Wireless networks enable ubiquitous information and computational resource access, and become a popular networking solution. Recently, wireless mesh networks (WMN) -  have attracted increasing attention and deployment as a highperformance and low-cost solution to last-mile broadband Internet access. In this chapter, we study the problem of resource allocation in wireless mesh networks. Our goal is to design effective resource allocation algorithms for wireless mesh networks, which are optimal with respect to resource utilization and fair across different network access points. Compared with traditional wireline networks, the unique characteristics of wireless mesh networks pose great challenges to such algorithms. Particularly, the wireless interference issue of mesh networks needs fresh treatment: flows not only contend at the same wireless mesh router (contention in the time domain), but also compete for the shared channel if they are within the interference ranges of each other (contention in the spatial domain). This challenge calls for a new resource allocation framework that could characterize the unique features of wireless mesh networks. To address this challenge, we present a price-based resource allocation framework for wireless mesh networks to achieve optimal resource utilization and fairness among competing aggregated flows. In this chapter, we first model the resource allocation problem as an optimization problem: given network resources with constrained capacities and a set of users (e.g., aggregated flows from access points of mesh networks), one tries to allocate resources to each user in a way that the overall satisfaction (so called utility) of all users are maximized. We show that such an optimization goal could naturally lead to different fairness objectives when appropriate utility functions are specified.We further present a price-based distributed algorithm which solves this optimization problem and thus provides fair and optimal resource allocation. We instantiate the above generalized resource allocation framework to the wireless mesh networks. The key challenge comes from the shared-medium multi-hop nature of such networks, namely location-dependent contention and spatial reuse. Based on solid theoretical analysis, we show that a resource element in a multihop wireless mesh network is a facet of the polytope defined by the independent set of the conflict graph of this network, which could be approximated by a maximal clique. Thus we build our price-based resource allocation framework on the notion of maximal cliques in wireless mesh networks, as compared to individual links in traditional wide-area wireline networks.We further present a price-based distributed algorithm, which is proven to converge to the global network optimum with respect to resource allocation. The algorithm is validated and evaluated through simulation study. Our theoretical resource allocation framework of wireless mesh networks possesses great practical advantages. First, with the evolution of wireless signaling technology, medium access and routing protocols, the solution space of this problem may keep reforming, but its nature of optimal resource allocation remains unchanged. A good theoretical framework can effectively decouple the "core" of the problem and its other components (e.g., definition of network resource, and the way it is assigned to users), so that the basic problem formulation and its solution methodology survive. Second, perfect solutions often do not exist, since finding the optimal resource allocation (optimal point in the solution space) is always extremely expensive, if not impossible. When one designs practical solutions to approximate this optimal point, the role of a theoretical framework becomes crucial as it provides philosophical guidance of what is a good intuition. The rest of this chapter is organized as follows. Section 6.2 introduces the generalized resource allocation framework. Section 6.3 instantiates this framework to the case of wireless mesh network. Section 6.4 presents the price-based decentralized resource allocation algorithm. Finally, we show simulation results in Section 6.5, discuss related works in Section 6.6, and then we conclude the chapter.
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