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Multi server machine repair problem with unreliable server and two types of spares under asynchronous vacation policy

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  • Anamika Jain
  • Madhu Jain

Abstract

In many industrial situations, machines are subjected to random breakdowns. In this paper, we consider the asynchronous vacation policy for the multi-server machine repair problem with server breakdown and two types of spares. According to this policy, when a certain number of servers become idle at a service completion instant, the servers will take an asynchronous vacation of random length together. If the servers find no waiting failed unit in the system and the number of servers on vacation is less than the total number of servers, then these servers can take vacation individually and continue to take vacation if the vacation condition is satisfied. Each server is subject to breakdowns in working state only and can be repaired according to exponential service time distribution. Matrix geometric method is used to obtain the queue size distribution. Various performance measures viz. the expected number of the idle servers, busy servers and vacationing servers, etc. are determined. The sensitivity analysis is made to examine the effect of parameters on various performance measures.

Suggested Citation

  • Anamika Jain & Madhu Jain, 2017. "Multi server machine repair problem with unreliable server and two types of spares under asynchronous vacation policy," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 10(3), pages 286-315.
    • Handle: RePEc:ids:ijmore:v:10:y:2017:i:3:p:286-315
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    Citations

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    Cited by:

    1. Wu, Hui & Li, Yan-Fu & Bérenguer, Christophe, 2020. "Optimal inspection and maintenance for a repairable k-out-of-n: G warm standby system," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    2. Sudeep Kumar & Ritu Gupta, 2023. "Reliability analysis of N-policy vacation based FTC system subject to standby switching failures," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 33(2), pages 53-80.

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