Single and Multiple Server Queues with Vacations: Analysis and Algorithms
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Date
2003-02-12
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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.
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Keywords
Supplementary variable, Vacations, Queues, State-Dependent
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Degree
MS
Discipline
Industrial Engineering
