  In this paper, we study joint queue-aware and channel-aware scheduling of
arbitrarily bursty traffic over multi-state time-varying channels, where the
bursty packet arrival in the network layer, the backlogged queue in the data
link layer, and the power adaptive transmission with fixed modulation in the
physical layer are jointly considered from a cross-layer perspective. To
achieve minimum queueing delay given a power constraint, a probabilistic
cross-layer scheduling policy is proposed, and characterized by a Markov chain
model. To describe the delay-power tradeoff, we formulate a non-linear
optimization problem, which however is very challenging to solve. To handle
with this issue, we convert the optimization problem into an equivalent Linear
Programming (LP) problem, which allows us to obtain the optimal threshold-based
scheduling policy with an optimal threshold imposed on the queue length in
accordance with each channel state.
