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Queuing Systems with Cyclic Control Processes

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Abstract

An analysis of queuing systems with control processes more general than cyclic ones is proposed. Conditions ensuring stochastic boundedness of cyclic systems and existence of their steady state are analyzed.

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REFERENCES

  1. D. G. Kendall, “Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain,” Ann. Math. Statist, 24, 338–354 (1953).

    Google Scholar 

  2. D. V. Lindley, “The theory of queues with a single server,” Proc. Cambridge Phil. Soc., 48, 277–289 (1952).

    Google Scholar 

  3. I. N. Kovalenko, Some queuing problems with constraints,” Teor. Veroyatn. i yeyo Primenen., 1, No.1, 222–228 (1961).

    Google Scholar 

  4. I. N. Kovalenko, Queuing System with Constraints for Waiting Period [in Russian], Inst. Matem. AN USSR, Kiev (1961).

    Google Scholar 

  5. I. N. Kovalenko, “About a queuing system with the service rate depending on the number of requests in the system and periodic channel disconnection,” Probl. Peredachi Inform., 7, No.2, 106–111 (1971).

    Google Scholar 

  6. B. V. Gnedenko and I. N. Kovalenko, “Some problems of queuing theory,” Izv. AN SSSR, Tekhn. Kibern., No. 5, 88–100 (1967).

  7. B. V. Gnedenko and I. N. Kovalenko, Introduction to Queuing Theory [in Russian], Nauka, Moscow (1987).

    Google Scholar 

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

    Google Scholar 

  9. G. S. Evdokimova, “Distribution of waiting time in case of periodic input flow,” Izv. AN SSSR, Tekhn. Kibern., No. 3, 114–118 (1974).

  10. J. M. Harrison and A. I. Lemoine, “Limit theorem for periodic queues,” J. Appl. Prob. 14, 566–576 (1977).

    Google Scholar 

  11. A.I. Lemoine, “On queues with periodic Poisson input,” J. Appl. Prob., 18, 889–900 (1981).

    Google Scholar 

  12. L. G. Afanas’eva, “On periodic distribution of waiting time process,” in: Lecture Notes in Mathematics. Stability Problems for Stochastic Models, Springer-Verlag, Berlin (1984), pp. 1–21.

    Google Scholar 

  13. T. Rolski, “Approximation of periodic queues,” in: Proc. 1st World Congr. of the A. Bernoulli Society of Mathematical Statistics and Probability Theory [in Russian], Vol. 2, Tashkent (1985).

  14. B. V. Gnedenko, “On some problems of queuing theory,” in: Proc. All-Union Conf. on Probability Theory and Math. Statistics [in Russian], Yerevan (1960), pp. 15–24.

  15. B. V. Gnedenko, “Some problem formulations and results of queuing theory,” in: Trans. on Mathematical Queuing Theory [in Russian], Fizmatgiz, Moscow (1963), pp. 221–223.

    Google Scholar 

  16. B. V. Gnedenko, “On some unsolved problems in queuing theory,” in: Proc. 6th Intern. Telegraphic Congr., Munich (1970).

  17. A. A. Borovkov, Probabilistic Processes in Queuing Theory [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  18. S. Grandell, “Double stochastic Poisson process,” in: Lect. Notes Math., Springer, Berlin (1976).

    Google Scholar 

  19. T. Rolski, “Upper bounds for single server queues with doubly stochastic Poisson arrivals,” Math. Oper. Res., 111, 442–550 (1986).

    Google Scholar 

  20. T. Rolski, “Queues with nonstationary input,” Queueing Systems, 5, 113–130 (1989).

    Article  Google Scholar 

  21. N. Baurele and T. Rolski, “A monotonicity result for the workload process in Markov-modulated queues,” J. Appl. Prob., 35, 741–747 (1998).

    Article  Google Scholar 

  22. W. L. Smith, “Regenerative stochastic processes,” Proc. Roy. Soc. Ser. A, 232 (1955).

  23. L. G. Afanas’eva and E. E. Bashtova, “The queue with periodic double stochastic Poisson input,” in: Trans. 24th Intern. Seminar on Stability Problems for Stochastic Models, Jurmala (2004), pp. 80–87.

  24. L. G. Afanas’eva, “Limit distributions for queue with double stochastic periodic Poisson arrival process,” in: Abstracts of Papers Read at “Kolmogorov and Modern Mathematics” Conf. (2003), pp. 379–380.

  25. A. A. Kibkalo, “Quasistationary mode in M(t)/D/1/∞ queuing systems,” Vestn. Mosk. Univ., Ser. 1, Matem. Mekh., No. 5, 41–45 (1985).

  26. V. V. Kalashnikov, Qualitative Analysis of Complex Systems by the Method of Trial Functions [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  27. L. G. Afanas’eva and A. A. Lustina, “On a periodic solution of the Takach equation,” in: Proc. of the VNIISI Sem. on Problems of Stability of Stochastic Models [in Russian] (1984), pp. 22–27.

  28. L. G. Afanas’eva and A. A. Kibkalo, “Uniform estimates for the periodic solution in the M(t)/G/1/∞ system,” in: Proc. of the VNIISI Sem. on Problems of Stability of Stochastic Models [in Russian] (1985), pp. 9–14.

  29. E. E. Bashtova, “Periodic distribution in a one-channel queue system. Conditions of small loading,” in: Abstracts of Papers Read at Voronezh. Winter Math. School-2004 [in Russian] (2004), pp. 19–20.

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, Moscow, Russia

    L. G. Afanas’eva

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  1. L. G. Afanas’eva
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Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 54–69, January–February 2005.

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Afanas’eva, L.G. Queuing Systems with Cyclic Control Processes. Cybern Syst Anal 41, 43–55 (2005). https://doi.org/10.1007/s10559-005-0040-9

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  • DOI: https://doi.org/10.1007/s10559-005-0040-9

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