  In this paper, we consider the delay-sensitive power and transmission
threshold control design in S-ALOHA network with FSMC fading channels. The
random access system consists of an access point with K competing users, each
has access to the local channel state information (CSI) and queue state
information (QSI) as well as the common feedback (ACK/NAK/Collision) from the
access point. We seek to derive the delay-optimal control policy (composed of
threshold and power control). The optimization problem belongs to the
memoryless policy K-agent infinite horizon decentralized Markov decision
process (DEC-MDP), and finding the optimal policy is shown to be
computationally intractable. To obtain a feasible and low complexity solution,
we recast the optimization problem into two subproblems, namely the power
control and the threshold control problem. For a given threshold control
policy, the power control problem is decomposed into a reduced state MDP for
single user so that the overall complexity is O(NJ), where N and J are the
buffer size and the cardinality of the CSI states. For the threshold control
problem, we exploit some special structure of the collision channel and common
feedback information to derive a low complexity solution. The delay performance
of the proposed design is shown to have substantial gain relative to
conventional throughput optimal approaches for S-ALOHA.
