The Community for Technology Leaders
RSS Icon
Issue No.06 - June (2008 vol.57)
pp: 780-794
Giuliano Casale , College of William and Mary
Giuseppe Serazzi , Politecnico di Milano
We propose the Geometric Bounds (GB), a new family of fast and accurate non-iterative bounds on closed queueing network performance metrics that can be used in the on-line optimization of distributed applications. Compared to state-of-the-art techniques such as the Balanced Job Bounds (BJB), the GB achieve higher accuracy at similar computational costs, limiting the worst-case bounding error typically within 5%-13% when for the BJB it is usually in the range 15%-35%. Optimization problems that are solved with the GB bounds return solutions that are much closer to the global optimum than with existing bounds. We also show that the GB technique generalizes as an accurate approximation to closed fork-join networks commonly used in disk, parallel and database models, thus extending the applicability of the method beyond the optimization of basic product-form networks.
Performance of Systems, Queuing theory, Performance, Operating Systems, Software/Software Engineering, Modeling techniques, Performance of Systems, Computer Systems Organization
Giuliano Casale, Richard Muntz, Giuseppe Serazzi, "Geometric Bounds: A Noniterative Analysis Technique for Closed Queueing Networks", IEEE Transactions on Computers, vol.57, no. 6, pp. 780-794, June 2008, doi:10.1109/TC.2008.37
[1] Proc. Fourth IEEE Int'l Conf. Autonomic Computing, 2007.
[2] K. Whisnant, Z. Kalbarczyk, and R.K. Iyer, “A System Model for Dynamically Reconfigurable Software,” IBM Systems J., vol. 42, no. 1, pp. 45-59, 2003.
[3] C.A. Floudas, Nonlinear and Mixed Integer Optimization. Oxford Univ. Press, 1995.
[4] M. Bennani and D.A. Menascè, “Resource Allocation for Autonomic Data Centers Using Analytic Performance,” Proc. Second IEEE Int'l Conf. Autonomic Computing, 2005.
[5] 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.
[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] W.C. Cheng and R.R. Muntz, “Bounding Errors Introduced by Clustering of Customers in Closed Product-Form Queueing Networks,” J. ACM, vol. 43, no. 4, pp. 641-669, 1996.
[8] P.J. Denning and J.P. Buzen, “The Operational Analysis of Queueing Network Models,” ACM Computing Surveys, vol. 10, no. 3, pp. 225-261, 1978.
[9] C.H. Hsieh and S. Lam, “Two Classes of Performance Bounds for Closed Queueing Networks,” Performance Evaluation, vol. 7, no. 1, pp. 3-30, 1987.
[10] J. Kriz, “Throughput Bounds for Closed Queueing Networks,” Performance Evaluation, vol. 4, no. 1, pp. 1-10, 1984.
[11] R.R. Muntz and J.W. Wong, “Asymptotic Properties of Closed Queueing Network Models,” Proc. Eighth Ann. Princeton Conf. Information Sciences and Systems, pp. 348-352, 1974.
[12] J. Zahorjan, K.C. Sevcik, D.L. Eager, and B. Galler, “Balanced Job Bound Analysis of Queueing Networks,” Comm. ACM, vol. 25, no. 2, pp. 134-141, 1982.
[13] E. Varki and L.W. Dowdy, “Analysis of Fork-Join Queueing Networks,” Proc. ACM SIGMETRICS '96, pp. 232-241, 1996.
[14] A. Thomasian and J. Menon, “Raid5 Performance with Distributed Sparing,” IEEE Trans. Parallel and Distributed Systems, vol. 8, no. 6, pp. 640-657, June 1997.
[15] E. Varki, A. Merchant, J. Xu, and X. Qiu, “Issues and Challenges in the Performance Analysis of Real Disk Arrays,” IEEE Trans. Parallel and Distributed Systems, vol. 15, no. 6, pp. 559-574, June 2004.
[16] S. Ceri, C. Gennaro, S. Paraboschi, and G. Serazzi, “Effective Scheduling of Detached Rules in Active Databases,” IEEE Trans. Knowledge and Data Eng., vol. 15, no. 1, pp. 2-13, Jan./Feb. 2003.
[17] J.C.S. Lui, R.R. Muntz, and D. Towsley, “Computing Performance Bounds of Fork-Join Parallel Programs under a Multiprocessing Environment,” IEEE Trans. Parallel and Distributed Systems, vol. 9, no. 3, pp. 295-311, Mar. 1998.
[18] G. Alvarez, E. Borowsky, S. Go, T. Romer, R. Becker-Szendy, R. Golding, A. Merchant, M. Spasojevic, A. Veitch, and J. Wilkes, “MINERVA: An Automated Resource Provisioning Tool for Large-Scale Storage Systems,” ACM Trans. Computer Systems, vol. 19, no. 4, pp. 483-518, 2001.
[19] E. Varki, “Mean Value Technique for Closed Fork-Join Networks,” Proc. ACM SIGMETRICS '99, pp. 103-112, 1999.
[20] H. Kobayashi, Modelling and Analysis: An Introduction to System Performance Evaluation Methodology. Addison-Wesley, 1978.
[21] M. Reiser and S.S. Lavenberg, “Mean-Value Analysis of Closed Multichain Queueing Networks,” J. ACM, vol. 27, no. 2, pp. 312-322, 1980.
[22] G. Bolch, S. Greiner, H. de Meer, and K.S. Trivedi, Queueing Networks and Markov Chains. John Wiley & Sons, 1998.
[23] D.L. Eager and K.C. Sevcik, “Bound Hierarchies for Multiple-Class Queueing Networks,” J. ACM, vol. 33, no. 1, pp. 179-206, 1986.
[24] M.M. Srinivasan, “Successively Improving Bounds on Performance Measures for Single Class Product Form Queueing Networks,” IEEE Trans. Computers, vol. 36, no. 9, pp. 1107-1112, Sept. 1987.
[25] J.D.C. Little, “A Proof of the Queueing Formula $L = \lambda W$ ,” Operations Research, vol. 9, pp. 383-387, 1961.
[26] L.W. Dowdy, D.L. Eager, K.D. Gordon, and L.V. Saxton, “Throughput Concavity and Response Time Convexity,” Information Processing Letters, vol. 19, no. 4, pp. 209-212, 1984.
[27] G. Balbo and G. Serazzi, “Asymptotic Analysis of Multiclass Closed Queueing Networks: Common Bottlenecks,” Performance Evaluation, vol. 26, no. 1, pp. 51-72, 1996.
[28] A. Harel, S. Namn, and J. Sturm, “Simple Bounds for Closed Queueing Networks,” Queueing Systems, vol. 47, no. 1, pp. 125-135, 1999.
[29] L. Lipsky, C.H. Lieu, A. Tehranipour, and A. van de Liefvoort, “On the Asymptotic Behavior of Time-Sharing Systems,” Comm. ACM, vol. 25, no. 10, pp. 707-714, 1982.
[30] 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.
[31] E. Varki, “Response Time Analysis of Parallel Computer and Storage Systems,” IEEE Trans. Parallel and Distributed Systems, vol. 12, no. 11, pp. 1146-1161, Nov. 2001.
[32] E. Varki and L.W. Dowdy, Quick Performance Bounding Techniques for Computer and Storage Systems with Parallel Resources, in review, abstract/E88-B/3/1244 669758.html, 2008.
[33] P.J. Schweitzer, “Approximate Analysis of Multiclass Closed Networks of Queues,” Proc. Int'l Conf. Stochastic Control and Optimization, pp. 25-29, 1979.
[34] Y. Bard, “Some Extensions to Multiclass Queueing Network Analysis,” Proc. Third Int'l Symp. Modelling and Performance Evaluation of Computer Systems, M. Arato, A. Butrimenko, and E.Gelenbe, eds., pp. 51-62, 1979.
[35] Z. Liu, L. Wynter, C.H. Xia, and F. Zhang, “Parameter Inference of Queueing Models for IT Systems Using End-to-End Measurements,” Performance Evaluation, vol. 63, no. 1, pp. 36-60, 2006.
[36] P. Bonami et al., “An Algorithmic Framework for Convex Mixed Integer Nonlinear Programs,” IBM Research Report RC23771 (W0511-023), 2005.
[37] R. Fourer, D.M. Gay, and B.W. Kernighan, AMPL—A Modeling Language for Mathematical Programming. Scientific Press, 1993.
[38] Y. Chen, A. Das, W. Qin, A. Sivasubramaniam, Q. Wang, and N. Gautam, “Managing Server Energy and Operational Costs in Hosting Centers,” Proc. ACM SIGMETRICS '05, pp. 303-314, 2005.
[39] B. Urgaonkar, G. Pacifici, P.J. Shenoy, M. Spreitzer, and N. Tantawi, “An Analytical Model for Multi-Tier Internet Services and Its Applications,” Proc. ACM SIGMETRICS '05, pp. 291-302, 2005.
[40] S. Kounev and A.P. Buchmann, “Performance Modeling and Evaluation of Large-Scale J2EE Applications,” Proc. 29th Int'l Computer Measurement Group Conf., pp. 273-283, 2003.
[41] M. Bertoli, G. Casale, and G. Serazzi, “Java Modelling Tools: An Open Source Suite for Queueing Network Modelling and Workload Analysis,” Proc. Third Int'l Conf. Quantitative Evaluation of Systems, pp. 119-120, http:/, 2006.
20 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool