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WAM—The Weighted Average Method for Predicting the Performance of Systems with Bursts of Customer Sessions
September/October 2011 (vol. 37 no. 5)
pp. 718-735
Diwakar Krishnamurthy, University of Calgary, Calgary
Jerry Rolia, Hewlett Packard Labs, Bristol
Min Xu, University of Calgary, Calgary
Predictive performance models are important tools that support system sizing, capacity planning, and systems management exercises. We introduce the Weighted Average Method (WAM) to improve the accuracy of analytic predictive performance models for systems with bursts of concurrent customers. WAM considers the customer population distribution at a system to reflect the impact of bursts. The WAM approach is robust with respect to distribution functions, including heavy-tail-like distributions, for workload parameters. We demonstrate the effectiveness of WAM using a case study involving a multitier TPC-W benchmark system. To demonstrate the utility of WAM with multiple performance modeling approaches, we developed both Queuing Network Models and Layered Queuing Models for the system. Results indicate that WAM improves prediction accuracy for bursty workloads for QNMs and LQMs by 10 and 12 percent, respectively, with respect to a Markov Chain approach reported in the literature.

[1] V. Almeida, M. Arlitt, and J. Rolia, "Analyzing a Web-Based System's Performance Measures at Multiple Time Scales," ACM SIGMETRICS Performance Evaluation Rev., vol. 30, no. 2, pp. 3-9, Sept. 2002.
[2] M. Andersson, J. Cao, M. Kihl, and C. Nyberg, "Performance Modeling of an Apache Web Server with Bursty Arrival Traffic," Proc. Int'l Conf. Internet Computing, pp. 508-514, 2003.
[3] M. Arlitt, D. Krishnamurthy, and J. Rolia, "Characterizing the Scalability of a Large Web-Based Shopping System," ACM Trans. Internet Technology, vol. 1, no. 1, pp. 44-69, 2001.
[4] S. Balsamo, A. Di Marco, P. Inverardi, and M. Simeoni, "Model-Based Performance Prediction in Software Development: A Survey," IEEE Trans. Software Eng., vol. 30, no. 5, pp. 295-310, May 2004.
[5] T. Bonald and J.W. Roberts, "Congestion at Flow Level and the Impact of User Behaviour," Computer Networks, vol. 42, pp. 521-536, 2003.
[6] A.B. Bondi and W. Whitt, "The Influence of Service-Time Variability in a Closed Network of Queues," Performance Evaluation, vol. 6, no. 3, pp. 219-234, Sept. 1986.
[7] J.P. Buzen, "Computation Algorithms for Closed Queuing Networks with Exponential Servers," Comm. ACM, vol. 16, no. 9, pp. 527-531, Sept. 1973.
[8] G. Casale, N. Mi, and E. Smirni, "Bound Analysis of Closed Queuing Networks with Workload Burstiness," Proc. ACM SIGMETRICS Int'l Conf. Measurement and Modeling of Computer Systems, pp. 13-24, 2008.
[9] G. Casale, "An Efficient Algorithm for the Exact Analysis of Multiclass Queuing Networks with Large Population Sizes," Proc. Joint Int'l Conf. Measurement and Modeling of Computer Systems, pp. 169-180, 2006.
[10] K.M. Chandy and D. Nuese, "Linearizer: A Heuristic Algorithm for Queuing Network Models of Computer Systems," Comm. ACM, vol. 25, no. 2, pp. 126-133, Feb. 1982.
[11] Y. Chen, S. Iyer, X. Liu, D. Milojicic, and A. Sahai, "SLA Decomposition: Translating Service Level Objectives to System Level Thresholds," Proc. Fourth Int'l Conf. Autonomic Computing, 2007.
[12] M.E. Crovella and L. Lipsky, "Long-Lasting Transient Conditions in Simulations with Heavy-Tailed Workloads," Proc. 29th Conf. Winter Simulation, pp. 1005-1012, 1997.
[13] D.L. Eager, D.J. Sorin, and M.K. Vernon, "AMVA Techniques for High Service Time Variability," Proc. ACM SIGMETRICS Int'l Conf. Measurement and Modeling of Computer Systems, pp. 217-228, 2000.
[14] M. Harchol-Balter, M. Crovella, and C. Murta, "On Choosing a Task Assignment Policy for a Distributed Server System," J. Parallel and Distributed Computing, vol. 59, no. 2, pp. 204-228, Nov. 1999.
[15] R. Jain, The Art of Computer Systems Performance Analysis: Techniques for Experimental Design, Measurement, Simulation, and Modeling. John Wiley & Sons, Inc., Apr. 1991.
[16] L. Kleinrock, Queuing Systems Volume 1: Theory. John Wiley & Sons, Inc., 1975.
[17] S. Kounev and A. Buchmann, "Performance Modeling of Distributed e-Business Applications Using Queuing Petri Nets," Proc. IEEE Int'l Symp. Performance Analysis of Systems and Software, pp. 145-153, Mar. 2003.
[18] D. Krishnamurthy, J. Rolia, and S. Majumdar, "A Synthetic Workload Generation Technique for Stress Testing Session-Based Systems," IEEE Trans. Software Eng., vol. 32, no. 11, pp. 868-882, Nov. 2006.
[19] D. Krishnamurthy, "Synthetic Workload Generation for Stress Testing Session-Based Systems," PhD thesis, Dept. of Systems and Computer Eng., Carleton Univ., Jan. 2004.
[20] W. Leland, M. Taqqu, W. Willinger, and D. Wilson, "On the Self-Similar Nature of Ethernet Traffic (Extended Version)," IEEE/ACM Trans. Networking, vol. 2, no. 1, pp. 1-15, Feb. 1994.
[21] D. Menasce and M. Bennani, "Analytic Performance Models for Single Class and Multiple Class Multithreaded Software Servers," Proc. Int'l Conf. Computer Measurement Group, pp. 475-482, 2006.
[22] D. Menasce and V. Almeida, Capacity Planning for Web Services: Metrics, Models and Methods. Prentice Hall, Inc., Sept. 2001.
[23] D. Menasce, V. Almeida, R. Reidi, F. Pelegrinelli, R. Fonesca, and W. MeiraJR, "In Search of Invariants in e-Business Workloads," Proc. ACM Conf. Electronic Commerce, pp. 56-65, Oct. 2000.
[24] D. Menasce and V. Almeida, Capacity Planning and Performance Modeling: From Mainframes to Client-Server Systems. Prentice Hall, 1994.
[25] J.F. Meyer and W.H. Sanders, "Specification and Construction of Performability Models," Proc. Int'l Workshop Performability Modeling of Computer and Comm. Systems, 1993.
[26] N. Mi, Q. Zhang, A. Riska, E. Smirni, and E. Riedel, "Performance Impacts of Autocorrelated Flows in Multi-Tiered Systems," Performance Evaluation, vol. 64, nos. 9-12, pp. 1082-1101, 2007.
[27] M.K. Molloy, "Performance Analysis Using Stochastic Petri Nets," IEEE Trans. Computers, vol. 31, no. 9, pp. 913-917, Sept. 1982.
[28] D. Mosberger and T. Jin, "httperf—A Tool for Measuring Web Server Performance," Proc. Workshop Internet Server Performance, pp. 59-67, 1998.
[29] K. Park, G.T. Kim, and M. Crovella, "On the Relationship Between File Sizes, Transport Protocols, and Self-Similar Network Traffic," Proc. Int'l Conf. Network Protocols, pp. 171-180, Oct. 1996.
[30] V. Paxon and S. Floyd, "Wide Area Traffic: The Failure of Poisson Modeling," IEEE/ACM Trans. Networking, vol. 3, no. 3, pp. 226-244, June 1995.
[31] K. Psounis, P. Molinero-Fernández, B. Prabhakar, and F. Papadopoulos, "Systems with Multiple Servers under Heavy-Tailed Workloads," Performance Evaluation, vol. 62, nos. 1-4, pp. 456-474, Oct. 2005.
[32] M. Reiser, "A Queuing Network Analysis of Computer Communication Networks with Window Flow Control," IEEE Trans. Comm., vol. 27, no. 8, pp. 1201-1209, Aug. 1979.
[33] J.A. Rolia and K.C. Sevcik, "The Method of Layers," IEEE Trans. Software Eng., vol. 21, no. 8, pp. 689-700, Aug. 1995.
[34] W.H. Sanders, W.D. OballII, M.A. Qureshi, and F.K. Widjanarko, "The UltraSAN Modeling Environment," Performance Evaluation, vol. 24, nos. 1/2, pp.89-115, Nov. 1995.
[35] M. Taqqu, V. Teverovsky, and W. Willinger, "Estimators for Long-Range Dependence: An Empirical Study," Fractals, vol. 3, no. 4, pp. 785-798, 1995.
[36] N. Tiwari and P. Mynampati, "Experiences of Using LQN and QPN Tools for Performance Modeling of a J2EE Application," Proc. Int'l Conf. Computer Measurement Group, pp. 537-548, 2006.
[37] TPC-W benchmark,, 2011.
[38] B. Urgaonkar, G. Pacifici, P. Shenoy, M. Spreitzer, and A. Tantawi, "Analytic Modeling of Multitier Internet Applications," ACM Trans. Web, vol. 1, no. 1, pp. 2-es, May 2007.
[39] U. Vallamsetty, K. Kant, and P. Mohapatra, "Characterization of e-Commerce Traffic," Electronic Commerce Research, vol. 3, nos. 1/2, pp. 167-192, 2003.
[40] M. Woodside, J.E. Nielsen, D.C. Petriu, and S. Majumdar, "The Stochastic Rendezvous Network Model for Performance of Synchronous Client-Server-Like Distributed Software," IEEE Trans. Computers, vol. 44, no. 1, pp. 20-34, Jan. 1995.
[41] Q. Zhang, L. Cherkasova, and E. Smirni, "A Regression-Based Analytic Model for Dynamic Resource Provisioning of Multi-Tier Applications," Proc. Int'l Conf. Autonomic Computing, pp. 27-27, June 2007.

Index Terms:
Performance of systems, modeling techniques, queuing theory, operational analysis.
Diwakar Krishnamurthy, Jerry Rolia, Min Xu, "WAM—The Weighted Average Method for Predicting the Performance of Systems with Bursts of Customer Sessions," IEEE Transactions on Software Engineering, vol. 37, no. 5, pp. 718-735, Sept.-Oct. 2011, doi:10.1109/TSE.2011.65
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