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

This paper considers a wireless link with randomly arriving data that is queued and served over a time-varying channel. It is known that any algorithm that comes within $ϵ$ of the minimum average power required for queue stability must incur average queue size at least $\mathrm{\Omega }(\log (1\mathrm{/}ϵ))$. However, the optimal convergence time is unknown, and prior algorithms give convergence time bounds of $O(1\mathrm{/}{ϵ}^2)$. This paper develops a scheduling algorithm that, for any $ϵ>0$, achieves the optimal $O(\log (1\mathrm{/}ϵ))$ average queue size tradeoff with an improved convergence time of $O(\log (1\mathrm{/}ϵ)\mathrm{/}ϵ)$. This is shown to be within a logarithmic factor of the best possible convergence time. The method uses the simple drift-plus-penalty technique with an improved convergence time analysis.