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Determining the stationary probabilities of states of the system GI|G|n|O with an almost-poisson input

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Literature Cited

  1. R. M. Fortet, “Random distributions with an application to telephone engineering,” Proc. Berkeley Symp. Mathematical Statistics and Probability (Berkeley, 1956), Vol. 2, Univ. California Press, Los Angeles (1956), pp. 81–88.

    Google Scholar 

  2. B. A. Sevast'yanov, “A limit theorem for Markov Processes and its application to telephone systems with lost calls,” Teor. Veroyatn. Ee. Primen.,2, No. 1, 106–116 (1957).

    Google Scholar 

  3. I. N. Kovalenko, “Condition for the probabilities of states of a service system to be independent of the form of the service-time distribution,” in: Problems of Information Transmission [in Russian], Izd. Akad. Nauk SSSR, Moscow (1962), pp. 147–151.

    Google Scholar 

  4. B. V. Gnedenko and I. N. Kovalenko, Introduction to Queuing Theory [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  5. D. König, K. Matthes, and K. Nawrotzki, Verallgemeinerungen der Erlangschen und Engsetschen Formeln, Acad. Verlag, Berlin (1967).

    Google Scholar 

  6. D. König, “Method for testing the invariance properties and computing the stationary probabilities for queing systems with interrupt and with functional and stochastic dependences,” in: Queuing Theory (Proc. Third All-Union School-Conf. Queuing Theory) [in Russian], Izd. Mosk. Univ., Moscow (1976), pp. 93–114.

    Google Scholar 

  7. D. König and U. Jansen, “Eine Inwarianzeigenschaft zufälliger Bedienungsprozesse mit positiwen Geschwindigkeiten,” Math. Nachr.,70, 321–364 (1976).

    Google Scholar 

  8. N. Yu. Kuznetsov, “Determination of the stationary probabilities of states of systems for which conditions close to the invariance conditions of I. N. Kovalenko are satisfied,” Dokl. Akad. Nauk UkrSSR, No. 7, 505–509 (1979).

    Google Scholar 

  9. N. Yu. Kuznetsov, “Formulation of estimates of the stationary probabilities of states of systems for which conditions close to the conditions of I. N. Kovalenko's theorem are satisfied,” in: Problems of Stability of Stochastic Models (Proc. Sem.) [in Russian], VNIISI, Moscow (1981), pp. 70–81.

    Google Scholar 

  10. N. Yu. Kuznetsov, “Quantitative estimates of the stability of the Erlang system under a perturbation of the input process,” in: Problems of Stability of Stochastic Models (Proc. Sem.) [in Russian], VNIISI, Moscow (1981), pp. 71–76.

    Google Scholar 

  11. I. N. Kovalenko, Studies in the Reliability Analysis of Complex Systems [in Russian], Naukova Dumka, Kiev (1975).

    Google Scholar 

  12. I. N. Kovalenko, “Statistical-analytic method for calculating the characteristics of high-reliability systems,” Kibernetika, No. 6, 82–92 (1976).

    Google Scholar 

  13. I. N. Kovalenko, “Calculation of the characteristics of high-reliability systems by a statistical-analytic method,” Électron. Modelirov., No. 4, 5–8 (1980).

    Google Scholar 

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Authors
  1. N. Yu. Kuznetsov
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Translated from Kibernetika, No. 2, pp. 74–79, March–April, 1984.

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Kuznetsov, N.Y. Determining the stationary probabilities of states of the system GI|G|n|O with an almost-poisson input. Cybern Syst Anal 20, 265–272 (1984). https://doi.org/10.1007/BF01069183

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  • DOI: https://doi.org/10.1007/BF01069183

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