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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Lan Shaojun & Tang Yinghui, 2017. "Performance Analysis of a Discrete-Time Queue with Working Breakdowns and Searching for the Optimum Service Rate in Working Breakdown Period," Journal of Systems Science and Information, De Gruyter, vol. 5(2), pages 176-192, April.
    • Handle: RePEc:bpj:jossai:v:5:y:2017:i:2:p:176-192:n:6
    DOI: 10.21078/JSSI-2017-176-17
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    References listed on IDEAS

    as
    1. I. Atencia, 2015. "A discrete-time queueing system with server breakdowns and changes in the repair times," Annals of Operations Research, Springer, vol. 235(1), pages 37-49, December.
    2. Cheng-Dar Liou, 2015. "Markovian queue optimisation analysis with an unreliable server subject to working breakdowns and impatient customers," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(12), pages 2165-2182, September.
    3. Ivan Atencia & Pilar Moreno, 2006. "A DISCRETE-TIMEGeo/G/1RETRIAL QUEUE WITH SERVER BREAKDOWNS," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 23(02), pages 247-271.
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