Analysis of the machine repair models with multi-threshold synchronous vacations

Chia-Huang Wu, Jau Chuan Ke*, Gautam Choudhury

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


In this paper, we present an analysis of a machine repair problem with M operating machines and S standbys, in which c repairmen are responsible for supervising these machines and follow a multi-threshold, synchronous vacation policy. With such a policy, at a repair completion instant, if the number of the failed machines in the system is less than a preset threshold value, partial idle servers together take a single vacation (or leave for a random amount of time doing other secondary job). At the end of a vacation, they return to repair the failed machines (or waits for the arrival). The steady-state probabilities are solved by using the matrix-analytic method, and formulae of system performance measures are thereby obtained. A cost model is then developed to formulate an optimization problem to find the minimum cost. The direct search and quasi- Newton methods are implemented to determine the optimal number of servers, the optimal threshold policy and the optimal repair rate. Copyright

Original languageEnglish
JournalJournal of Testing and Evaluation
Issue number3
StatePublished - 1 May 2013


  • Direct search method
  • Machine repair model
  • Quasi-Newton method
  • Standby
  • Synchronous vacation policy


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