Busy period analysis of the state dependent M/M/1/K queue

Ahmad Al Hanbali*, Onno Boxma

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


In this paper, we study the transient behavior of a state dependent M/M/1/K queue during the busy period. We derive in closed-form the joint transform of the length of the busy period, the number of customers served during the busy period, and the number of losses during the busy period. For two special cases called the threshold policy and the static policy we determine simple expressions for their joint transform.

Original languageEnglish
Pages (from-to)1-6
Number of pages6
JournalOperations Research Letters
Issue number1
StatePublished - Jan 2010
Externally publishedYes


  • Absorbing Markov chains
  • Busy period
  • Level dependent
  • M/M/1/K queue
  • Performance metrics

ASJC Scopus subject areas

  • Software
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics


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