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Research on the M/G/1 Retrial G-queueing Model with N-policy, Feedback, Preemptive Resome and Unreliable Server

Author: DuShaoAn
Tutor: AiNi·WuFuEr
School: Xinjiang University
Course: Applied Mathematics
Keywords: the M/G/1 retrial G-queueing model with N-policy feedback preemptive resume and unreliable server C0-semigroup dispersive operator quasi-compact operator eigenvalue
CLC: O226
Type: Master's thesis
Year: 2010
Downloads: 17
Quote: 0
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Abstract


This thesis is divided into two chapters. Chapter 1 is divided into two sections. In Sec-tion 1, we introduce briefly the history of queueing theory. In Section 2, we first introduce supplementary variable technique, then we put forward the problems that we study in this thesis. Chapter 2 is split into three sections. In Section 1, first we introduce the M/G/1 retrial G-queueing model with N-policy, feedback, preemptive resume and unreliable server, next we convert the model into an abstract Cauchy problem in a Banach space by introduc-ing a state space, operators and their domains. In Section 2, we study well-posedness of this queueing model and prove existence and uniqueness of a positive time-dependent solution of this queueing model by using the Hille-Yosida theorem and the Phillips theorem in func-tional analysis. In Section 3, we study asymptotic property of the time-dependent solution of the model when the failure rate functions are constants and obtain that its time-dependent solution is exponentially stable.

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