Low delay file transmissions over power constrained quasi-static fading channels
The ubiquitous deployment of battery-operated wireless devices has resulted in the need for efficient low latency power allocation schemes. A common phenomenon in wireless transmission systems is congestion, where the transmitter backlog grows due to restrictions in channel usage on a resource-constrained shared access medium. In this research work, we aim to achieve low communication delay of wireless downlink file transmissions operating on power-constrained quasi-static fading channels, using state-dependent transmission rate control and admission of file transmission requests. We employ a Markov queueing model to formulate the low delay objective for exponentially distributed file sizes as a constrained average queue length minimization problem. The corresponding primal problem is known to be expressible as a linear program in occupation measures, and therefore strong duality holds. In our work, we show the primal feasibility of the dual optimal policy w.r.t. the average throughput and power constraints, which is proved under the assumption the optimal average power and throughput are continuous with respect to the Lagrange dual variables at the optimal point. The dual problem is simplified to an iterative optimization using Dinkelbach’s fractional programming method and solved using gradient analysis techniques to analytically derive the ON-OFF threshold characteristics of the admission policy and the recursive structure of the transmission rate policy. We first apply our solution method to a wireless transmission system using the M/M/1 queueing model. Our objective is to minimize the average queue length subject to an upper bound on average transmission power and a lower bound on average admission rate. This constrained average queue length minimization problem is solved using Lagrange dual method. We substitute the individual stationary probabilities in the Lagrange dual function using the product form distribution expressed in terms of the stationary probability of the maximum queue length. The resulting objective function then corresponds to a fractional minimization problem which is solved using Dinkelbach’s method. We analytically derive the ON-OFF threshold characteristic of the optimal admission rates and the recursive structure of the optimal transmission rates. We illustrate the results of our algorithm for different values of throughput and power requirements. We also demonstrate the efficiency of optimal state-dependent rate control for exponentially distributed file sizes compared to benchmark state-independent transmission schemes. We next apply the solution techniques to an energy harvesting wireless transmission system, extending the M/M/1 queueing model. The model uses energy stored in a battery as well as energy packets available from an auxiliary power supply for file transmission. We use the product-form stationary distribution to establish a correspondence between the energy harvesting system and the M/M/1 queueing system. Using the solution approach using Dinkelbach’s method, we derive similar characteristics for the optimal admission and transmission rates. We finally extend the analysis to model a cache-aided wireless transmission system operating under the assumption the cache-hit probability is uniform for all files and queue length states. The system is modeled as a quasi-one-dimensional Markov chain. The stationary probabilities in the Lagrange dual function are expressed in terms of the stationary probability of the empty buffer state using the product of matrices. The solution methods and insights developed from the previous models simplify the analysis of this problem, and we analytically characterize the structure of the optimal admission and transmission rates. The applicability of our solution methodology to these three models of transmission systems illustrates its simplicity and versatility.