Proportionally fair rate allocation in regular Wireless Sensor Networks

In this paper, we consider the problem of fair rate allocation that maximizes the network throughput in regular topologies of Wireless Sensor Networks (WSNs). In order to monitor the entire coverage area of the WSN while maintaining acceptable network throughput, we need to find the optimal rate allocation for the individual/competing end-to-end sessions that maximizes the total proportionally fair throughput of the network. We provide closed form expressions for the optimal end-to-end session rates for square, triangular and hexagonal topologies as well as the bounds for the link layer transmission probabilities. We study the aforementioned problem for regular WSNs with a slotted Aloha MAC layer, which provides us with a lower bound for more realistic MAC protocols. Real world experiments using Telosb nodes validate our theories and results. Simulations carried out in Qualnet verify our comparisons of the different regular topologies as the size of network grows.