Performance Analysis of a Discrete-Time Queue with Working Breakdowns and Searching for the Optimum Service Rate in Working Breakdown Period

Lan Shaojun () and Tang Yinghui ()
Additional contact information
Lan Shaojun: School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong643000, China
Tang Yinghui: School of Fundamental Education, Sichuan Normal University, Chengdu610066, China

Journal of Systems Science and Information, 2017, vol. 5, issue 2, 176-192

Abstract: This paper deals with a discrete-time Geo/Geo/1 queueing system with working breakdowns in which customers arrive at the system in variable input rates according to the states of the server. The server may be subject to breakdowns at random when it is in operation. As soon as the server fails, a repair process immediately begins. During the repair period, the defective server still provides service for the waiting customers at a lower service rate rather than completely stopping service. We analyze the stability condition for the considered system. Using the probability generating function technique, we obtain the probability generating function of the steady-state queue size distribution. Also, various important performance measures are derived explicitly. Furthermore, some numerical results are provided to carry out the sensitivity analysis so as to illustrate the effect of different parameters on the system performance measures. Finally, an operating cost function is formulated to model a computer system and the parabolic method is employed to numerically find the optimum service rate in working breakdown period.

Keywords: discrete-time queue; working breakdowns; different arrival rates; performance measures; optimum service rate (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.21078/JSSI-2017-176-17 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:jossai:v:5:y:2017:i:2:p:176-192:n:6

DOI: 10.21078/JSSI-2017-176-17

Access Statistics for this article

Journal of Systems Science and Information is currently edited by Shouyang Wang

More articles in Journal of Systems Science and Information from De Gruyter
Bibliographic data for series maintained by Peter Golla ().