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.
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页码：4705 / 4716
页数：12
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