Busy period distribution in state-dependent queues

C. Knessl*, B. J. Matkowsky, Z. Schuss, C. Tier

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We consider a state-dependent M/M/1 queue in which the arrival rate is a function of the instantaneous unfinished work (work backlog) in the system, and the customer's exponential service time distribution is allowed to depend on the unfinished work in the system at the instant that customer arrived. We obtain asymptotic approximations to both the busy period distributions as well as the residual busy period distribution. Our approximations are valid for systems with a rapid arrival rate and small mean service times.

Original languageEnglish (US)
Pages (from-to)285-305
Number of pages21
JournalQueueing Systems
Issue number3
StatePublished - Sep 1987
Externally publishedYes


  • State-dependent queues
  • busy period analysis
  • singular perturbations

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Management Science and Operations Research
  • Computational Theory and Mathematics


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