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Tractable Computation of Optimal Schedules and Routing in Multihop Wireless Networks

Interference and collisions greatly limit the throughput of mesh networks that used contention-based MAC protocols such as 802.11. Significantly higher throughput is achievable if transmissions are scheduled. However, traditional methods to compute optimal schedules are computationally intractable (unless co-channel interference is neglected). This paper presents a tractable technique to compute optimal schedules and routing in multihop wireless networks. The resulting algorithm consists of three layers of optimization. The inner-most optimization computes an estimate of the capacity. This optimization is a linear or nonlinear optimization with linear constraints. The middle iteration uses the Lagrange multipliers from the inner iteration to modify the space over which the inner optimization is performed. This is a graph theoretic optimization known as the maximum weighted independent set problem. The outermost optimization uses the Lagrange multipliers from the innermost optimization to find optimal routes. This optimization requires solving several least cost paths problems and several maximum weighted independent set problems. The impact of optimal scheduling and routing is examined on realistic models of mesh networks where it is found that the capacity provided by optimal scheduling and routing is between a factor of 5 and 15 greater than that provided by 802.11’s CSMA/CD with least hop routing.