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A new computational approach for stochastic fluid models of multiplexers with heterogeneous sources

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Abstract

In this paper we derive an efficient computational procedure for the system in which fluid is produced byN 1 on-off sources of type 1,N 2 on-off sources of type 2 and transferred to a buffer which is serviced by a channel of constant capacity. This is a canonical model for multiservice ATM multiplexing, which is hard to analyze and also of wide interest. This paper's approach to the computation of the buffer overflow probability,G(x) = Pr{buffer content >x}, departs from all prior approaches in that it transforms the computation ofG(x) for a particularx into a recursive construction of an interpolating polynomial. For the particular case of two source types the interpolating polynomial is in two variables. Our main result is the derivation of recursive algorithms for computing the overflow probabilityG(x) and various other performance measures using their respective relations to two-dimensional interpolating polynomials. To make the computational procedure efficient we first derive a new system of equations for the coefficients in the spectral expansion formula forG(x) and then use specific properties of the new system for efficient recursive construction of the polynomials. We also develop an approximate method with low complexity and analyze its accuracy by numerical studies. We computeG(x) for different values ofx, the mean buffer content and the coefficient of the dominant exponential term in the spectral expansion ofG(x). The accuracy of the approximations is reasonable when the buffer utilization characterized by G(0) is more than 10−2.

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References

  1. D. Anick, D. Mitra and M.M. Sondhi, Stochastic theory of a data-handling system with multiple sources, Bell Syst. Tech. J. 61 (1982) 1871–1894.

    Google Scholar 

  2. A. Baiocchi and N. Blefari-Melazzi, An error-controlled approximate analysis of a stochastic fluid model applied to an ATM multiplexer with heterogeneous on-off sources, submitted to IEEE Trans. Commun.

  3. E.G. Coffman, Jr., B. Igelnik and Ya. Kogan, Controlled stochastic model of a communication system with multiple sources, IEEE Trans. Inf. Theory 37 (1991) 1379–1387.

    Google Scholar 

  4. J.P. Coudreuse, G. Pays and M. Trouvat, Asynchronous transfer mode, Commutation and Transmission 3 (1990) 5–16.

    Google Scholar 

  5. A.I. Elwalid and D. Mitra, Analysis and design of rate-based congestion control of high speed networks, I: stochastic fluid models, access regulation, Queueing Systems 9 (1991) 29–64.

    Google Scholar 

  6. A.I. Elwalid and D. Mitra, Effective bandwidth of general Markovian traffic sources and admission control of high speed networks, to appear in IEEE/ACM Trans. Networking. A short version is inProc. IEEE Infocom '93.

  7. S. Karlin and J.L. McGregor, The differential equations of birth-and-death processes, and the Stieltjes moment problem, Trans. Amer. Math. Soc. 85 (1957) 489–546.

    Google Scholar 

  8. L. Kosten, Stochastic theory of data-handling system with groups of multiple source, in:Performance of Computer-Communication Systems, eds. H. Rudin and W. Bux (Elsevier, Amsterdam, 1984) pp. 321–331.

    Google Scholar 

  9. L. Kosten, Liquid models for a type of information buffer problems, Delft Progress Report 11 (1986) 71–86.

    Google Scholar 

  10. D. Mitra, Stochastic theory of a fluid model of producers and consumers coupled by a buffer, Adv. Appl. Prob. 20 (1988) 646–673.

    Google Scholar 

  11. W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling,Numerical Recipes (Cambridge University Press, 1986).

  12. J.W. Roberts (ed.), Performance evaluation and design of multiservice networks,Final Report of the COST 224 Project, Commission of the European Communities.

  13. T.E. Stern and A.I. Elwalid, Analysis of separable Markov-modulated models for information-handling systems, Adv. Appl. Prob. 23 (1991) 105–139.

    Google Scholar 

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Igelnik, B., Kogan, Y., Kriman, V. et al. A new computational approach for stochastic fluid models of multiplexers with heterogeneous sources. Queueing Syst 20, 85–116 (1995). https://doi.org/10.1007/BF01158433

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