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This paper considers a wireless link with randomly arriving data that isqueued and served over a time-varying channel. It is known that any algorithmthat comes within $\epsilon$ of the minimum average power required for queuestability must incur average queue size at least $\Omega(\log(1/\epsilon))$.However, the optimal convergence time is unknown, and prior algorithms giveconvergence time bounds of $O(1/\epsilon^2)$. This paper develops a schedulingalgorithm that, for any $\epsilon>0$, achieves the optimal$O(\log(1/\epsilon))$ average queue size tradeoff with an improved convergencetime of $O(\log(1/\epsilon)/\epsilon)$. This is shown to be within alogarithmic factor of the best possible convergence time. The method uses thesimple drift-plus-penalty technique with an improved convergence time analysis.

Energy-Aware Wireless Scheduling with Near Optimal Backlog and Convergence Time Tradeoffs