Maximizing the lifetime of energy constrained wireless sensor networks having tree topology

This paper aims at maximizing the lifetime of wireless sensor networks (WSN) in tree topology assuming limited energy of the battery at each sensor. We formulate the linear programming problem for maximizing the lifetime for a given tree topology, having as variables the number of times in which each node communicates with the base station. For a given tree, the policy that maximizes the lifetime is such that a certain group of nodes becomes energy depleted, while the other nodes still have considerable energy unused. We then generalize the linear programming problem to the case when a number of different trees are used along the lifetime. By properly selecting the trees so that each has a different group of early depletion nodes we obtain a scheduling algorithm which performs very well, surpassing in several cases the performance of the chain based optimized topologies. In addition, the tree topology has the advantage of having a shorter delay in transmitting the information during the convergecast from the leaves to the base station.