Journal of Mathematical Sciences

, Volume 72, Issue 2, pp 3032–3034 | Cite as

Diffusion approximation of systems with repeated calls and an unreliable server

  • V. V. Anisimov
  • Kh. L. Atadzhanov
Applied Topics in Control Theory, Mathematical Cybernetics, and Statistics

Abstract

We consider single-server queueing systems with repeated calls and an unreliable server, which may fail both when free and when busy. A central limit theorem and a diffusion approximation theorem are obtained for the queue as a time-dependent process in the case of a low rate of repeated calls.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    I. V. Prangishvili, V. S. Podlazov, and G. G. Stetyura, Local Area Computer Networks [in Russian], Moscow (1984).Google Scholar
  2. 2.
    M. A. Shpens, Information Distribution Systems [in Russian], Moscow (1979).Google Scholar
  3. 3.
    I. I. Khimichkov, "A model of local area computer network with random multiple access," Avtomat. Vychisl. Tekh., No. 1, 58–62 (1978).Google Scholar
  4. 4.
    V. V. Anisimov and A. O. Aliev, "Limit theorems for semi-Markov recurrent processes," Teor. Veroyatn. Mat. Stat., No. 41, 9–15 (1989).Google Scholar
  5. 5.
    V. V. Anisimov and A. O. Aliev, Diffusion Approximation of Semi-Markov Recursive Algorithms and Its Applications in Queueing Systems [in Russian], Preprint Akad. Nauk Ukr. SSR, Inst. Kibern., No. 89–90, Kiev (1989).Google Scholar
  6. 6.
    V. V. Anisimov and Kh. L. Atadzhanov, "Diffusion approximation of systems with repeated calls," Teor. Veroyatn. Mat. Stat., No. 44, 3–6 (1990).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • V. V. Anisimov
  • Kh. L. Atadzhanov

There are no affiliations available

Personalised recommendations