Delay-Optimal Buffer-Aware Scheduling With Adaptive Transmission

In this paper, we aim to obtain the optimal tradeoff between the average delay and the average power consumption in a communication system. In our system, the arrivals occur at each timeslot according to a Bernoulli arrival process, and are buffered at the transmitter waiting to be scheduled. We consider a finite buffer and allow the scheduling decision to depend on the buffer occupancy. In order to capture the realism in communication systems, the transmission power is assumed to be an increasing and convex function of the number of packets transmitted in each timeslot. This problem is modeled as a constrained Markov decision process (CMDP). We first prove that the optimal policy of the Lagrangian relaxation of the CMDP is deterministic and threshold-based. We then show that the optimal delay-power tradeoff curve is convex and piecewise linear, and the optimal policies of the original problem are also threshold-based. Based on the results, we propose an algorithm to obtain the optimal policy and the optimal tradeoff curve. We also show that the proposed algorithm is much more efficient than using general methods. The theoretical results and the algorithm are validated by linear programming and simulations.