Transform-free analyses and two-moment approximations for the GI/G/c queue with finite capacity

Abstract

In this dissertation, we consider the stationary queue length of the general multi-server GI/G/c queue with finitely many r waiting places, which has applications in various areas such as computer, communications and industrial manufacturing systems. As a result, using the sample-path approach combined with some fundamental results such as the one-step rate-balance equation, the elementary renewal theorem, the renewal reward theorem, and the stochastic mean value theorem, we first obtain the exact transform-free expressions for the stationary queue-length distribution of the GI/G/c/c+r queue in product form. Making use of these results, we then also 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. The results presented in this dissertation would be valuable not only to queueing theorist but also to practitioners who prefer simple and quick practical answers to their finite-capacity multi-server queueing systems.