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Asymptotic analysis for closed multichain queueing networks with bottlenecks

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Abstract

We consider a two-chain exponential queueing network with a large number of customers that consists of one infinite-server (IS) station and two processor-sharing (PS) or FCFS single-server stations. The asymptotic behavior of the partition function is studied for such a network when one or both PS (FCFS) nodes are heavily loaded. The results are derived using methods of multidimensional complex analysis (the theory of homologies and residues) and the saddle-point method.

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References

  1. L.V. Ahlfors and L. Sario,Riemann Surfaces (Princeton Univ. Press, Princeton, NJ, 1960).

    Google Scholar 

  2. L.A. Aizenberg and A.P. Yuzhakov,Integral Representations and Residues in Multidimensional Complex Analysis (American Mathematical Society, Providence, RI, 1983).

    Google Scholar 

  3. F. Baskett, K.M. Chandy, R.R. Muntz and F.G. Palacios, Open, closed, and mixed networks of queues with different classes of customers,J. ACM 22 (1975) 248–260.

    Google Scholar 

  4. A. Bertozzi and J. McKenna, Multidimensional residues, generating functions, and their application to queueing networks,SIAM Review 35 (1993) 239–268.

    Google Scholar 

  5. A. Birman and Y. Kogan, Asymptotic evaluation of closed queueing networks with many stations,Communications in Statistics. Stochastic Models 8 (1992) 543–564.

    Google Scholar 

  6. J.J. Gordon, The evaluation of normalizing constants in closed queueing networks,Operations Research 38 (1990) 863–869.

    Google Scholar 

  7. P. Griffiths and J. Harris,Principles of Algebraic Geometry (Wiley, New York, 1978).

    Google Scholar 

  8. Y. Kogan and A. Birman, Asymptotic analysis of closed queueing networks with bottlenecks, in:IFIP Transactions C-5, Performance of Distributed Systems and Integrated Communication Networks, eds. T. Hasegawa, H. Takagi and Y. Takahashi (North-Holland, Amsterdam, 1992).

    Google Scholar 

  9. Y. Kogan, Another approach to asymptotic expansions for large closed queueing networks,Operations Research Letters 11 (1992) 317–321.

    Google Scholar 

  10. V.A. Malyshev and A.V. Yakovlev, Condensation in large closed Jackson networks, Rapports de Recherche de l'INRIA-Rocquencourt, #1854 (1993).

  11. J. McKenna and D. Mitra, Integral representations and asymptotic expansions for closed Markovian queueing networks: Normal usage,Bell System Technical Journal 61 (1982) 661–683.

    Google Scholar 

  12. J. McKenna, D. Mitra and K.G. Ramakrishnan, A class of closed Markovian queueing networks: Integral representations, asymptotic expansions, generalizations,The Bell System Technical Journal 60 (1981) 599–641.

    Google Scholar 

  13. J.J. Rotman,An Introduction to Algebraic Topology (Springer-Verlag, New York, 1988).

    Google Scholar 

  14. A.G. Vitushkin (ed.),Several Complex Variables I (Springer-Verlag, Berlin, 1990).

    Google Scholar 

  15. J. Wang and K.W. Ross, Asymptotic analysis for closed multiclass queueing networks in critical usage,Queueing Systems 16 (1994) 167–191.

    Google Scholar 

  16. R. Wong,Asymptotic Approximations of Integrals (Academic Press, Boston, 1986).

    Google Scholar 

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Authors and Affiliations

  1. AT&T Labs, 07733, Holmdel, NJ, USA

    Yaakov Kogan

  2. Département de Mathématiques, U.F.R. Faculté des Sciences, Université d'Orléans, B.P. 6759, 45067, Orleans, Cedex 2, France

    Andrei Yakovlev

Authors
  1. Yaakov Kogan
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  2. Andrei Yakovlev
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Kogan, Y., Yakovlev, A. Asymptotic analysis for closed multichain queueing networks with bottlenecks. Queueing Syst 23, 235–258 (1996). https://doi.org/10.1007/BF01206559

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  • DOI: https://doi.org/10.1007/BF01206559

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