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On the Problems of Queues in Mixed Type Queuing Systems with Random Quantity of Sources and Size-Limited Queues

  • Alexander Kirpichnikov
  • Anton TitovtsevEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 800)

Abstract

The article proposes the technique to investigate the behavior of the moments of numerical characteristics of mixed-type queuing system with a random number of sources upon the change of demands input stream intensity and size-limited queues based on the calculation of boundary values of the number of servicing devices at which the mean squared deviation (MSD) of the investigated quantity does not exceed its mathematical expectation. For the first time the linear nature of behavior of boundary values of the number of service facilities with the change of the given intensity of demands input stream is determined numerically. The article also considers various types of queues arising in queuing systems. The concept of an N-th order queue is introduced, and generalized Little’s formulas for N-th order queues in queuing systems of various types are presented.

Keywords

Queue Physical queue Real queue Quality of service (QoS) Queuing system M/M/m/K Service facility 

References

  1. 1.
    Cohen, J.W.: Certain delay problems for a full availability trunk group loaded by two sources. Commun. News 16(3), 105–113 (1956)MathSciNetGoogle Scholar
  2. 2.
    Takagi, H.: Explicit delay distribution in first-come first-served M/M/m/K and M/M/m/K/n queues and mixed loss-delay system. Int. J. Pure Appl. Math. 40(2), 185–200 (2007)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Kirpichnikov, A.P., Titovtsev, A.S.: Open systems of multicomponent flows differentiated service. Ciência e Técnica Vitivinícola 29(7), 108–122 (2014)Google Scholar
  4. 4.
    Titovtsev, A.: Sistemy differentsirovannogo obsluzhivaniya polikomponentnykh potokov. Modeli i kharakteristiki [Systems of differentiated services multicomponent flows. Models and specifications]. LAP LAMBERT Academic Publishing GmbH & Co. KG Publ., Saarbrücken (2012). (in Russian)Google Scholar
  5. 5.
    Kirpichnikov, A.P.: Prikladnaya teoriya massovogo obsluzhivaniya [Applied queuing theory]. Publishing office of KSU Publ., Kazan (2008). (in Russian)Google Scholar
  6. 6.
    Kirpichnikov, A.P.: Metody prikladnoy teorii massovogo obsluzhivaniya. Publishing office of KSU Publ., Kazan (2011). (in Russian)Google Scholar
  7. 7.
    Kirpichnikov, A., Titovtsev, A.: Mathematical model of a queuing system with arbitrary quantity of sources and size-limited queue. Int. J. Pure Appl. Math. 106(2), 649–661 (2016)CrossRefGoogle Scholar
  8. 8.
    Kirpichnikov, A., Titovtsev, A.: Physical and mathematical queues in the applied queuing theory. Int. J. Pure Appl. Math. 108(2), 409–418 (2016)CrossRefGoogle Scholar
  9. 9.
    Titovtsev, A.: The concept of higher orders queues in the queuing theory. Int. J. Pure Appl. Math. 109(2), 451–457 (2016)CrossRefGoogle Scholar
  10. 10.
    Saaty, T.L.: Elements of Queueing Theory with Applications. McGRAW-HILL book company Inc., New York, Toronto, London (1961)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Kazan National Research Technological UniversityKazanRussia

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