Optimal Power Control for Wireless Queueing Networks

In this paper, we address the problem of power control in wireless queueing networks. We consider a discrete time (slotted) wireless system of single link. Data arrive in packets according to a Bernoulli process of rate λ. A simple ARQ (send and wait) retransmission policy is used for the transmission of packets. The control parameter in this system is the transmission power of a packet, which is decided at every time slot if there is a packet to be transmitted at the queue. We consider choosing dynamically from two power levels dependent on the system state (number of packets in the system and previous decision). Our goal is to jointly minimize energy expenditure and queue overflow. Using the dynamic programming framework, we prove that the optimal policy that chooses one of the two power levels is of threshold type, that is, the optimal policy switches from small to large and large to small power at certain queue length states.