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Markov skeleton processes in the two types of GI/G/1 queuing system

Author: PengDan
Tutor: HouZhenTing
School: Central South University
Course: Probability Theory and Mathematical Statistics
Keywords: Markov Skeleton Processes Doob skeleton process Distributed Repairable system Multiple vacations
CLC: O226
Type: Master's thesis
Year: 2006
Downloads: 100
Quote: 1
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Abstract


Markov skeleton process is a random process more comprehensive. It contains the many random process model, such as: Markov processes, piecewise deterministic Markov processes, semi-Markov process, such as a series of classical stochastic process, has important theoretical and practical values. Professor Hou Zhenting et al 1997 Markov skeleton process concept was first proposed and used in the field of queuing theory, storage theory, reliability, successfully resolving the instantaneous distribution of the queuing theory, limit distribution ergodicity classic conundrum It also put forward a number of new problems and new ideas. GI/G/1 queuing system is the most typical of queuing theory queuing model. This paper uses Markov skeleton process theory GI/G/1 queuing system of two types of promotion. One class is the GI/G/1 repairable queuing system, the other is the multiple vacation GI/G/1 queuing systems. The first chapter outlines the history of the development of the queuing theory, the main structure of the status quo and research methods, and this article; second chapter summarizes the basic knowledge of the Markov process and Markov skeleton processes. Discussed in the third chapter focuses server might malfunction and repair GI/G/1 queuing system with Markov skeleton process theory gives the equation satisfied by the instantaneous distribution of GI/G/1 repairable queuing system captain group, and prove that the probability distribution of these equations are minimal nonnegative solution. Doob skeleton process further identify the system, and the use of Doob skeleton process limit theory given GI/G/1 queuing system repair statistical equilibrium theory. In the fourth chapter discusses exhaustive service GI/G/1 queuing system, multiple vacations. System only services and leave the state, once the system is vacated, the waiter on the vacation state, start a random length of vacation. End a vacation system remains the customer, to continue an independent and identically distributed vacation until the end of a vacation in some customer wait waiter termination of leave and began to serve a customer, become idle until the service desk again. The exhaustive service using Markov skeleton process theory GI/G/1 queuing system multiple vacations captain instantaneous distribution satisfy the equations, and probability distribution of these equations the minimal nonnegative solution. Further identify the statistical equilibrium theory when the customer arrival time interval follow a negative exponential distribution system Doob skeleton process and use of Doob skeleton process limit theory given exhaustive service GI/G/1 queuing system with multiple vacations.

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CLC: > Mathematical sciences and chemical > Mathematics > Operations Research > Queuing theory (random system)
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