End-to-end fairness over non-convex capacity region in IEEE 802.11-based wireless networks

Fair resource allocation for end-to-end flows is an important yet challenging problem in multi-hop wireless networks. Recent research on fair resource allocation is mainly based on the assumption of convex resource regions, which has been theoretically proven untrue. Thus, the definition of fairness in IEEE 802.11 is intriguing for two reasons: non-convexity of the IEEE 802.11, and the intrinsically deficient MAC scheduling. Two key questions that emerge unanswered are 1) How to define end-to-end fairness under IEEE 802.11. 2) How to achieve end-to-end fairness. In this paper, we present a new fairness model for IEEE 802.11 wireless network where the capacity region is non-convex. To characterize the desired fairness property, we adopt an axiomatic approach based on the game theoretic framework. Our new fairness model grounds on the Nash Extension Solution (NES), which is shown to be consistent with the concept of proportional fairness under the convex cases and approximate it under the non-convex cases. We further present an efficiency enhanced version of Nash extension solution, which pushes the NES to the strong Pareto frontier. Based on the construction method of NES and its extension solution, we present a time-decomposed price-based rate allocation algorithm and prove its stability. The simulation study over a variety of topologies (e. g., random and dynamic) validates the performance of our algorithms and demonstrates this theoretically sound new fairness model for IEEE 802.11 networks.