  In this work, we address the delay optimal scheduling problem for wireless
transmission with fixed modulation over multi-state fading channels. We propose
a stochastic scheduling policy which schedules the source to transmit with
probability jointly based on the buffer and channel states, with an average
power constraint at the transmitter. Our objective is to minimize the average
queueing delay by choosing the optimal transmission probabilities. Using Markov
chain modeling, we formulate a power-constrained delay minimization problem,
and then transform it into a Linear Programming (LP) one. By analyzing its
property, we can derive the optimal threshold-based scheduling policy together
with the corresponding transmission probabilities. Our theoretical analysis is
corroborated by simulation results.
