Connectivity, Transmission Power, and Lifetime Optimization in Asymmetric Networks: A Distributed Approach

One of the fundamental challenges of deploying sensor networks in applications, such as environmental monitoring and surveillance, is power management in the presence of various constraints. To address this challenge, in this paper, three problems over asymmetric networks represented by weighted directed graphs (digraphs) are investigated using a distributed approach. The first problem relates to transmission power control over the network to maximize connectivity. It is assumed that different nodes use different transmission power levels to communicate with their neighbors. The notion of generalized algebraic connectivity (GAC), used as a network connectivity measure, is formulated as an implicit function of the network's transmission power matrix. An optimization problem is introduced to maximize the network GAC while satisfying constraints on communication transmission powers. The second problem is the dual of the first one, i.e., minimizing the total transmission power of the network while controlling the network GAC. Ultimately, a third optimization problem is formulated to maximize the lifetime of the network and control its connectivity. Asymptotic convergence of the proposed algorithms to a local or global optima of the original optimization problems are demonstrated analytically. The effectiveness of the proposed distributed algorithm is verified by simulations.