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In cellular communication systems, an important problem is to allocate the communication resource (bandwidth) so as to maximize the service provided to a set of mobile callers whose demand for service changes randomly. This problem is formulated as a dynamic programming problem and we use a reinforcement learning (RL) method to find dynamic channel allocation policies that are better than previous heuristic solutions. The policies obtained perform well for a broad variety of call traffic patterns. The superior performance of the proposed technique in terms of empirical blocking probability is illustrated in simulation examples.