  Cross-layer scheduling is a promising way to improve Quality of Service (QoS)
given a power constraint. In this paper, we investigate the system with random
data arrival and adaptive transmission. Probabilistic scheduling strategies
aware of the buffer state are applied to generalize conventional deterministic
scheduling. Based on this, the average delay and power consumption are analysed
by Markov reward process. The optimal delay-power tradeoff curve is the Pareto
frontier of the feasible delay-power region. It is proved that the optimal
delay-power tradeoff is piecewise-linear, whose vertices are obtained by
deterministic strategies. Moreover, the corresponding strategies of the optimal
tradeoff curve are threshold-based, hence can be obtained by a proposed
effective algorithm. On the other hand, we formulate a linear programming to
minimize the average delay given a fixed power constraint. By varying the power
constraint, the optimal delay-power tradeoff curve can also be obtained. It is
demonstrated that the algorithm result and the optimization result match each
other, and are further validated by Monte-Carlo simulation.
