Optimal Power Control for Wireless Queueing Networks

The problem considered is that of optimally con- trolling the transmission power in a time-slotted wireless link containing a finite-capacity buffer. The packets are of fixed length and have Bernoulli arrival characteristics at each time slot. A simple ARQ (send and wait) retransmission policy is used, that is the packets are retransmitted until they are successfully received. There are two alternative power levels and one of them is chosen based on the number of packets waiting in the buffer. The goal is to minimize a weighted combination of energy expenditure and buffer overflow. It is shown that optimal policy is of threshold type. That is, the optimal policy switches from small to large power when the queue length exceeds a certain threshold value. I. I NTRODUCTION AND SYSTEM MODEL A key concern in wireless networks is the energy efficiency. Lim- ited and non-renewable battery supplies in most of the wireless de- vices led to some adaptive transmission schemes that efficiently use these resources. Power control is one of those adaptive schemes. Choice of transmission power has many implications in wireless net- working, such as interference, success probability, energy, delay and buffer overflow. The main motivation in the past work on power con- trol was mitigating the effects of interference in order to maximize the achievable capacity (e.g. (1), (2)). Optimizing power control strategy to maximize battery lifetime under QoS constraints was considered in (3). The paper assumed an environment in which the interference has a known distribution and they find the optimal power as a function of the instantaneous interference power, so that the average power is minimized with the constraint that the average success rate must be larger than some minimum. The considered model was memoryless and no error control mechanism was specified. (4) et. al. consid- ered ARQ error control in an energy constrained environment, as it arises in mobile data communications. They assumed a rayleigh fad- ing channel modelled as a Gilbert channel and investigated the trade off between instantaneous performance and total energy efficiency in a wireless link. They observed that decreasing transmission power in favor of increased number of retransmission attempts may be a more energy efficient strategy then maximizing throughput at each slot. An important issue that is not considered in the above studies is the random characteristic of packet arrivals to the buffer. For in- stance, considering a limited buffer capacity, if the power is lowered when the queue length is close to the capacity, success rate decreases and buffer overflows can occur in case of an arrival burst. In order to minimize energy expenditure in the presence of queueing related constraints such as queueing delay or buffer overflow, power control decisions must also be a function of the queue size. This paper considers a wireless link with random message arrivals and a finite capacity buffer, and addresses the problem of jointly minimizing energy expenditure and queue overflow by dynamically choosing from two alternative power levels. We prove by using the Dynamic Programming framework that the optimal strategy of select- ing transmission power is of threshold type. Previously the works in (6), (7) and (8) used the Dynamic Programming approach in proving the optimality of threshold policies for different problems. In (7) and (8) the optimal control of a queueing system with two heterogeneous servers is considered, whereas in (6), the authors address the problem of modulation level control in a fading environment. The general assumptions on the system considered in this work is as follows. A source supplies a wireless node with packets that arrive according to a Bernoulli process of rate 0 < λ < 1 packets/time slot. Initially we assume that the number of bits per packet (B) is equal to one. The arriving packets enter in the input queue that has a capacity of K packets, where the bits arriving in excess of K packets are lost. Packets (bits) are transmitted by using BPSK modulated signals of duration Ts, where Ts is also equal to the time slot length (Rs = 1=Ts is the symbol rate). P is the power that is used in transmission, and PTs is the energy per single transmission.