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Probl. Peredachi Inf., 2016, Volume 52, Issue 1, Pages 16–26 (Mi ppi2194)  

This article is cited in 7 scientific papers (total in 7 papers)

Large Systems

Analysis of queues with hyperexponential arrival distributions

V. N. Tarasov

Povolzhskiy State University of Telecommunications and Informatics, Samara, Russia

Abstract: We study $\mathrm{H_2/H}_2/1$, $\mathrm{H_2/M}/1$ and $\mathrm{M/H}_2/1$ queueing systems with hyperexponential arrival distributions for the purpose of finding a solution for the mean waiting time in the queue. To this end we use the spectral decomposition method for solving the Lindley integral equation. For practical application of the obtained results, we use the method of moments. Since the hyperexponential distribution law has three unknown parameters, it allows to approximate arbitrary distributions with respect to the first three moments. The choice of this distribution law is due to its simplicity and the fact that in the class of distributions with coefficients of variation greater than 1, such as log-normal, Weibull, etc., only the hyperexponential distribution makes it possible to obtain an analytical solution.

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English version:
Problems of Information Transmission, 2016, 52:1, 14–23

Bibliographic databases:

UDC: 621.391.1+621.395
Received: 17.11.2014
Revised: 10.11.2015

Citation: V. N. Tarasov, “Analysis of queues with hyperexponential arrival distributions”, Probl. Peredachi Inf., 52:1 (2016), 16–26; Problems Inform. Transmission, 52:1 (2016), 14–23

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. Tarasov, N. Bakhareva, I. Kartashevskiy, L. Lipilina, “Comparison of Different Approaches to Determining the Mean Delay Time in a Queuing System H2/M/1”, 2017 4Th International Scientific-Practical Conference Problems of Infocommunications-Science and Technology (PIC S&T), IEEE, 2017, 273–276  crossref  isi
    2. A. V. Lebedev, “Maximum remaining service time in infinite-server queues”, Problems Inform. Transmission, 54:2 (2018), 176–190  mathnet  crossref  isi  elib
    3. V. N. Tarasov, E. G. Akhmetshina, “Srednee vremya ozhidaniya v sisteme massovogo obsluzhivaniya $H_2/H_2/1$ s zapazdyvaniem”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 22:4 (2018), 702–713  mathnet  crossref  elib
    4. V. N. Tarasov, “Extension of the class of queueing systems with delay”, Autom. Remote Control, 79:12 (2018), 2147–2158  mathnet  crossref  crossref  isi  elib
    5. V. Tarasov, “Research of dual systems H$_2$/M/1 and M/H$_2$/1 with exponential and hyperexponential input distributions”, 2018 International Scientific-Practical Conference: Problems of Infocommunications Science and Technology (PIC S&T), IEEE, 2018, 793–796  crossref  isi
    6. V. Tarasov, N. Bakhareva, “Research of non-Markovian queuing networks”, 2018 International Scientific-Practical Conference: Problems of Infocommunications Science and Technology (PIC S&T), IEEE, 2018, 824–828  crossref  isi
    7. V. N. Tarasov, “Analysis and comparison of two queueing systems with hypererlangian input distributions”, Radio Electron. Comput. Sci. Control, 2018, no. 4, 61–70  crossref  isi
  • Проблемы передачи информации Problems of Information Transmission
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