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A decomposition approximation method for multiclass BCMP queueing networks with multiple-server stations

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Abstract

Closed multiclass separable queueing networks can in principle be analyzed using exact computational algorithms. This, however, may not be feasible in the case of large networks. As a result, much work has been devoted to developing approximation techniques, most of which is based on heuristic extensions of the mean value analysis (MVA) algorithm. In this paper, we propose an alternative approximation method to analyze large separable networks. This method is based on an approximation method for non-separable networks recently proposed by Baynat and Dallery. We show how this method can be efficiently used to analyze large separable networks. It is especially of interest when dealing with networks having multiple-server stations. Numerical results show that this method has good accuracy.

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References

  1. I.F. Alkyildz and G. Bolch, Mean value analysis approximation for multiple server queueing networks, Perf. Eval. 8 (1988) 77–91.

    Google Scholar 

  2. Y. Bard, Some extensions to multiclass queueing network analysis, in:4th Int. Symp. on Modeling and Performance Evaluation of Computer Systems, Vol. 1, Vienna (1979).

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

    Google Scholar 

  4. B. Baynat and Y. Dallery, A unified view of product-form approximation techniques for general closed queueing networks, Perf. Eval. 18 (1993).

  5. B. Baynat, Une méthode approximative d'analyse des résaux de files d'attente fermés mutliclasses, Ph.D. Thesis, Université Pierre et Marie Curie (June 1991).

  6. B. Baynat and Y. Dallery, A product-form approximation method for general closed queueing networks with several classes of customers, Technical Report MASI No. 91-50 (October 1991).

  7. A. Brandwajn, Equivalence and decomposition in queueing systems: a unified approach, Perf. Eval. 5 (1985) 175–186.

    Google Scholar 

  8. S. Bruel and G. Balbo,Computational Algorithms for Closed Queueing Networks, Operating and Programming Systems Series (1980).

  9. J. P. Buzen, Computational algorithms for closed queueing networks with exponential servers, Commun. ACM 16 (1973) 527–531.

    Google Scholar 

  10. K.M. Chandy and D. Neuse, Linearizer: a heuristic algorithm for queueing network models of computing systems, Commun. ACM 25 (1982) 126–134.

    Google Scholar 

  11. Y. Dallery and X.R. Cao, Operational analysis of closed stochastic queueing networks, Perf. Eval. 14 (1992) 43–61.

    Google Scholar 

  12. W.J. Gordon and G.F. Newell, Closed queueing networks with exponential servers, Oper. Res. 15 (1967) 252–267.

    Google Scholar 

  13. F.P. Kelly,Reversibility and Stochastic Networks (Wiley, New York, 1979).

    Google Scholar 

  14. A.E. Krzesinski and A. Greyling, Improved linearizer methods for queueing networks with queue dependent centers,ACM Sigmetrics Conf., Cambridge (1984) pp. 41–51.

  15. E.D. Lazowska, J. Zahorjan, G.S. Graham and K.C. Sevick,Quantitative System Performance (Prentice-Hall, New Jersey, 1984).

    Google Scholar 

  16. R. Marie, An approximate analytical method for general queueing networks, IEEE Trans. Software Eng. SE-5 (1979) 530–538.

    Google Scholar 

  17. R. Marie, P. Snyder and W.J. Stewart, Extensions and computational aspects of an iterative method,ACM Sigmetrics Conf., Washington (September 1982).

  18. D. Neuse and K.M. Chandy, SCAT: A heuristic algorithm for queueing network models of computing systems, Perf. Eval. 10 (1981) 59–79.

    Google Scholar 

  19. M. Reiser and S.S. Lavenberg, Mean Value analysis of closed multichain queueing networks, J. ACM 27 (1980) 313–323.

    Google Scholar 

  20. K.W. Ross, D. Tsang and J. Wang, Monte Carlo summation and integration applied to multichain queueing networks, submitted.

  21. K.W. Ross and J. Wang, Asymptotically optimal importance sampling for multiclass queueing networks, submitted.

  22. P.J. Schweitzer, Approximate analysis of multiclass closed networks of queues,Proc. Int. Conf. on Stochastic Control and Optimization, Amsterdam (1979).

  23. P.J. Schweitzer, A survey of Mean Value Analysis, its generalizations, and applications, for networks of queues, to appear.

  24. D. Tsang and K.W. Ross, Algorithms for determining exact blocking probabilities in tree networks, IEEE Trans. Commun. COM-38 (1990) 1266–1271.

    Google Scholar 

  25. J. Zahorjan and E.D. Lazowska, Incorporating load dependent servers in approximate mean value analysis,ACM Sigmetrics Conf., Vol. 12 (1984) pp. 52–62.

    Google Scholar 

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Baynat, B., Dallery, Y. & Ross, K. A decomposition approximation method for multiclass BCMP queueing networks with multiple-server stations. Ann Oper Res 48, 273–294 (1994). https://doi.org/10.1007/BF02024661

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