A MAP-modulated fluid flow model with multiple vacations

Jung Woo Baek, Ho Woo Lee, Se Won Lee, Soohan Ahn

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


We consider a MAP-modulated fluid flow queueing model with multiple vacations. As soon as the fluid level reaches zero, the server leaves for repeated vacations of random length V until the server finds any fluid in the system. During the vacation period, fluid arrives from outside according to the MAP (Markovian Arrival Process) and the fluid level increases vertically at the arrival instance. We first derive the vector Laplace-Stieltjes transform (LST) of the fluid level at an arbitrary point of time in steady-state and show that the vector LST is decomposed into two parts, one of which the vector LST of the fluid level at an arbitrary point of time during the idle period. Then we present a recursive moments formula and numerical examples.

Original languageEnglish
Pages (from-to)19-34
Number of pages16
JournalAnnals of Operations Research
Issue number1
StatePublished - Jan 2013


  • Markov-modulated fluid flows
  • Markovian arrival process
  • Multiple vacations
  • Server control policy


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