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In this paper, we formulate and solve a problem of resource allocation over a given time horizon with uncertain demands and uncertain capacities of the available resources. In particular, we consider a number of data sources with uncertain bit rates, sharing a set of parallel channels with time-varying and possibly uncertain transmission capacities. We present a method for allocating the channels so as to maximize the expected system throughput. The framework encompasses quality-of-service (QoS) requirements, e.g., minimum-rate constraints, as well as priorities represented by a user-specific cost per transmitted bit. We assume only limited statistical knowledge of the source rates and channel capacities. Optimal solutions are found by using the maximum entropy principle and elementary probability theory. The suggested framework explains how to make use of multiuser diversity in various settings, a field of recently growing interest in communication theory. It admits scheduling over multiple base stations and includes transmission buffers to obtain a method for optimal resource allocation in rather general multiuser communication systems.