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Exact and asymptotic solutions for models of new telecommunication services

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Abstract

A new product-form, finite capacity network model is described for the blocking analysis of modern telecommunication services such as automatic redial, video on demand, interactive TV and video telephony. It allows multiple finite sources requiring random routes and a random number of resource units from one or several resource types. We obtain a simple closed-form expression for the generating partition function and from that derive three computational methods based on numerical inversions, asymptotic approximations and recursion relations. The main concepts from the asymptotic method are also used in the numerical inversion method to justify speed-up of this method for large models. Numerical examples are presented to illustrate the effectiveness of the procedures.

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References

  1. J. Abate and W. Whitt, The Fourier-series method for inverting transforms of probability distributions, Queueing Systems 10(1992)5 - 88.

    Google Scholar 

  2. 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 

  3. N.G. De Bruijn, Asymptotic Methods in Analysis Dover, New York, 1981.

    Google Scholar 

  4. G.L. Choudhury, K.K. Leung and W. Whitt, An algorithm to compute blocking probabilities in multi-rate multi-class multi-resource loss models, Advances in Applied Probability 27(1995) 1104 - 1143.

    Google Scholar 

  5. G.L. Choudhury, K.K. Leung and W. Whitt, An inversion algorithm to compute blocking probabilities in loss networks with state-dependent rates, IEEE/ACM Transactions on Networking 3(1995) 585 - 601.

    Google Scholar 

  6. G.L. Choudhury, D.M. Lucantoni and W. Whitt, Multidimensional transform inversion with applications to the transient M/G/1 queue, Annals of Applied Probability 4(1994)719 - 740.

    Google Scholar 

  7. G.L. Choudhury and W. Whitt, Probabilistic scaling for the numerical inversion of non-probability transforms, Informs Journal on Computing, to appear.

  8. J.W. Cohen, The generalized Engset formulae, Philips Telecommunications Review 18(4)(1957) 158 - 170.

    Google Scholar 

  9. B.G. Hornbach, 5ESS-2000 switch: The next generation switching system, AT&T Technical Journal 72(5)(1993)4 - 13.

    Google Scholar 

  10. F.P. Kelly, Reversibility and Stochastic Network Wiley, Chichester, 1979.

    Google Scholar 

  11. F.P. Kelly, Loss networks, Annals of Applied Probability (1991)319 - 378.

  12. H. Kobayashi and B.L. Mark, On queueing networks and loss networks, in: Proc. 1994 Conference on Information Science and Systems ed. H. Kobayashi, Princeton University, Princeton, NJ, 1994, pp. 794 - 799.

    Google Scholar 

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

    Google Scholar 

  14. Y. Kogan and A. Birman, Asymptotic analysis of closed queueing networks with bottlenecks, IFIP Transactions C-5, Performance of Distributed Systems and Integrated Communication Networks eds. T. Hasegawa, H. Takagi and Y. Takahashi, North-Holland, Amsterdam, 1992, pp. 265 - 280.

    Google Scholar 

  15. Y. Kogan and M. Shenfild, Asymptotic solution of generalized multiclass Engset model, in: The Fundamental Role of Teletraffic in the Evolution of Telecommunications Networks Proc. ITC 14 Vol. 1b, eds. J. Labetoulle and J.W. Roberts, Elsevier, Amsterdam, 1994, pp. 1239 - 1249.

    Google Scholar 

  16. D. Mitra and J.A. Morrison, Erlang capacity and uniform approximations for shared unbuffered resources, IEEE/ACM Transactions on Networking 2(1994)558 - 570.

    Google Scholar 

  17. Video Technology Special Issue, Telephony, July 25, 1994, in particular: P. Bernier, Finding a winning combination, pp. 16 - 21.

  18. E. Pinsky and A. Conway, Exact computation of blocking probabilities in state-dependent multifacility blocking models, in: Proc. Intern. Conf. Performance of Distributed Systems and Integrated Communication Networks eds. T. Hasegawa, H. Takagi and Y. Takahashi, Kyoto, 1991, pp. 353 - 362.

  19. R. Wong, Asymptotic Approximations of Integrals Academic Press, Boston, 1986.

    Google Scholar 

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Choudhury, G., Kogan, Y. & Susskind, S. Exact and asymptotic solutions for models of new telecommunication services. Annals of Operations Research 79, 393–407 (1998). https://doi.org/10.1023/A:1018939209097

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