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A Cyclic Queueing System with Priority Customers and T-Strategy of Service

  • Anatoly Nazarov
  • Svetlana Paul
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 678)

Abstract

We review the queuing system, the input of which is supplied with the Poisson process of priority customers and N number of the Poisson processes of non-priority customers. Durations of service for both priority and non-priority customers have a distribution functions of A(x) and \(B_n(x)\) for applications from priority flow and for customers from n flow (\(n = 1\ldots N\)) respectively. By using methods of systems with server vacations and asymptotic analysis in conditions of a large load we have found the asymptotic probability distribution of a value of an unfinished work. It is shown that this distribution is exponential.

Keywords

Cyclic queueing system with server vacations Priority customers Asymptotic analysis Exponential distribution 

Notes

Acknowledgments

The work is performed under the state order of the Ministry of Education and Science of the Russian Federation (No. 1.511.2014/K).

References

  1. 1.
    Pechinkin, A.V., Sokolov, I.A.: Queueing system with an unreliable device in discrete time. J. Inform. Appl. 5(4), 6–17 (2005). (in Russian)Google Scholar
  2. 2.
    Saksonov, E.A.: Method of the calculation of probabilities of modes for one-line queueing systems with the server vacation. J. Autom. Tele-Mech. 1, 101–106 (1995). (in Russian)MathSciNetGoogle Scholar
  3. 3.
    Nazarov, A.A., Terpugov, A.F.: Queueing Theory: Educational Material. NTL, Tomsk (2004). (in Russian)Google Scholar
  4. 4.
    Nazarov, A.A., Paul, S.V.: Research of queueing system with the server vacation that is controlled by T-strategy. In: Proceedings of International Science Conference Theory of Probabilies, Random Processes, Mathematical Statistics and Applications, pp. 202–207 (2015). (in Russian)Google Scholar
  5. 5.
    Nazarov, A., Paul, S.: A number of customers in the system with server vacations. In: Vishnevsky, V., Kozyrev, D. (eds.) DCCN 2015. CCIS, vol. 601, pp. 334–343. Springer, Heidelberg (2016). doi: 10.1007/978-3-319-30843-2_35 CrossRefGoogle Scholar
  6. 6.
    Moiseeva, E.A., Nazarov, A.A.: Research of RQ-system MMP—GI—1 by using method of asymptotic analysis under large load. TSUs herald/messenger. Adm. Calc. Tech. Inform. 4(25), 83–94 (2013). (in Russian)Google Scholar
  7. 7.
    Nazarov, A.A., Moiseev, A.N.: Analysis of an open non-Markovian GI(GI—\(\rm \infty \))K queueing network with high-rate renewal arrival process. Probl. Inf. Transm. 49(2). doi: 10.1134/S0032946013020063

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Tomsk State UniversityTomskRussia

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