Skip to main content
SpringerLink
Log in

Asymptotic analysis of multidimensional characteristics of Markov queueing systems

  • Published:
Cybernetics Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature Cited

  1. A. A. Borovkov, Asymptotic Methods in Queueing Theory [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  2. B. V. Gnedenko, “On a two-unit redundant system,” Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 4, 3–12 (1964).

    Google Scholar 

  3. B. V. Gnedenko, “Doubling with renewal,” Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 5, 111–118 (1964).

    Google Scholar 

  4. I. M. Kovalenko, “An algorithm for the asymptotic of the occuptation time of a Markov chain in a set of states,” Dopovidi Akad. Nauk URSR, Ser. A, No. 6, 497–500 (1973).

    Google Scholar 

  5. I. N. Kovalenko, “Limit theorems for reliability theory,” Kibernetika, No. 6, 106–116 (1977).

    Google Scholar 

  6. I. N. Kovalenko, The Analysis of Rare Events at the Estimation of System Efficiency [in Russian], Sov. Radio, Moscow (1980).

    Google Scholar 

  7. V. S. Korolyuk and A. F. Turbin, Semi-Markov Processes and Their Applications [in Russian], Naukova Dumka, Kiev (1976).

    Google Scholar 

  8. A. D. Solov'ev, “Standby with rapid renewal,” Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 1, 56–71 (1970).

    Google Scholar 

  9. A. D. Solov'ev, “The asymptotic behavior of the time of the first occurrence of a rare event in a regenerating process,” Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 6, 79–89 (1971).

    Google Scholar 

  10. V. S. Korolyuk, “On the asymptotic behavior of the occupation time of a semi-Markov process in a subset of states,” Ukr. Mat. Zh.,21, No. 6, 842–845 (1969).

    Google Scholar 

  11. V. V. Anisimov, “Limit distributions of functionals of semi-Markov processes given on a fixed set of states, up to the time of the first exit,” Dokl. Akad. Nauk SSSR,193, No. 4, 743–745 (1970).

    Google Scholar 

  12. V. V. Anisimov, “The description of limit laws for sums of random variables on a Markov chain when the number of terms is determined by the exit time from a finite subset,” in Random Processes and Statistical Inference [in Russian], No. 3, FAN, Tashkent (1973), pp. 22–31.

    Google Scholar 

  13. A. V. Skorokhod, “Limit theorems for random processes,” Teor. Veroyatn. Ee Primen.,1, No. 3, 289–319 (1956).

    Google Scholar 

  14. V. V. Anisimov, “The description of multidimensional limit laws for finite Markov chains in a scheme of arrays,” Teor. Veroyatn. Mat. Statist., No. 9, 8–22 (1973).

    Google Scholar 

  15. K. L. Chung, Markov Chains with Stationary Transition Probabilities, Springer, Berlin (1967).

    Google Scholar 

  16. V. V. Anisimov, Limit Theorems for Random Processes and Their Application to Discrete Summation Schemes [in Russian], Vyshcha Shkola, Kiev (1976).

    Google Scholar 

  17. P. Billingsley, Convergence of Probability Measures, Wiley, New York (1968).

    Google Scholar 

Download references

Authors
  1. V. V. Anisimov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. I. Lukashuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Kibernetika, No. 4, pp. 82–88, July–August, 1984.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Anisimov, V.V., Lukashuk, L.I. Asymptotic analysis of multidimensional characteristics of Markov queueing systems. Cybern Syst Anal 20, 567–576 (1984). https://doi.org/10.1007/BF01068932

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01068932

Keywords

Search

Navigation