Markov Skeleton Processes Two Types Of Gi/g/1 Queuing System

Markov skeleton processes is a kind of comprehensive stochastic process, which contains many known classical processes: such as Markov processes, Piecewise Deterministic Markov skeleton processes, Semi-Markov processes etc. They have important value in theory and application. In 1997, Prof Hou Zhenting and his colleagues raised this kind of processes, which then was applied in queuing systems, inventory and reliable systems etc. It solved a series of typical difficult problems, such as the transient distribution, the limit distribution and the ergodicity in queueing system etc. At the same time they present several new problems and new ideals.The GI/G/1 queuing system is the most typical queueing model. In this paper, the author uses the Markov skeleton process to discusses two generalized GI/G/1 queuing system: The GI/G/1 queueing system with repairable service station and the GI/G/1 queueing system with multiple vacation under exhaustive service.In chapter 1, the author states briefly the developmental history and the present condition of queueing theory. And then induces the main methods of queueing theory.In chapter 2, the author induces the preliminary knowledge of Markov process and Markov skeleton processes. In chapter 3, the author mainly focuses on the GI/G/1 queueing system with repairable service station. Considered the server may be bad, and can be repaired. Using Markov skeleton processes theory to present the equations of the transient distribution. And prove that the length of this queueing system satisfy these equations and are their minimal nonnegative solutions. Furthermore, the author finds out the Doob skeleton process of this queueing system and give out several results about the limit behavior by using limit theory of Doob skeleton process.In chapter 4, the author discusses GI/G/1 queueing system with the multiple vacation under exhaustive service. This system has only two conditions: service and vacation. If there is waiting guest, the server will be work after its vacations until there is no guest. Using Markov skeleton processes theory to present the equations of the transient distribution. And prove that the length of this system satisfy these equations and are their minimal nonegative solutions. Furthermore, the author finds out the Doob skeleton process of the special case of this queueing system and give out several results about the limit behavior by using limit theory of Doob skeleton process.