A Markov-modulated M/G/1 queue II: Busy period and time for buffer overflow

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We consider an M/G/1 queue where the arrival and service processes are modulated by a two state Markov chain. We assume that the arrival rate, service time density and the rates at which the Markov chain switches its state, are functions of the total unfinished work (buffer content) in the queue. We compute asymptotic approximations to performance measures such as the mean residual busy period, mean length of a busy period, and the mean time to reach capacity.

Original languageEnglish (US)
Pages (from-to)375-399
Number of pages25
JournalQueueing Systems
Volume1
Issue number4
DOIs
StatePublished - May 1 1987

Keywords

  • Markov modulated queues
  • State dependent M/G/1 queue
  • busy period
  • 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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