  In this paper, delay-optimal and energy-efficient communication is studied
for a single link under Markov random arrivals. We present the optimal tradeoff
between delay and power over Additive White Gaussian Noise (AWGN) channels and
extend the optimal tradeoff for block fading channels. Under time-correlated
traffic arrivals, we develop a cross-layer solution that jointly considers the
arrival rate, the queue length, and the channel state in order to minimize the
average delay subject to a power constraint. For this purpose, we formulate the
average delay and power problem as a Constrained Markov Decision Process
(CMDP). Based on steady-state analysis for the CMDP, a Linear Programming (LP)
problem is formulated to obtain the optimal delay-power tradeoff. We further
show the optimal transmission strategy using a Lagrangian relaxation technique.
Specifically, the optimal adaptive transmission is shown to have a threshold
type of structure, where the thresholds on the queue length are presented for
different transmission rates under the given arrival rates and channel states.
By exploiting the result, we develop a threshold-based algorithm to efficiently
obtain the optimal delay-power tradeoff. We show how a trajectory-sampling
version of the proposed algorithm can be developed without the prior need of
arrival statistics.
