We consider a wireless basestation transmitting high-speed data to multiple mobile users in a cell. The channel conditions between the basestation and the users are time-varying and user-dependent. We wish to define which user to schedule at each time step. Previous work on this problem has typically assumed that the channel conditions are governed by a stationary stochastic process. In this setting a popular algorithm known as Max-Weight has been shown to have good performance. However, the

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... tionarity assumption is not always reasonable. In this paper we study a more general worst-case model in which the channel conditions are governed by an adversary and are not necessarily stationary. In this model, we show that the non-stationarities can cause Max-Weight to have extremely poor performance. In particular, even if the set of possible transmission rates is finite, as in the CDMA 1xEV-DO system, Max-Weight can produce queues size that are exponential in the number of users. On the positive side, we describe a set of Tracking Algorithms that aim to track the performance of a schedule maintained by the adversary. For one of these Tracking Algorithms the queue sizes are only quadratic. We discuss a number of practical issues associated with the Tracking Algorithms. We also illustrate the performance of Max-Weight and the Tracking Algorithms using simulation.