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


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
Issue number4
StatePublished - May 1987


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


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