The Community for Technology Leaders
RSS Icon
Issue No.02 - March/April (2009 vol.35)
pp: 162-177
Giuliano Casale , College of William and Mary, Williamsburg
We introduce the Class-oriented Method of Moments (CoMoM), a new exact algorithm to efficiently compute normalizing constants and marginal queue-length probabilities in closed multiclass queueing networks. Closed models are important for performance evaluation of multi-tier applications, but when the number of service classes is large they become too expensive to solve with existing methods, such as Mean Value Analysis (MVA). CoMoM addresses this limitation by a new recursion that scales efficiently with the number of classes. Compared to the MVA algorithm, which recursively computes mean queue-lengths, CoMoM carries on in the recursion also information on higher-order moments of queue-lengths. We show that this additional information minimizes the number of recursive steps needed to solve the model and makes CoMoM the best-available algorithm for networks with several classes. For example, we show a model of a real J2EE application where CoMoM is several orders of magnitude faster and more memory-efficient than MVA. We conclude the paper by generalizing CoMoM to the efficient computation of marginal queue-length probabilities, which finds application in the evaluation of state-dependent indexes such as energy consumption or quality-of-service metrics.
Performance of Systems, Modeling techniques, Queuing theory
Giuliano Casale, "CoMoM: Efficient Class-Oriented Evaluation of Multiclass Performance Models", IEEE Transactions on Software Engineering, vol.35, no. 2, pp. 162-177, March/April 2009, doi:10.1109/TSE.2008.79
[1] R. Barrett etal., Templates for the Solution of Linear Systems. SIAM, 1994.
[2] 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, vol. 22, no. 2, pp.248-260, 1975.
[3] G. Casale, “An Efficient Algorithm for the Exact Analysis of Multiclass Queueing Networks with Large Population Sizes,” Proc. ACM SIGMETRICS/IFIP Performance 2006, pp.169-180, 2006.
[4] G. Casale, “Exact Analysis of Performance Models by the Method of Moments,” available from the author.
[5] G. Casale, “CoMoM: A Class-Oriented Algorithm for Probabilistic Evaluation of Multiclass Queueing Networks,” Technical Report WM-CS-2008-04, Dept. of Computer Science, College of William and Mary, 2008.
[6] K.M. Chandy and C.H. Sauer, “Computational Algorithms for Product-Form Queueing Networks Models of Computing Systems,” Comm. ACM, vol. 23, no. 10, pp.573-583, 1980.
[7] Y. Chu, C.J. Antonelli, and T.J. Teorey, “Performance Modeling of the PeopleSoft Multi-Tier Remote Computing Architecture,” Technical Report CITI 975, Univ. of Michigan, Dec. 1997.
[8] D.J.A. Cohen, Basic Techniques of Combinatorial Theory. John Wiley and Sons, 1978.
[9] A.E. Conway and N.D. Georganas, “RECAL—A New Efficient Algorithm for the Exact Analysis of Multiple-Chain Closed Queueing Networks,” J. ACM, vol. 33, no. 4, pp.768-791, 1986.
[10] E.N. Elnozahy, M. Kistler, and R. Rajamony, “Energy-Efficient Server Clusters,” Proc. Second Workshop Power-Aware Computer Systems, pp.179-196, 2002.
[11] P.G. Harrison and S. Coury, “On the Asymptotic Behaviour of Closed Multiclass Queueing Networks,” Performance Evaluation, vol. 47, no. 2, pp.131-138, 2002.
[12] P.G. Harrison and T.T. Lee, “A New Recursive Algorithm for Computing Generating Functions in Closed Queueing Networks,” Proc. IEEE MASCOTS, pp.223-230, 2004.
[13] S. Kounev and A. Buchmann, “Performance Modeling and Evaluation of Large-Scale J2EE Applications,” Proc. 29th Int'l Conf. Computer Measurement Group, pp.273-283, 2003.
[14] B.A. LaMacchia and A.M. Odlyzko, “Solving Large Sparse Linear Systems over Finite Fields,” Proc. CRYPTO Conf., pp.109-133, 1990.
[15] S. Lam, “Dynamic Scaling and Growth Behavior of Queueing Network Normalization Constants,” J. ACM, vol. 29, no. 2, pp.492-513, 1982.
[16] S. Lam, “A Simple Derivation of the mva and lbanc Algorithms from the Convolution Algorithm,” IEEE Trans. Computers, vol. 32, pp.1062-1064, 1983.
[17] E.D. Lazowska, J. Zahorjan, G.S. Graham, and K.C. Sevcik, Quantitative System Performance. Prentice-Hall, 1984.
[18] D. Menasce and V.A.F. Almeida, Capacity Planning for Web Performance: Metrics, Models, and Methods. Prentice Hall, 1998.
[19] M. Reiser and H. Kobayashi, “Queueing Networks with Multiple Closed Chains: Theory and Computational Algorithms,” IBM J. Research and Development, vol. 19, no. 3, pp.283-294, 1975.
[20] M. Reiser and S.S. Lavenberg, “Mean-value Analysis of Closed Multichain Queueing Networks,” J. ACM, vol. 27, no. 2, pp.312-322, 1980.
[21] A. Schonhage and V. Strassen, “Schnelle Multiplikation Groer Zahlen,” Computing, vol. 7, pp.281-292, 1971.
[22] B. Urgaonkar, G. Pacifici, P.J. Shenoy, M. Spreitzer, and A.N. Tantawi, “An Analytical Model for Multi-Tier Internet Services and its Applications,” Proc. ACM SIGMETRICS, pp.291-302, 2005.
[23] G. Villard, “Some Recent Progress in Exact Linear Algebra and Related Questions,” Proc. Int'l Symp. Symbolic and Algebraic Computation, pp.391-392, 2007.
[24] J. Zahorjan, “The Distribution of Network States During Residence Times in Product form Queueing Networks,” Performance Evaluation, vol. 4, pp.99-104, 1984.
15 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool