Asymptotic stability of the M/G/1 queueing system with optional second service

被引：2

作者：

Gao, Chao ^{[1
]}

Chen, Xing-Min ^{[2
]}

Zheng, Fu ^{[3
]}

Zhu, Guangtian ^{[4
]}

机构：

[1] Dalian Polytech Univ, Sch Informat Sci & Engn, Dalian 116034, Peoples R China

[2] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

[3] Bohai Univ, Dept Math, Jinzhou 121002, Peoples R China

[4] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China

来源：

APPLIED MATHEMATICAL MODELLING | 2014年 / 38卷 / 19-20期

基金：

中国国家自然科学基金;

关键词：

C-0-semigroup; Queueing system; Stability condition; Asymptotic stability; STARTUP;

D O I：

10.1016/j.apm.2014.03.032

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

An M/G/1 queueing system with second optional service is considered in this paper. We are devoted to studying the asymptotic stability of this kind of system by using C-0-semigroup theory. By analyzing the spectral distribution of the system operator, we derive that 0 is an eigenvalue and is the only spectral point on the imaginary axis. It shows that the time-dependent solution of the system converges to the steady-state solution as time approaches infinity. Using the steady-state solution, we obtain the mean queue length. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：4705 / 4716

页数：12

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