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A geometric process model for /(/)/1/ queue with new service machine procurement lead time

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  • Miaomiao Yu
  • Yinghui Tang
  • Yonghong Fu

Abstract

In this article, we consider a geometric process model for M/PH(M/PH)/1/K queue with new service machine procurement lead time. A maintenance policy (N − 1, N) based on the number of failures of the service machine is introduced into the system. Assuming that a failed service machine after repair will not be ‘as good as new’, and the spare service machine for replacement is only available by an order. More specifically, we suppose that the procurement lead time for delivering the spare service machine follows a phase-type (PH) distribution. Under such assumptions, we apply the matrix-analytic method to develop the steady state probabilities of the system, and then we obtain some system performance measures. Finally, employing an important Lemma, the explicit expression of the long-run average cost rate for the service machine is derived, and the direct search method is also implemented to determine the optimal value of N for minimising the average cost rate.

Suggested Citation

  • Miaomiao Yu & Yinghui Tang & Yonghong Fu, 2013. "A geometric process model for /(/)/1/ queue with new service machine procurement lead time," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(6), pages 1061-1075.
    • Handle: RePEc:taf:tsysxx:v:44:y:2013:i:6:p:1061-1075
    DOI: 10.1080/00207721.2011.652228
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    Cited by:

    1. Guan Jun Wang & Yuan Lin Zhang, 2016. "Optimal replacement policy for a two-dissimilar-component cold standby system with different repair actions," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(5), pages 1021-1031, April.
    2. Arnold, Richard & Chukova, Stefanka & Hayakawa, Yu & Marshall, Sarah, 2020. "Geometric-Like Processes: An Overview and Some Reliability Applications," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    3. Liping Liu & Lining Jiang & Ding Zhang, 2017. "An integrated model of statistical process control and condition-based maintenance for deteriorating systems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1452-1460, November.
    4. Hu, Lu & Jiang, Yangsheng & Zhu, Juanxiu & Chen, Yanru, 2015. "A PH/PH(n)/C/C state-dependent queuing model for metro station corridor width design," European Journal of Operational Research, Elsevier, vol. 240(1), pages 109-126.

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