Single and Multiple Server Queues with Vacations: Analysis and Algorithms

Abstract

In this thesis we are concerned with the analysis and algorithm development of multiple server queueing systems with finite buffer and vacations.

In chapter 2, we analyze a G/M(n)/1/K queueing system where the server applies an N policy and takes multiple exponential vacations when the system is empty. This includes G/M/n/K queues with vacation and other multiple server models. Using the method of supplementary variables to derive the system equations, we develop a recursive algorithm for numerically computing the stationary queue length distribution of the system. The only input requirement is the Laplace-Stieltjes transform of the arrival distribution. In chapter 3, we extend the above results to the case where the server takes multiple state-dependent exponential vacations.

In chapter 4, we study a M(n)/G/1/K queueing system where the server applies an N policy and takes multiple arbitrary vacations when the system is empty. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. The only input requirements are the Laplace-Stieltjes transforms of the service time distribution and the vacation time distribution.

The results of this research can be applied to the design and optimization of computer and communication systems.