Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2014-10-01

Journal: APPLIED MATHEMATICAL MODELLING

Included Journals: EI、SCIE

Volume: 38

Issue: 19-20

Page Number: 4705-4716

ISSN: 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.