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Computational Algorithm for an Analysis of a Single-Line Queueing System with Arrived Alternating Poisson Flow

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Distributed Computer and Communication Networks: Control, Computation, Communications (DCCN 2021)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 13144))

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Abstract

The M/G/1 queue is considered for a case when an alternating Poisson flow takes place on the input. The analysis is based on an embedded Markov chain, built on the instants of service ending. Various algorithms are elaborated for the calculation of the distribution of the system’ states and various numerical indices.

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References

  1. van Hoorn, M.H., Seelen, L.P.: The SPP/G/1 queue: a single server queue with a switched Poisson process as input process. Oper. Res. Spektrum 5(4), 207–218 (1983). https://doi.org/10.1007/BF01719844

    Article  MATH  Google Scholar 

  2. Regterschot, G.J.K., De Smit, J.H.A.: The queue M/G/1 with Markov modulated arrivals and services. Math. Oper. Res. 11(3), 465–483 (1986)

    Article  MathSciNet  Google Scholar 

  3. Neuts, M.F.: Structured stochastic matrices of MG-1 type and their applications. Dekker (1989)

    Google Scholar 

  4. Rossiter, M.H.: The switched Poisson process and the SPP/G/1 queue. In: Bonatti, M. (ed.) ITC-12, pp. 1406–1412. North-Holland (1989)

    Google Scholar 

  5. Takine, T., Takahashi, Y.: On the relationship between queue lengths at a random instant and at a departure in the stationary queue with BMAP arrivals. Communications in statistics. Stochast. Models 14(3), 601–610 (1998)

    Google Scholar 

  6. Asmussen, S.: Ladder heights and the Markov-modulated M/G/1 queue. Stochast. Processes Appl. 37(2), 313–326 (1991)

    Article  MathSciNet  Google Scholar 

  7. Takine, T.: A new recursion for the queue length distribution in the stationary BMAP/G/1 queue. Stoch. Model. 16(2), 335–341 (2000)

    Article  MathSciNet  Google Scholar 

  8. Du, Q.: A monotonicity result for a single-server queue subject to a Markov-modulated Poisson process. J. Appl. Probability, 1103–1111 (1995)

    Google Scholar 

  9. Fischer, W., Meier-Hellstern, K.: The Markov-modulated Poisson process (MMPP) cookbook. Perform. Eval. 18(2), 149–171 (1993)

    Article  MathSciNet  Google Scholar 

  10. Andronov, A.M., Dalinger, I.M.: Poisson flows with alternating intensity and their application. Autom. Control. Comput. Sci. 54(5), 403–411 (2020). https://doi.org/10.3103/S0146411620050028

    Article  Google Scholar 

  11. Tang, L.C., Prabhu, N.U., Pacheco, A.: Markov-modulated processes and semiregenerative phenomena. World Scientific (2008)

    Google Scholar 

  12. Sleeper, A.: Six sigma distribution modeling. McGraw Hill Professional (2007)

    Google Scholar 

  13. Gnedenko, B.V., Kovalenko, I.N.: Introduction to queueing theory. Birkhäuser (1989)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Transport and Telecommunication Institute, Lomonosov Street, 1, Riga, 1019, Latvia

    Alexander M. Andronov & Nadezda Spiridovska

  2. Saint-Petersburg State University of Civil Aviation, Pilotov Street, 38, Saint-Petersburg, 196210, Russia

    Iakov M. Dalinger

Authors
  1. Alexander M. Andronov
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  2. Iakov M. Dalinger
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  3. Nadezda Spiridovska
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Corresponding author

Correspondence to Nadezda Spiridovska .

Editor information

Editors and Affiliations

  1. V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia

    Vladimir M. Vishnevskiy

  2. Applied Probability and Informatics Department, RUDN University, Moscow, Russia

    Konstantin E. Samouylov

  3. V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia

    Dmitry V. Kozyrev

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Andronov, A.M., Dalinger, I.M., Spiridovska, N. (2021). Computational Algorithm for an Analysis of a Single-Line Queueing System with Arrived Alternating Poisson Flow. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2021. Lecture Notes in Computer Science(), vol 13144. Springer, Cham. https://doi.org/10.1007/978-3-030-92507-9_13

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  • DOI: https://doi.org/10.1007/978-3-030-92507-9_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92506-2

  • Online ISBN: 978-3-030-92507-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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