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Wireless scheduling algorithms for the download of a single cell that can maximize the asymptotic decay rate of the queue-overflow probability as the overflow threshold approaches infinity. We first derive an upper bound on the decay rate of the queue-overflow probability over all scheduling policies. Specifically, we focus on the class of "αalgorithms," the base station picks the user for service at each time that has the largest product of the transmission rate multiplied by the backlog raised to the power α. The α-algorithms arbitrarily achieve the highest decay rate of the queueoverflow probability. We design a scheduling algorithm that is both close to optimal in terms of the asymptotic decay rate of the overflow probability and to maintain small queue-overflow probabilities over queue-length ranges of practical interest.

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