  Throughput-optimal transmission scheduling in wireless networks has been a
well considered problem in the literature, and the method for achieving
optimality, MaxWeight scheduling, has been known for several decades. This
algorithm achieves optimality by adaptively scheduling transmissions relative
to each user's stochastic traffic demands. To implement the method, users must
report their queue backlogs to the network controller and must rapidly respond
to the resulting resource allocations. However, many currently-deployed
wireless systems are not able to perform these tasks and instead expect to
occupy a fixed assignment of resources. To accommodate these limitations,
adaptive scheduling algorithms need to interactively estimate these
uncooperative users' queue backlogs and make scheduling decisions to account
for their predicted behavior. In this work, we address the problem of
scheduling with uncooperative legacy systems by developing algorithms to
accomplish these tasks. We begin by formulating the problem of inferring the
uncooperative systems' queue backlogs as a partially observable Markov decision
process and proceed to show how our resulting learning algorithms can be
successfully used in a queue-length-based scheduling policy. Our theoretical
analysis characterizes the throughput-stability region of the network and is
verified using simulation results.
