A Convex Optimization Framework for Service Rate Allocation in Finite Communications Buffers

We study the convexity of loss probability in communications and networking optimization problems that involve finite buffers, where the arrival process has a general distribution. Examples of such problems include scheduling, energy management and revenue, and cost optimization problems. To achieve a computationally tractable optimization framework, we propose to adjust an existing nonconvex loss probability formula for G/D/1 queues to present a convex and even more accurate loss probability model. We then use empirical data and computer simulations to examine the performance of the proposed design.