Single and Multiple Server Queues with Vacations: Analysis and Algorithms

Supplementary variable;Vacations;Queues;State-Dependent

Ayyar, Sajidul Rahman A ; Dr. Mihail Devetsikiotis, Committee Member,Dr. Michael G Kay, Committee Member,Dr. Xiuli Chao, Committee Chair,Ayyar, Sajidul Rahman A ; Dr. Mihail Devetsikiotis ; Committee Member ; Dr. Michael G Kay ; Committee Member ; Dr. Xiuli Chao ; Committee Chair

University:North Carolina State University

关键词: Supplementary variable;    Vacations;    Queues;    State-Dependent;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/2619/etd.pdf?sequence=1&isAllowed=y

美国|英语

来源: null

【 摘 要 】

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.