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On the Blocking Probability and Loss Rates in Nonpreemptive Oscillating Queueing Systems

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Analytical and Stochastic Modelling Techniques and Applications (ASMTA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9845))

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Abstract

We analyze busy period related characteristics for oscillating systems, proposing a method to compute the mean length of busy periods for nonpreemptive oscillating \(M^ X/G/1/(n,a,b)\) systems. We further evaluate customer loss rates in busy cycles and the long-run blocking probability for such systems using the proposed method and earlier results from the authors for the mean number of customer losses in busy periods.

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References

  1. Chydzinski, A.: The \(M/G-G/1\) oscillating queueing system. Queueing Syst. 42(3), 255–268 (2002)

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  2. Chydzinski, A.: The oscillating queue with finite buffer. Perform. Eval. 57(3), 341–355 (2004)

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  3. Ferreira, F., Pacheco, A., Ribeiro, H.: Moments of losses during busy-periods of regular and nonpreemptive oscillating \(M^X/G/1/n\) systems. Annals of Operations Research (2016, in press)

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  4. Kulkarni, V.G.: Modeling and Analysis of Stochastic Systems. Chapman and Hall, London (1995)

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  5. Pacheco, A., Ribeiro, H.: Consecutive customer losses in regular and oscillating \(M^X/G/1/n\) systems. Queueing Syst. 58(2), 121–136 (2008)

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  6. Pacheco, A., Ribeiro, H.: Moments of the duration of busy-periods of \(M^X/G/1/n\) systems. Probab. Eng. Inf. Sci. 22, 1–8 (2008)

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Acknowledgments

This research was financed by Portuguese funds through FCT (Fundação para a Ciência e a Tecnologia), within the Projects UID/MAT/00013/2013 and UID/Multi/04621/2013.

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Authors and Affiliations

  1. Departamento de Matemática, CMAT and CEMAT, Universidade de Trás-os-Montes e Alto Douro, UTAD, Quinta dos Prados, 5000-801, Vila Real, Portugal

    Fátima Ferreira

  2. CEMAT and Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

    António Pacheco

  3. Escola Superior de Tecnologia e Gestão and CEMAT, Instituto Politécnico de Leiria, Campus 2, Morro do Lena - Alto do Vieiro, 2411-901, Leiria, Portugal

    Helena Ribeiro

Authors
  1. Fátima Ferreira
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  2. António Pacheco
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  3. Helena Ribeiro
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Corresponding author

Correspondence to António Pacheco .

Editor information

Editors and Affiliations

  1. Ghent University , Gent, Belgium

    Sabine Wittevrongel

  2. University of Tsukuba , Tsukuba, Japan

    Tuan Phung-Duc

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© 2016 Springer International Publishing Switzerland

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Ferreira, F., Pacheco, A., Ribeiro, H. (2016). On the Blocking Probability and Loss Rates in Nonpreemptive Oscillating Queueing Systems. In: Wittevrongel, S., Phung-Duc, T. (eds) Analytical and Stochastic Modelling Techniques and Applications. ASMTA 2016. Lecture Notes in Computer Science(), vol 9845. Springer, Cham. https://doi.org/10.1007/978-3-319-43904-4_11

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  • DOI: https://doi.org/10.1007/978-3-319-43904-4_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-43903-7

  • Online ISBN: 978-3-319-43904-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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