This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Unifying Framework for the Approximate Solution of Closed Multiclass Queuing Networks
December 2002 (vol. 51 no. 12)
pp. 1423-1434

Abstract—Queuing network models of modern computing systems must consider a large number of components (e.g., Web servers, DB servers, application servers, firewall, routers, networks) and hundreds of customers with very different resource requirements. The complexity of such models makes the application of exact solution techniques prohibitively expensive, motivating research on approximate methods. This paper proposes an interpolation-matching framework that allows a unified view of approximate solution techniques for closed product-form queuing networks. Depending upon the interpolating functional form and the matching populations selected, a large versatile family of new approximations can be generated. It is shown that all the known approximation strategies, including Linearizer, are instances of the interpolation-matching framework. Furthermore, a new approximation technique, based on a third-order polynomial, is obtained using the interpolation-matching framework. The new technique is shown to be more accurate than other known methods.

[1] G.A. Baker and P. Graves-Morris, “PadéApproximations,” Encyclopedia of Math. and Its Applications, second ed., vol. 59, Cambridge, U.K.: Cambridge Univ. Press, 1996.
[2] Y. Bard, “Some Extensions to Multiclass Queueing Network Analysis,” Proc. Fourth Int'l Symp. Modeling and Performance Evaluation of Computer Systems, A. Butrimenko M. Arato, and E. Gelenbe, eds., pp. 51-62, 1979.
[3] F. Baskett, K.M. Chandy, R.R. Muntz, and R. Palacios, “Open, Closed and Mixed Networks of Queues with Different Classes of Customers,” J. ACM, vol. 22, no. 2, pp. 248-260, 1975.
[4] J.P. Buzen, “Computational Algorithms for Closed Queueing Networks with Exponential Servers,” Comm. ACM, vol. 16, no. 9, pp. 527-531, 1973.
[5] W.M. Chow, “Approximations for Large Scale Closed Queueing Networks,” Performance Evaluation, vol. 3, no. 1, pp. 1-12, 1983.
[6] K.M. Chandy and D. Neuse, “Linearizer: A Heuristic Algorithm for Queueing Network Models of Computing Systems,” Comm. ACM, vol. 25, no. 2, pp. 126-134, 1982.
[7] D.L. Eager and K.C. Sevcik, “Performance Bound Hierarchies for Queueing Networks,” ACM Trans. Computer Systems, vol. 1, no. 2, pp. 99-115, 1983.
[8] D.L. Eager and K.C. Sevcik, “Bound Hierarchies for Multiple-Class Queueing Networks,” J. ACM, vol. 33, no. 4, pp. 179-206, 1986.
[9] M. Reiser and S. Lavenberg, “Mean-Value Analysis of Closed Multichain Queueing Networks,” J. ACM, vol. 27, no. 2, pp. 313-322, 1980.
[10] M. Reiser and H. Kobayashi, “Queueing Networks with Multiple Closed Chains: Theory and Computational Algorithms,” IBM J. Research and Development, vol. 19, pp. 283-294, 1975.
[11] P.J. Schweitzer, “Approximate Analysis of Multiclass Closed Queueing Networks of Queues,” Proc. Int'l Conf. Stochastic Control and Optimization, Apr. 1979.
[12] P.J. Schweitzer, “A Survey of Mean Value Analysis, Its Generalizations, and Applications, for Networks of Queues,” Proc. Second Int'l Workshop Netherlands Nat'l Network for the Math. on Operations Research, Feb. 1991.
[13] E. de Souza e Silva and R.R. Muntz, “A Note on the Computational Cost of the Linearizer Algorithm,” IEEE Trans. Computers, vol. 39, no. 6, pp. 840-842, June 1990.
[14] J.R. Spirn, “Queueing Networks with Random Selection for Service,” IEEE Trans. Software Eng., vol. 3, no. 1, pp. 287-289, 1979.
[15] J. Zahorjan, D.L. Eager, and H.M. Sweillam, “Accuracy, Speed and Convergence of Approximate Mean Value Analysis,” Performance Evaluation, vol. 8, no. 4, pp. 255-270, 1988.
[16] H. Wang and K.C. Sevcik, “Experiences with Improved Approximate Mean Value Analysis Algorithms,” Proc. 10th Int'l Conf. Modeling Techniques and Tools, R. Puigjaner, N.N. Savino, and B. Serra, eds., pp. 280-291, 1998.
[17] P. Cremonesi, F. Schiavoni, P.J. Schweitzer, and G. Serazzi, “An Interpolation-Matching Framework for the Approximate Solution of Closed Multiclass Queuing Networks,” Internal Report N 27/1997, Dipartimento di Elettronica e Informazione, Politecnico di Milano, 1997.

Index Terms:
Queuing network models, approximate solution techniques, multiclass workloads.
Citation:
Paolo Cremonesi, Paul J. Schweitzer, Giuseppe Serazzi, "A Unifying Framework for the Approximate Solution of Closed Multiclass Queuing Networks," IEEE Transactions on Computers, vol. 51, no. 12, pp. 1423-1434, Dec. 2002, doi:10.1109/TC.2002.1146708
Usage of this product signifies your acceptance of the Terms of Use.