Deriving lower bounds for energy consumption in Wireless Sensor Networks

Wireless Sensor Networks (WSNs) are a special kind of ad hoc networks designed to comprise a high density of sensor nodes. These networks have high traffic of data and waste energy with an unnecessary number of active sensor nodes. In this paper we address the Density Control, Coverage and Connectivity Problem (DCCCP) in WSNs, that consists in activating a subset of sensor nodes, which assure the area coverage and the nodes connectivity, and minimize the energy consumption. We propose Multiperiod and Periodic approaches to solve the DCCCP. The Multiperiod approach divides the expected network lifetime in time periods and calculates, in a global way, a solution for each period, that minimizes the network energy consumption considering all time periods at once. The Multiperiod Approach has a global view of the nodes and the network expected lifetime. The Periodic Approach solves the problem as an static problem, updates the list of available nodes and repeats the procedure. The Periodic Approach has a global view of the nodes but not of the network lifetime, it finds local solutions (considering the periods) that together form a global solution, represented by the sum of all local solutions. These approaches are modeled through Integer Linear Programming (ILP). We compare our optimal solutions with Geographical Adaptive Fidelity (GAF) and Hierarchical Geographical Adaptive Fidelity (HGAF). Given the global aspects of our approaches we expect to derive lower bound for energy consumption for density control algorithms in WSNs.