A Markov-modulated M/G/1 queue I: Stationary distribution

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

Research output: Contribution to journalArticlepeer-review

Abstract

We consider an M/G/1 queueing system in which the arrival rate and service time density are functions of a two-state stochastic process. We describe the system by the total unfinished work present and allow the arrival and service rate processes to depend on the current value of the unfinished work. We employ singular perturbation methods to compute asymptotic approximations to the stationary distribution of unfinished work and in particular, compute the stationary probability of an empty queue.

Original languageEnglish
Pages (from-to)355-374
Number of pages20
JournalQueueing Systems
Volume1
Issue number4
DOIs
StatePublished - May 1987

Keywords

  • Markov modulated queues
  • State dependent M/G/1 queue
  • singular perturbations

Fingerprint

Dive into the research topics of 'A Markov-modulated M/G/1 queue I: Stationary distribution'. Together they form a unique fingerprint.

Cite this