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 $\epsilon$ of the minimum average power required for queue stability must incur average queue size at least $\Omega(\log(1/\epsilon))$. However, the optimal convergence time is unknown, and prior algorithms give convergence time bounds of $O(1/\epsilon^2)$. This paper develops a scheduling algorithm that, for any $\epsilon>0$, achieves the optimal $O(\log(1/\epsilon))$ average queue size tradeoff with an improved convergence time of $O(\log(1/\epsilon)/\epsilon)$. 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. 
Michael J. Neely
math.OC