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Estimation of the Probability Density Parameters of the Interval Duration Between Events in Correlated Semi-synchronous Event Flow of the Second Order by the Method of Moments

  • Lyudmila Nezhelskaya
  • Diana TumashkinaEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1109)

Abstract

We consider a correlated semi-synchronous event flow of the second order with two states; it is one of the mathematical models for an incoming stream of claims (events) in modern digital integral servicing networks, telecommunication systems and satellite communication networks. We solve the problem of estimating the probability density parameters of the values of the interval duration between the moments of the events occurrence by the method of moments for general and special cases of setting the flow parameters. The results of statistical experiments performed on a flow simulation model are given.

Keywords

Correlated semi-synchronous event flow of the second order Probability density Estimation of the parameters Method of moments 

References

  1. 1.
    Basharin, G.P., Kokotushkin, V.A., Naumov, V.A.: On the equivalent substitutions method for computing fragments of communication networks. Izv. Akad. Nauk USSR. Tekhn. Kibern. 6, 92–99 (1979). (in Russian)zbMATHGoogle Scholar
  2. 2.
    Neuts, M.F.: A versatile Markov point process. J. Appl. Probab. 16, 764–779 (1979)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cox, D.R.: The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables. In: Proceedings of the Cambridge Philosophical Society, vol. 51, no. 3, pp. 433–441 (1955)Google Scholar
  4. 4.
    Lucantoni, D.M.: New results on the single server queue with a bath Markovian arrival process. Commun. Stat. Stoch. Models 7, 1–46 (1991)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Dudin, A.N., Klimenok, V.I.: Queueing Systems with Correlated Flows. Belarus Gos. Univ., Minsk (2000). (in Russian)Google Scholar
  6. 6.
    Basharin, G.P., Gaidamaka, Y.V., Samouylov, K.E.: Mathematical theory of teletraffic and its application to the analysis of multiservice communication of next generation networks. Autom. Control Comput. Sci. 47(2), 62–69 (2013)CrossRefGoogle Scholar
  7. 7.
    Klimenok, V., Dudin, A., Vishnevsky, V.: Tandem queueing system with correlated input and cross-traffic. In: Kwiecień, A., Gaj, P., Stera, P. (eds.) CN 2013. CCIS, vol. 370, pp. 416–425. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-38865-1_42CrossRefGoogle Scholar
  8. 8.
    Vishnevsky, V.M., Semenova, O.V.: Polling Systems: Theory and Applications for Broadband Wireless Networks. Academic Publishing, London (2012)Google Scholar
  9. 9.
    Nezhelskaya, L.: Optimal state estimation in modulated MAP event flows with unextendable dead time. In: Dudin, A., Nazarov, A., Yakupov, R., Gortsev, A. (eds.) ITMM 2014. CCIS, vol. 487, pp. 342–350. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-13671-4_39CrossRefGoogle Scholar
  10. 10.
    Nezhelskaya, L., Tumashkina, D.: Optimal state estimation of semi-synchronous event flow of the second order under its complete observability. In: Dudin, A., Nazarov, A., Moiseev, A. (eds.) ITMM/WRQ -2018. CCIS, vol. 912, pp. 93–105. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-97595-5_8CrossRefGoogle Scholar
  11. 11.
    Kalyagin, A.A., Nezhelskaya, L.A.: Comparison of MP- and MM-estimates of the duration of the dead time in generalized semi-synchronous event flow. Tomsk State Univ. J. Control Comput. Sci. 3(32), 23–32 (2015). (in Russian)Google Scholar
  12. 12.
    Nezhel’skaya, L.: Probability density function for modulated MAP event flows with unextendable dead time. In: Dudin, A., Nazarov, A., Yakupov, R. (eds.) ITMM 2015. CCIS, vol. 564, pp. 141–151. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-25861-4_12CrossRefGoogle Scholar
  13. 13.
    Gortsev, A.M., Nezhel’skaya, L.A.: Estimate of parameters of synchronously alternating Poisson stream of events by the moment method. Telecommun. Radio Eng. 50(1), 56–63 (1996)Google Scholar
  14. 14.
    Gortsev, A.M., Klimov, I.S.: Estimation of the parameters of an alternating Poisson stream of events. Telecommun. Radio Eng. 48(10), 40–45 (1993)Google Scholar
  15. 15.
    Nezhelskaya, L.A., Tumashkina, D.A.: Optimal state estimation of semi-synchronous event flow of the second order with non-extending dead time. Tomsk State Univ. J. Control Comput. Sci. 46, 73–82 (2019). (in Russian)Google Scholar
  16. 16.
    Nezhelskaya, L.A.: The joint probability density of the duration of the intervals of modulated MAP-flow of events and the conditions of the flow recurrence. Tomsk State Univ. J. Control Comput. Sci. 1(30), 57–67 (2015). (in Russian)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.National Research Tomsk State UniversityTomskRussia

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