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International Conference on Queueing Theory and Network Applications

QTNA 2019: Queueing Theory and Network Applications pp 295–313Cite as

Sojourn Time Distribution in Fluid Queues

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 11688)

Abstract

We consider a fluid flow model with infinite buffer. We compute the Laplace-Stieltjes transform of the sojourn time proceeding in two steps. We first compute the stationary distribution of the buffer at arrival instants, using a change of clock. Secondly, we compute the transform of the time spent to empty the buffer. Numerical examples of sojourn time in a fluid flow are finally examined.

Keywords

  • Markov-modulated fluid flow
  • Sojourn time
  • Laplace-Stieljes transform

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  • DOI: 10.1007/978-3-030-27181-7_18
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References

  1. Asmussen, S.: Applied Probability and Queues. Springer, New York (2003). https://doi.org/10.1007/b97236

    CrossRef  MATH  Google Scholar 

  2. Bean, N.G., O’Reilly, M., Taylor, P.: Algorithms for return probabilities for stochastic fluid flows. Stoch. Models 21(1), 149–184 (2005)

    CrossRef  MathSciNet  Google Scholar 

  3. Horvàth, G., Horvàth, I., Almousa, S.A.D., Telek, M.: Numerical inverse Laplace transformation by concentrated matrix exponential distributions. In: Hautphenne, S., O’Reilly, M., Poloni, F. (eds.) Proceedings of the Tenth International Conference on Matrix-Analytic Methods in Stochastic Models, pp. 37–40 (2019). iSBN 978-0-646-99825-1 (Electronic version)

    Google Scholar 

  4. Horváth, G., Telek, M.: Sojourn times in fluid queues with independent and dependent input and output processes. Perform. Eval. 79, 160–181 (2014)

    CrossRef  Google Scholar 

  5. Kobayashi, H., Mark, B.L.: System Modeling and Analysis: Foundations of System Performance Evaluation, 1st edn. Prentice Hall Press, Upper Saddle River (2008)

    Google Scholar 

  6. Latouche, G., Nguyen, G.: Analysis of fluid flow models. Queueing Models Serv. Manage. 1(2), 1–29 (2018). arXiv:1802.04355

  7. Masuyama, H., Takine, T.: Multiclass markovian fluid queues. Queueing Syst. 56(3), 143–155 (2007). https://doi.org/10.1007/s11134-007-9019-8

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Ozawa, T.: Sojourn time distributions in the queue defined by a general QBD process. Queueing Syst. 53(4), 203–211 (2006)

    CrossRef  MathSciNet  Google Scholar 

  9. Whitt, W.: A unified framework for numerically inverting laplace transforms. INFORMS J. Comput. 18, 408–421 (2006)

    CrossRef  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Faculté d’informatique, Université de Namur, Avenue Grandgagnage, 21, 5000, Namur, Belgium

    Eleonora Deiana & Marie-Ange Remiche

  2. Département d’informatique, Université libre de Bruxelles, CP 212 - Boulevard du Triomphe, 1050, Bruxelles, Belgium

    Guy Latouche

Authors
  1. Eleonora Deiana
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  2. Guy Latouche
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  3. Marie-Ange Remiche
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Corresponding author

Correspondence to Eleonora Deiana .

Editor information

Editors and Affiliations

  1. University of Tsukuba, Tsukuba, Japan

    Prof. Tuan Phung-Duc

  2. Nara Institute of Science and Technology, Nara, Japan

    Prof. Shoji Kasahara

  3. Ghent University, Ghent, Belgium

    Sabine Wittevrongel

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Deiana, E., Latouche, G., Remiche, MA. (2019). Sojourn Time Distribution in Fluid Queues. In: Phung-Duc, T., Kasahara, S., Wittevrongel, S. (eds) Queueing Theory and Network Applications. QTNA 2019. Lecture Notes in Computer Science(), vol 11688. Springer, Cham. https://doi.org/10.1007/978-3-030-27181-7_18

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  • DOI: https://doi.org/10.1007/978-3-030-27181-7_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-27180-0

  • Online ISBN: 978-3-030-27181-7

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