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This paper is motivated by the observation that the average queueing delaycan be decreased by sacrificing power efficiency in wireless communications. Inthis sense, we naturally wonder what is the minimum queueing delay when theavailable power is limited and how to achieve the minimum queueing delay. Toanswer these two questions in the scenario where randomly arriving packets aretransmitted over multi-state wireless fading channel, a probabilisticcross-layer scheduling policy is proposed in this paper, and characterized by aconstrained Markov Decision Process (MDP). Using the steady-state probabilityof the underlying Markov chain, we are able to derive the mathematicalexpressions of the concerned metrics, namely, the average queueing delay andthe average power consumption. To describe the delay-power tradeoff, weformulate a non-linear programming problem, which, however, is very challengingto solve. By analyzing its structure, this optimization problem can beconverted into an equivalent Linear Programming (LP) problem via variablesubstitution, which allows us to derive the optimal delay-power tradeoff aswell as the optimal scheduling policy. The optimal scheduling policy turns outto be dual-threshold-based, which means transmission decisions should be madebased on the optimal thresholds imposed on the queue length and the channelstate.

Joint Queue-Aware and Channel-Aware Delay Optimal Scheduling of Arbitrarily Bursty Traffic over Multi-State Time-Varying Channels