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A 2-class maintenance model with dynamic server behavior

Author

Listed:
  • Kevin Granville

    (University of Waterloo)

  • Steve Drekic

    (University of Waterloo)

Abstract

We analyze a 2-class maintenance system within a single-server polling model framework. There are $$C+f$$C+f machines in the system, where C is the cap on the number of machines that can be turned on simultaneously (and hence, be at risk of failure), and the excess f machines comprise a maintenance float which can be used to replace machines that are taken down for repair. The server’s behavior is dynamic, capable of switching queues upon a machine failure or service completion depending on both queue lengths. This generalized server behavior permits the analysis of several classic service policies, including preemptive resume priority, non-preemptive priority, and exhaustive. More complicated polices can also be considered, such as threshold-based ones and a version of the Bernoulli service rule. The system is modeled as a level-dependent quasi-birth-and-death process and matrix analytic methods are used to find the steady-state joint queue length distribution, as well as the distribution for the sojourn time of a broken machine. An upper bound on the expected number of working machines as a function of C is derived, and Little’s Law is used to find the relationship between the expected number of working machines and the expected sojourn time of a failed machine when $$f=0$$f=0 or $$f \ge 1$$f≥1. Several numerical examples are presented, including how one might optimize an objective function depending on the mean number of working machines, with penalty costs attributed to increasing C or f.

Suggested Citation

  • Kevin Granville & Steve Drekic, 2020. "A 2-class maintenance model with dynamic server behavior," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 34-96, April.
    • Handle: RePEc:spr:topjnl:v:28:y:2020:i:1:d:10.1007_s11750-019-00509-1
    DOI: 10.1007/s11750-019-00509-1
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    References listed on IDEAS

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    Cited by:

    1. Kevin Granville & Steve Drekic, 2021. "The unobserved waiting customer approximation," Queueing Systems: Theory and Applications, Springer, vol. 99(3), pages 345-396, December.

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