  We consider the problem of long term power allocation in dense wireless
networks. The framework considered in this paper is of interest for
machine-type communications (MTC). In order to guarantee an optimal operation
of the system while being as power efficient as possible, the allocation policy
must take into account both the channel and queue states of the devices. This
is a complex stochastic optimization problem, that can be cast as a Markov
Decision Process (MDP) over a huge state space. In order to tackle this state
space explosion, we perform a mean-field approximation on the MDP. Letting the
number of devices grow to infinity the MDP converges to a deterministic control
problem. By solving the Hamilton-Jacobi-Bellman Equation, we obtain a
well-performing power allocation policy for the original stochastic problem,
which turns out to be a threshold-based policy and can then be easily
implemented in practice.
