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In this paper, we consider the optimisation of transmission schedules for infrastructure Wireless Mesh Networks in which data is forwarded through mesh routers from a single Internet Gateway node. The mesh routers receive and aggregate data from local mobile devices and each mesh router has an assigned data allowance to ensure fairness, set depending on its geographical position or the predicted usage patterns. We examine the use of fair and efficient link scheduling for Wireless Mesh Networks and provide an integer program for maximising the throughput allowance for each mesh router in a network given the topology. The program uses a slotted time approach to maximise the throughput within a given number of slots N, thus allowing a network to be split into sub networks for local access to the mesh routers, and back-haul transmissions to the gateway. Results are presented showing the optimised throughput for a selection of networks and a range of values for N.