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Estimating parameters of the synchronous twofold-stochastic flow of events

  • Queueing Systems
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Abstract

Consideration was given to estimation of the parameters of the synchronous twofold-stochastic flow of events which makes up a mathematical model of the information flow of demands circulating in the queuing systems and networks. Two variants were studied. For the first variant, the problem of optimal estimation of the parameters of a synchronous flow of events with a finite arbitrary number of states was solved. The second variant differs in that the event flow operates in the environment where part of events is lost during the so-called dead time. Consideration was given to a synchronous flow with two states. The problem of estimating the length of the dead time in the conditions of continued dead time was solved. The results of numerical estimation based on the simulation model of the synchronous flow were presented for both variants.

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References

  1. Basharin, G.P., Kokotushkin, V.A., and Naumov, V.A., On the Method of Equivalent Changes of Calculation of Communication Network Fragments. I, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1979, no. 6, pp. 92–99.

  2. Basharin, G.P., Kokotushkin, V.A., and Naumov, V.A., On the Method of Equivalent Changes of Calculation of Communication Network Fragments. II, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1980, no. 1, pp. 55–61.

  3. Neuts, M.F., A Versatile Markov Point Process, J. Appl. Probab., 1979, vol. 16, pp. 764–779.

    Article  MATH  MathSciNet  Google Scholar 

  4. Lucantoni, D.M., New Results on the Single Server Queue with a Batch Markovian Arrival Process, Commun. Stat. Stochast. Models, 1991, vol. 7, pp. 1–46.

    Article  MATH  MathSciNet  Google Scholar 

  5. Lucantoni, D.M. and Neuts, M.F., Some Steady-state Distributions for the MAP/SM/1 Queue, Commun. Statist. Stochast. Models, 1994, vol. 10, pp. 575–598.

    Article  MATH  MathSciNet  Google Scholar 

  6. Vasilevskaya, T.P., Zavgorodnyaya, M.E., and Shmyrin, I.S., On the Relation betwen the Models of MAP-flow of Events and Asynchronous, Half-synchronous, and Synchronous Twofold-stochastic Flows of Events, Vest. Tomsk. Gos. Univ., 2004, no. 9 (II), pp. 138–144.

  7. Bushlanov, I.V. and Gortsev, A.M., Optimal Estimation of the States of Synchronous Twofold-stochastic Flow of Events, Avtom. Telemekh., 2004, no. 9, pp. 40–51.

  8. Khazen, E.M., Metody optimal’nykh statisticheskikh reshenii i zadachi optimal’nogo upravleniya (Methods of Optimal Statistical Solutions and Problems Optimal Control), Moscow: Sovetskoe Radio, 1968.

    Google Scholar 

  9. Kurochkin, S.S., Mnogomernye statisticheskie analizatory (Multidimensional Statistical Analyzers), Moscow: Atomizdat, 1968.

    Google Scholar 

  10. Gortsev, A.M. and Nezhel’skaya, L.A., Estimation of the “Dead Time” Length and Intensity of Synchronous Twofold-stochastic Flow of Events, Radiotekhnika, 2004, no. 10, pp. 8–16.

  11. Ivchenko, G.I., Kashtanov, V.A., and Kovalenko, I.N., Teoriya massovogo obsluzhivaniya (Queuing Theory), Moscow: Vysshaya Shkola, 1982.

    MATH  Google Scholar 

  12. Khinchin, A.Ya., Raboty po mathematicheskoi teorii massovogo obsluzhivaniya (Works on the Mathematical Queuing Theory), Moscow: Fizmatgiz, 1963.

    Google Scholar 

  13. Cramer, H., Mathematical Methods of Statistics, Princeton: Princeton Univ. Press, 1937. Translated under the title Matematicheskie metody statistiki, Moscow: Mir, 1975.

    Google Scholar 

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Original Russian Text © I.V. Bushlanov, A.M. Gortsev, L.A. Nezhel’skaya, 2008, published in Avtomatika i Telemekhanika, 2008, No. 9, pp. 76–93.

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Bushlanov, I.V., Gortsev, A.M. & Nezhel’skaya, L.A. Estimating parameters of the synchronous twofold-stochastic flow of events. Autom Remote Control 69, 1517–1533 (2008). https://doi.org/10.1134/S0005117908090075

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  • DOI: https://doi.org/10.1134/S0005117908090075

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