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Diffusion approximation for a closed Jackson network

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Abstract

We investigate the asymptotic behavior of a vector queueing process in the Markov model of a closed queueing network. The number of jobs circulating in the network is assumed to increase without bound, while the processing rate at each node is directly proportional to the number of jobs at that node.

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Literature Cited

  1. O. I. Aven, N. N. Gurin, and Ya. A. Kogan, Performance Evaluation and Optimization of Computing Systems [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  2. V. V. Anisimov, V. S. Donchenko, and O. K. Zakusilo, Elements of Queueing Theory and Asymptotic System Analysis [in Russian], Vishcha Shkola, Kiev (1987).

    Google Scholar 

  3. G. P. Basharin and A. L. Tolmachev, Queueing Network Theory and Its Application to the Analysis of Information and Computing Systems [in Russian], Itogi Nauki i Tekhniki, Ser. Probability Theory, Mathematical Statistics, Theoretical Cybernetics, Vol. 21, VINITI, Moscow (1983).

    Google Scholar 

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

    Google Scholar 

  5. G. I. Ivchenko, V. A. Kashtanov, and I. N. Kovalenko, Queueing Theory [in Russian], Vysshaya Shkola, Moscow (1982).

    Google Scholar 

  6. L. Kleinrock, Queueing Systems, Vol. II: Computer Applications, Wiley, New York (1976).

    Google Scholar 

  7. A. A. Borovkov, “Limit theorems for queueing networks, I”, Teor. Veoryatn. Primen.,31, No. 3, 474–490 (1986).

    Google Scholar 

  8. A. A. Borovkov, Stochastic Processes in Queueing Theory [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  9. R. Boel, P. Varaiya, and E. Wong, “Martingales on jump processes, I, II,” SIAM J. Control,13, No. 5, 999–1061 (1975).

    Google Scholar 

  10. P. Brémaud, Point Processes and Queues. Martingale Dynamics, Springer, New York (1981).

    Google Scholar 

  11. V. S. Korolyuk, N. I. Portenko, A. V. Skorokhod, and A. F. Turbin, Handbook of Probability Theory and Mathematical Statistics [in Russian], Naukova Dumka, Kiev (1978).

    Google Scholar 

  12. I. I. Gikhman and A. V. Skorokhod, Theory of Random Processes [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  13. Yu. A. Rozanov, Stochastic Processes [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  14. I. I. Gikhman and A. A. Skorokhod, Stochastic Differential Equations and Their Applications [in Russian], Naukova Dumka, Kiev (1982).

    Google Scholar 

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

    Google Scholar 

  16. R. Sh. Liptser and A. N. Shiryaev, Theory of Martingales [in Russian], Nauka, Moscow (1986).

    Google Scholar 

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Authors
  1. L. I. Lukashuk
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Additional information

Translated from Kibernetika, No. 1, pp. 30–33, January–February, 1989.

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Lukashuk, L.I. Diffusion approximation for a closed Jackson network. Cybern Syst Anal 25, 36–40 (1989). https://doi.org/10.1007/BF01074881

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  • DOI: https://doi.org/10.1007/BF01074881

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