  In this paper we consider energy efficient scheduling in a multiuser setting
where each user has a finite sized queue and there is a cost associated with
holding packets (jobs) in each queue (modeling the delay constraints). The
packets of each user need to be sent over a common channel. The channel
qualities seen by the users are time-varying and differ across users; also, the
cost incurred, i.e., energy consumed, in packet transmission is a function of
the channel quality. We pose the problem as an average cost Markov Decision
Problem, and prove that this problem is Whittle Indexable. Based on this
result, we propose an algorithm in which the Whittle index of each user is
computed and the user who has the lowest value is selected for transmission. We
evaluate the performance of this algorithm via simulations and show that it
achieves a lower average cost than the Maximum Weight Scheduling and Weighted
Fair Scheduling strategies.
