the standard. This formulation provides the optimal solution for the network capacity: this constitutes an upper bound for any distributed algorithm permitting to construct a cluster-tree. This framework can also be used to evaluate the capacity and to compare quantitatively different cluster-tree algorithms.