Stochastic disaster recovery systems with external resources

Song Kyoo Kim, J. H. Dshalalow

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


This paper deals with a complex reliability system of main unreliable, spare, and auxiliary spare machines, subject to random breakdowns, repairs, and two replacement policies: one for busy, and another for idle or vacation periods. During vacation periods, when the system performs a mandatory routine maintenance, auxiliary machines are being used for back-ups; the information on the system is naturally delayed. We utilize an analog of the N-policy to restrict the usage of auxiliary machines to some reasonable quantity. Analytically, tractable results are obtained by using a duality principle (which enables us to treat a more rudimentary system), semiregenerative analysis, and the theory of fluctuations of multivariate marked renewal processes. The results are demonstrated in the framework of optimization problems.

Original languageEnglish
Pages (from-to)1235-1257
Number of pages23
JournalMathematical and Computer Modelling
Issue number11-13
Publication statusPublished - 6 Dec 2002
Externally publishedYes


  • Closed queues
  • Disaster recovery
  • Duality
  • First exceed level process
  • Multichannel queue
  • Repairman
  • Semi-Markov process
  • Semiregenerative process
  • Stochastic optimization
  • Weak Markov process


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