On the ergodicity condition of random walks with a periodic control sequence

  • L. G. Afanas'eva
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1546)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    V. A. Malyshev, Classification of two-dimensional positive random walks and almost linear semimartingales, Soviet Math. Dokl., 13 (1972), pp. 526–528.zbMATHGoogle Scholar
  2. [2]
    V. A. Malyshev and M. V. Menshikov, Ergodicity, continuity and analiticity of countable Marcov chains, Trans. Moskow Math. Soc., 39 (1979), pp. 2–48.MathSciNetGoogle Scholar
  3. [3]
    G. Fayolle, n random walks arising in queuering systems: ergodicity and transience via quadratic forms as Lyapounov functions I, Queueing Systems: Theory and Appl., S (1989), pp. 167–184.Google Scholar
  4. [4]
    L. Takacs, Theory of Queues, Oxford Univ. Press, New York, 1962.zbMATHGoogle Scholar
  5. [5]
    B. Natvig, On the transient state probabilities for a queueing model where potential customers are discouraged by queue length. J. Appl. Probab., 11, (1974), pp. 345–354.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    V. Doorn, The transient state probabilities for a queueing model where potential cuestomers are discouranged by queue length, 18 (1981), pp. 499–506.Google Scholar
  7. [7]
    J. Kieger and J. Wolfowitz, On the theory of queues with many servers, Trans. mer. Math. Soc., 78 (1955), pp. 1–18.MathSciNetCrossRefGoogle Scholar
  8. [8]
    L. G. Afanas'eva and E. V. Bulinskaja, Stochastic Processes in the Theory of Queues Storages, Moscow State Univ. Publ., Moscow, 1980. (In Russion.)Google Scholar
  9. [9]
    L. G. Afanas'eva, On the output in the queueing model with imputient customers, Izv. Akad. Nauk SSSR, Ser. Techn. Kibern., 3 (1966), pp. 57–65. (In Russian.)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • L. G. Afanas'eva
    • 1
  1. 1.Dept. of Math. and Mech.Moscow State Univ.MoscowRussia

Personalised recommendations