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Indexed by:期刊论文

Date of Publication:2014-10-01

Journal:APPLIED MATHEMATICAL MODELLING

Included Journals:SCIE、EI

Volume:38

Issue:19-20

Page Number:4705-4716

ISSN No.:0307-904X

Key Words:C-0-semigroup; Queueing system; Stability condition; Asymptotic stability

Abstract: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.