Queueing Systems

, Volume 46, Issue 3, pp 353–361

On Existence of Limiting Distribution for Time-Nonhomogeneous Countable Markov Process

  • V. Abramov
  • R. Liptser

DOI: 10.1023/B:QUES.0000027990.74497.b2

Cite this article as:
Abramov, V. & Liptser, R. Queueing Systems (2004) 46: 353. doi:10.1023/B:QUES.0000027990.74497.b2


In this paper, sufficient conditions are given for the existence of limiting distribution of a nonhomogeneous countable Markov chain with time-dependent transition intensity matrix. The method of proof exploits the fact that if the distribution of random process Q=(Qt)t≥0 is absolutely continuous with respect to the distribution of ergodic random process Q°=(Q°t)t≥0, then \(Q_t \xrightarrow[{t \to \infty }]{{law}}\pi \) where π is the invariant measure of Q°. We apply this result for asymptotic analysis, as t→∞, of a nonhomogeneous countable Markov chain which shares limiting distribution with an ergodic birth-and-death process.

countable Markov processexistence of the limiting distributionbirth-and-death process

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • V. Abramov
    • 1
    • 2
  • R. Liptser
    • 3
  1. 1.Department of Mathematics, The Faculty of Exact SciencesTel Aviv UniversityTel Aviv, and
  2. 2.College of Judea and SamariaArielIsrael
  3. 3.Department of Electrical Engineering-SystemsTel Aviv UniversityTel AvivIsrael