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Belarusian Workshop on Queueing Theory

BWWQT 2013: Modern Probabilistic Methods for Analysis of Telecommunication Networks pp 11–19Cite as

On Mean Return Time in Queueing System with Constant Service Time and Bi-level Hysteric Policy

  • Conference paper

Part of the Communications in Computer and Information Science book series (CCIS,volume 356)

Abstract

Single server queueing system with two Poisson input flows of rate λ 1 and λ 2, finite queue of size R − 1 < ∞ and bi-level hysteretic policy is considered. Customers of λ 1 flow are served with relative priority. Customers of both flows are served with the same constant service time. Bi-level hysteretic policy implies that system may be in three states (normal, overload, blocking), depending on the total number of customers present in it. New method for calculation of mean return time to normal operation state is proposed.

Keywords

  • SIP
  • hysteric control
  • constant service rate
  • queueing system
  • mean return time

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References

  1. ITU-T Recommendation Q.704. Signalling System No.7 – Message Transfer Part, Signalling network functions and messages (1996)

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  2. Abaev, P., Gaidamaka, Y., Pechinkin, A., Razumchik, R., Shorgin, S.: Simulation of overload control in SIP server networks. In: Proc. of the 26th European Conference on Modelling and Simulation, pp. 533–539 (2012)

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  3. Hilt, V., Noel, E., Shen, C., Abdelal, A.: Design Considerations for Session Initiation Protocol (SIP) Overload Control. RFC6357 (2011)

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  4. Abaev, P., Pechinkin, A., Razumchik, R.: Analysis of queueing system with constant service time for SIP server hop-by-hop overload control. In: Dudin, A., et al. (eds.) BWWQT 2012. CCIS, vol. 356. Springer, Heidelberg (2012)

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Author information

Authors and Affiliations

  1. Peoples Friendship University, Ordzhonikidze str., 3, 117198, Moscow, Russia

    Pavel Abaev, Alexander Pechinkin & Rostislav Razumchik

  2. Institute of Informatics Problems of Russian Academy of Sciences, Vavilova str., 44-2, 119333, Moscow, Russia

    Alexander Pechinkin & Rostislav Razumchik

Authors
  1. Pavel Abaev
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  2. Alexander Pechinkin
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  3. Rostislav Razumchik
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Editor information

Editors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Belarusian State University, 220030, Minsk, Belarus

    Alexander Dudin & Valentina Klimenok & 

  2. Laboratory of Applied Probabilistic Analysis, Belarusian State University, 4 Nezavisimosti Avenue, 220030, Minsk, Belarus

    Gennadiy Tsarenkov & Sergey Dudin & 

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Cite this paper

Abaev, P., Pechinkin, A., Razumchik, R. (2013). On Mean Return Time in Queueing System with Constant Service Time and Bi-level Hysteric Policy. In: Dudin, A., Klimenok, V., Tsarenkov, G., Dudin, S. (eds) Modern Probabilistic Methods for Analysis of Telecommunication Networks. BWWQT 2013. Communications in Computer and Information Science, vol 356. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35980-4_2

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  • DOI: https://doi.org/10.1007/978-3-642-35980-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35979-8

  • Online ISBN: 978-3-642-35980-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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