A Two-Moment Approximation for the <i>GI</i>/<i>G</i>/<i>c</i> Queue with Finite Capacity

Abstract

In this paper, we consider the steady-state queue length of the multiserver finite-capacity GI/G/c/c+r queue. As a result, we first obtain an exact transform-free expression for the steady-state queue-length distribution. Making use of this result, we then present a simple two-moment approximation for the queue-length distribution. From this, approximations for some important performance measures, such as the loss probability, the mean queue length, and the mean waiting time, are also obtained. In addition, we propose an approximation for the minimal buffer size that keeps the loss probability below an acceptable level. Extensive numerical experiments show that our approximation is extremely simple yet fairly good in its performance.