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Proportionally Fair Rate Allocation in Regular Wireless Sensor Networks
Vaibhav Pandit, Jung Hyun Jun, Sriram Narayanan and Dharma P. Agrawal

In this work, we consider the problem of fair rate allocation that maximizes the network throughput in Wireless Sensor Networks (WSNs). We find the optimal rate allocation for the individual and competing end-to-end sessions that maximizes the total proportionally fair throughput for the square, triangular and hexagonal regular topologies. We provide the closed form expressions for the optimal end-to-end session rates as well as the bounds for the link layer transmission probabilities. We study this problem with a slotted Aloha MAC layer, which provides us with a lower bound for more realistic MAC protocols. A comparison of the topologies based on their maximum total proportionally fair throughput, with different network sizes, data generation rates and clustering provides an insight into which topology would be ideal for any desired scale and application. Simulations and real world experiments using Telosb nodes validate our theories and results.

Keywords: Cross layer optimization, large Hop sensor networks, proportionally fair rate allocation, regular topologies, sensor network deployment, Telosb implementation.

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