Stationary distributions and convergence for M/M/1 queues in interactive random environment

Guodong Pang, Andrey Sarantsev, Yana Belopolskaya, Yuri Suhov

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


A Markovian single-server queue is studied in an interactive random environment. The arrival and service rates of the queue depend on the environment, while the transition dynamics of the random environment depend on the queue length. We consider in detail two types of Markov random environments: a pure jump process and a reflected jump diffusion. In both cases, the joint dynamics are constructed so that the stationary distribution can be explicitly found in a simple form (weighted geometric). We also derive an explicit estimate for the exponential rate of convergence to the stationary distribution via coupling.

Original languageEnglish (US)
Pages (from-to)357-392
Number of pages36
JournalQueueing Systems
Issue number3-4
StatePublished - Apr 1 2020

All Science Journal Classification (ASJC) codes

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


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