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Workload analysis of a two-queue system by formulating a boundary value problem

  • Queues And Networks 4
  • Conference paper
  • First Online:
Modelling and Performance Evaluation Methodology

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 60))

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Résumé

Nous étudions un nouveau protocole de communication qui réalise l'insertion de messages spéciaux dans un flot de messages réguliers. L'analyse se ramène à l'étude de deux files d'attente et d'un serveur unique. La discipline de service dépend de la charge d'une des files. Nous calculons, à l'état stationnaire, les transformées de Fourier -Stieltjes et Laplace- Stieltjes de la distribution de la charge du système, en résolvant deux équations fonctionnelles.

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References

  1. BLANC, J.P.C.: Application of the theory of boundary value problems in the analysis of a queueing model with paired services. Thesis, University of Utrecht, Utrecht, (1982).

    Google Scholar 

  2. BACCELLI, F. and FAYOLLE, G.: Two dimensional diffusion processes with boundary and jumps. Application to coupled queues. Rapport de Recherche INRIA, No 160, (1982).

    Google Scholar 

  3. BOXMA, O.J. and COHEN, J.W.: The M/G/1 queue with alternating service formaluted as a Riemann-Hilbert problem. Performance 81, F.J. Kylstra Ed. North-Holland Publishing Company, (1981).

    Google Scholar 

  4. COHEN, J.W.: The single server. Amsterdam, North-Holland Publishing Company, (1969).

    Google Scholar 

  5. COHEN, J.W.: On the M/G/2 queueing model. Stoch. Proc. Appl. 12, 3, (1982).

    Google Scholar 

  6. FAYOLLE, G.: Méthodes analytiques pour les files d'attente couplées. Thèse, Université Paris VI, (1979).

    Google Scholar 

  7. FAYOLLE, G. and IASNOGORODSKI, R.: Two coupled processors: the reduction to a Riemann-Hilbert problem. Wahrscheinlichkeitsth 47, 325–351, (1979).

    Google Scholar 

  8. FAYOLLE, G. and KING, P.J.B. and MITRANI, I.: The solution of certain two-dimensional Markov models. Adv. Appl. Prob. 14, 295–308, (1982).

    Google Scholar 

  9. GHAKOV, F.D.: Boundary value problems. Pergamon Press, Oxford, (1966).

    Google Scholar 

  10. IASNOGORODSKI, R.: Problèmes-frontières dans les files d'attente. Thèse, Université Paris VI, (1979).

    Google Scholar 

  11. KLEINROCK, L.: Queueing systems. Vol. 1, Academic Press, (1975).

    Google Scholar 

  12. MIKOU, N.: Modèles de réseaux de files d'attente avec pannes. Thèse, Université Paris XI, Orsay, (1981).

    Google Scholar 

  13. MUSKHELISHVILI, N.I.: Singular integral equations. Groningen, Holland-Moscow, P. Noordhoff, (1946).

    Google Scholar 

  14. TAKÁCS, L.: Introduction to the theory of queues. Oxford Univ. Press, (1952).

    Google Scholar 

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Authors and Affiliations

  1. INRIA Domaine de Voluceau Rocquencourt, 78150, Le Chesnay, France

    Philippe Nain

Authors
  1. Philippe Nain
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F. Baccelli G. Fayolle

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© 1984 Springer-Verlag

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Nain, P. (1984). Workload analysis of a two-queue system by formulating a boundary value problem. In: Baccelli, F., Fayolle, G. (eds) Modelling and Performance Evaluation Methodology. Lecture Notes in Control and Information Sciences, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0005190

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  • DOI: https://doi.org/10.1007/BFb0005190

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13288-2

  • Online ISBN: 978-3-540-38838-8

  • eBook Packages: Springer Book Archive

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