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On Regenerative Estimation of Extremal Index in Queueing Systems

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Distributed Computer and Communication Networks: Control, Computation, Communications (DCCN 2021)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 13144))

Abstract

In this paper, the extremal behavior of the waiting time and queue size in some queueing systems is considered, based on the regenerative property of these systems. The basic properties of the extremal index of a stationary sequence are discussed, which further relate to the maximum waiting time and queue size processes. Simulation results are presented with the aim to construct estimate and to evaluate the sensitivity of the extremal index to the level of the exceedance of the process of a threshold. We discuss the additional conditions placed on the normalizing sequences to compare extremal indexes of two different stationary sequences of random variables. This analysis is then applied to compare the waiting time extremal indexes in two M/G/1 systems with the ordered service times having Pareto distribution.

The research of E. Morozov is supported by Russian Foundation for Basic Research, projects No. 19-07-00303. The research of I. Peshkova, M. Maltseva has been prepared with the support of Russian Science Foundation according to the research project No.21-71-10135 https://rscf.ru/en/ project/21-71-10135/.

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Authors and Affiliations

  1. Petrozavodsk State University, Lenin Street 33, Petrozavodsk, 185910, Russia

    Irina Peshkova, Evsey Morozov & Maria Maltseva

  2. Institute of Applied Mathematical Research of the Karelian Research Centre of RAS, Pushkinskaya Street 11, Petrozavodsk, 185910, Russia

    Evsey Morozov

  3. Moscow Center for Fundamental and Applied Mathematics, Moscow State University, Moscow, 119991, Russia

    Evsey Morozov

Authors
  1. Irina Peshkova
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  2. Evsey Morozov
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  3. Maria Maltseva
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Corresponding author

Correspondence to Irina Peshkova .

Editor information

Editors and Affiliations

  1. V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia

    Vladimir M. Vishnevskiy

  2. Applied Probability and Informatics Department, RUDN University, Moscow, Russia

    Konstantin E. Samouylov

  3. V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia

    Dmitry V. Kozyrev

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Peshkova, I., Morozov, E., Maltseva, M. (2021). On Regenerative Estimation of Extremal Index in Queueing Systems. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2021. Lecture Notes in Computer Science(), vol 13144. Springer, Cham. https://doi.org/10.1007/978-3-030-92507-9_21

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  • DOI: https://doi.org/10.1007/978-3-030-92507-9_21

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-92507-9

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