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We consider a wireless system comprising of multiple users that communicate with a base station. When there are a large number of users with time varying channels, it has been shown that multiuser diversity can be exploited to achieve high throughput in these systems. In a system employing multiuser diversity, the base station estimates the channel quality for each user during each time slot, and schedules the user with the best channel condition for that time slot. There has been a considerable amount of work towards developing scheduling mechanisms to provide quality of service guarantees to the individual users in addition to maximizing total throughput. In this paper, we consider the achievable rate region of a multiuser TDM system when the average transmit power is bounded. Our objective is to develop efficient algorithms to determine if a given rate vector is achievable within the average power bound. We characterize the achievable rate region when the channel behavior can be approximated by the on-off Gilbert-Elliot channel model. We first show that the problem of determining if a rate vector is achievable can be formulated as a convex optimization problem over a suitably denned polymatroid. We derive optimal waterfilling algorithms for solving the achievable rate region problem.