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Analysis of Queueing Tandem with Feedback by the Method of Limiting Decomposition

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Information Technologies and Mathematical Modelling. Queueing Theory and Applications (ITMM 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 800))

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Abstract

The paper presents the study of a two-stage infinite-server queueing system with feedback. The service time at each stage is given by an arbitrary distribution function. The method of limiting decomposition is used for the study. As a result of the research, stationary distributions of the number of customers at each stage of the system are found. The obtained analytical results are compared with the asymptotic ones which were obtained in previous papers.

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References

  1. Boxma, O.J.: \(M/G/\infty \) Tandem Queues. Stoch. Proc. Apps. 18, 153–164 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ahn, H.-S., Duenyas, I., Lewis, M.E.: Optimal control of a two-stage tandem queuing system with flexible servers. Prob. Eng. Inf. Sci. 16, 453–469 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Moiseev, A., Nazarov, A.: Tandem of infinite-server queues with Markovian arrival process. In: Vishnevsky, V., Kozyrev, D. (eds.) DCCN 2015. CCIS, vol. 601, pp. 323–333. Springer, Cham (2016). doi:10.1007/978-3-319-30843-2_34

    Chapter  Google Scholar 

  4. Coffman, E.G., Kleinrock, L.: Feedback queueing models for time-shared systems. J. Ass. Comput. Mach. 15(4), 549–576 (1968)

    Article  MATH  Google Scholar 

  5. Foley, R.D., Disney, R.L.: Queues with delayed feedback. Adv. Appl. Probab. 15(1), 162–182 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  6. Moiseeva, S., Zadiranova, L.: Feedback in infinite-server queuing systems. In: Vishnevsky, V., Kozyrev, D. (eds.) DCCN 2015. CCIS, vol. 601, pp. 370–377. Springer, Cham (2016). doi:10.1007/978-3-319-30843-2_38

    Chapter  Google Scholar 

  7. König, D., Stoyan, D.: Methoden der Bedienungstheorie. Akademie-Verlag, Berlin (1976)

    MATH  Google Scholar 

  8. Kleinrock, L.: Queueing Systems: Volume 1, Theory, vol. 1. Wiley Interscience, New York (1975)

    MATH  Google Scholar 

  9. Sevastyanov, B.A.: An ergodic theorem for Markov processes and its application to telephone systems with fefusals. Theor. Prob. Appl. 2, 104–112 (1957)

    Article  Google Scholar 

  10. Takács, L.: On Erlang’s formula. Annal. Math. Stat. 40, 71–78 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  11. Grigelionis, B.: Asymptotic expansions in the compound Poisson limit theorem. Acta Applicandae Math. 58(1), 125–134 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  12. Iglehart, D.L.: Limit diffusion approximations for the many server queue and repairman problem. J. Appl. Prob. 2, 429–441 (1965)

    Article  MATH  Google Scholar 

  13. Borovkov, A.A.: On limit laws for service processes in multi-channel systems. Siberian Math. J. 8, 746–763 (1967)

    Article  MATH  Google Scholar 

  14. Whitt, W.: On the heavy-traffic limit theorem for \(GI/G/\infty \) queues. Adv. Appl. Prob. 14, 171–190 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  15. Nazarov, A.A., Moiseev, A.N.: Analysis of an open Non-Markovian \(GI-(GI|\infty )^K\) queueing network with high-rate renewal arrival process. Prob. Inf. Trans. 49(2), 167–178 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  16. Moiseev, A., Nazarov, A.: Queueing network \(MAP-(GI-\infty )^K\) with high-rate arrivals. Europ. J. Oper. Res. 254, 161–168 (2016)

    Article  MATH  MathSciNet  Google Scholar 

  17. Nazarov, A.A., Moiseeva, S.P., Morozova, A.S.: Analysis of infinite-server queueing system with feedback by the method of limiting decomposition (in Russian). Comput. Technol. 13(55), 88–92 (2008)

    MATH  Google Scholar 

  18. Nazarov, A.A., Terpugov, A.F.: Queueing Theory - Tutorial. NTL, Tomsk (2010). (in Russian)

    Google Scholar 

  19. Nazarov, A.A., Moiseev, A.N.: Distributed system of processing of data of physical experiments. Rus. Phys. J. 57(7), 984–990 (2014)

    Article  Google Scholar 

  20. Moiseev, A., Nazarov, A.: Investigation of high intensive general flow. In: 4th International Conference Problems of Cybernetics and Informatics (PCI 2012), pp. 161–163. IEEE, Baku (2012)

    Google Scholar 

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Acknowledgments

This work was partially supported (A. Moiseev) by the Ministry of Education and Science of the Russian Federation [Agreement number 02.a03.21.0008].

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Authors and Affiliations

  1. Tomsk State University, Tomsk, Russia

    Maria Shklennik, Svetlana Moiseeva & Alexander Moiseev

  2. Peoples’ Friendship University of Russia (RUDN University), Moscow, Russia

    Alexander Moiseev

Authors
  1. Maria Shklennik
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  2. Svetlana Moiseeva
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  3. Alexander Moiseev
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Corresponding author

Correspondence to Maria Shklennik .

Editor information

Editors and Affiliations

  1. Belarusian State University, Minsk, Belarus

    Alexander Dudin

  2. Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Kazan National Research Technological University, Kazan, Russia

    Alexander Kirpichnikov

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Shklennik, M., Moiseeva, S., Moiseev, A. (2017). Analysis of Queueing Tandem with Feedback by the Method of Limiting Decomposition. In: Dudin, A., Nazarov, A., Kirpichnikov, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2017. Communications in Computer and Information Science, vol 800. Springer, Cham. https://doi.org/10.1007/978-3-319-68069-9_12

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  • DOI: https://doi.org/10.1007/978-3-319-68069-9_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68068-2

  • Online ISBN: 978-3-319-68069-9

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