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Filter Design and Analysis in Frequency Domain for Server Scheduling and Optimization
November 2010 (vol. 21 no. 11)
pp. 1573-1585
Cheng-Zhong Xu, Wayne State University, Detroit
Minghua Xu, Wayne State University, Detroit
Le Yi Wang, Wayne State University, Detroit
George Yin, Wayne State University, Detroit
Internet traffic often exhibits a structure with rich high-order statistical properties like self-similarity and long-range dependency (LRD). This greatly complicates the problem of server performance modeling and optimization. Existing tools like queuing models in most cases only hold in mean value analysis under the assumption of simplified traffic structures. In this paper, we present a filter model to characterize the relationship among the factors of server capacity, request scheduling, and service quality for general input traffic. By the model, a server scheduler operates as an finite-duration impulse response (FIR) filter that transforms request processes into workload processes with the objective of minimizing load variation or overload probability, and meanwhile, without violating request response deadlines as defined in service-level agreements. We present a design and analysis of the filter for traffic with strong LRD in the frequency domain. Most Internet traffic has monotonically decreasing strength of variation functions over frequency. For this type of input traffic, we prove that optimal schedulers must have a convex structure. Uniform resource allocation is an extreme case of the convexity and is proved to be optimal for Poisson traffic. We integrate the convex structural principle with the Generalized Processor Sharing (GPS) discipline and show that the enhanced GPS policy improves the service quality significantly. Furthermore, we show that the presence of LRD in the input traffic results in shift of variation strength from high frequency to lower frequency bands and consequently leads to a degradation of the service quality.

[1] P. Abry and D. Veitch, "Wavelet Analysis of Long-Range Dependent Traffic," IEEE Trans. Information Theory, vol. 44, no. 1, pp. 2-15, Jan. 1998.
[2] ACM SIGCOMM, "The Internet Traffic Archive," http:/ gov, 2010.
[3] M.F. Arlitt and C.L. Williamson, "Internet Web Servers: Workload Characterization and Performance Implications," IEEE/ACM Trans. Networking, vol. 5, no. 5, pp. 631-645, Oct. 1997.
[4] A. Baiocchi and N. Blefari-Melazzi, "Steady-State Analysis of the MMPP/G/1/k Queue," IEEE Trans. Comm., vol. 41, no. 4, pp. 531-534, Apr. 1993.
[5] P. Barford and M. Crovella, "Critical Path Analysis of TCP Transactions," IEEE/ACM Trans. Networking, vol. 9, no. 3, pp. 238-248, 2001.
[6] S. Basu, A. Mukherjee, and S. Klivansky, "Time Series Models for Internet Traffic," Proc. IEEE INFOCOM, pp. 611-620, 1996.
[7] J. Cao, W. Cleveland, D. Lin, and D. Sun, "On the Nonstationarity of Internet Traffic," Proc. ACM SIGMETRICS, pp. 102-112, 2001.
[8] M. Crovella and A. Bestavros, "Self-Similarity in World Wide Web Traffic—Evidence and Possible Causes," Proc. ACM SIGMETRICS, 1996.
[9] A. Dembo and O. Zeitouni, Large Deviation Techniques and Applications, second ed. Springer, 1998.
[10] S. Elnikety, J. Tracey, E. Nahum, and W. Zwaenepoel, "A Method for Transparent Admission Control and Request Scheduling in e-Commerce Web Sites," Proc. Int'l Conf. World Wide Web (WWW), 2004.
[11] A. Erramilli, O. Narayan, and W. Willinger, "Experimental Queuing Analysis with Long-Range Dependent Packet Traffic," IEEE/ACM Trans. Networking, vol. 4, no. 2, pp. 209-223, 1996.
[12] M. Harchol-Balter, B. Schroeder, M. Agrawal, and N. Bansal, "Size-Based Scheduling to Improve Web Performance," ACM Trans. Computer Systems, vol. 21, no. 2, May 2003.
[13] J. Hellerstein, Y. Diao, S. Parekh, and D. Tilbury, Feedback Control of Computing Systems. Joh Wiley & Sons, Inc., 2004.
[14] S. Jin and Z. Bestavros, "Temporal Locality in Web Request Streams—Sources, Characteristics, and Chaching Implications," Proc. ACM SIGMETRICS, 2000.
[15] J. Jin and K. Nahrstedt, "QoS-Aware Service Management for Component-Based Distributed Applications," ACM Trans. Internet Technology, vol. 8, no. 3, 2008.
[16] M. Karagiannis, M. Molle, and A. Broido, "A Nonstationary Poisson View of Internet Traffic," Proc. IEEE INFOCOM, 2004.
[17] M.A. Khojastepour and A. Sabharwal, "Delay-Constrained Scheduling: Power Efficiency, Filter Design, and Bounds," Proc. IEEE INFOCOM, 2004.
[18] G. Latouche and V. Ramaswami, Introduction to Matrix Geometric Methods in Stochastic Modeling. SIAM, 1999.
[19] J.-Y. Le Boudec and P. Thiran, Network Calculus: A Theory of Deterministic Queueing Systems for the Internet. Springer-Verlag, 2001.
[20] S. Li and C. Hwang, "On the Convergence of Traffic Measurement and Queueing Analysis: A Statistical-Matching and Queueing (smaq) Tool," IEEE/ACM Trans. Networking, vol. 5, no. 1, pp. 95-110, Feb. 1997.
[21] S. Li and C. Hwang, "Queue Response to Input Correlation Functions: Discrete Spectral Analysis," IEEE/ACM Trans. Networking, vol. 1, no. 5, pp. 522-533, Oct. 1993.
[22] Y. Lu, T. Abdelzaher, and C. Lu, "Feedback Control with Queueing-Theoretic Prediction for Relative Delay Guarantees in Web Servers," Proc. Real-Time and Embedded Technology and Applications Symp. (RTSA), 2003.
[23] S. Ma and C. Ji, "Modeling Heterogeneous Network Traffic in Wavelet Domain," IEEE/ACM Trans. Networking, vol. 9, no. 5, pp. 634-649, Oct. 2001.
[24] D. Menasce and V. Almeida, Scaling for E-Business Technologies, Models, Performance, and Capacity Planning. Prentice Hall, 2000.
[25] N. Mi, G. Casale, L. Cherkasova, and E. Smirni, "Burstiness in Multi-Tier Applications: Symptoms, Causes, and New Models," Proc. Middleware Conf., 2008.
[26] I. Norros, "A Storage Model with Self-Similar Input," Queueing Systems, vol. 16, pp. 387-396, 1994.
[27] V. Paxson, "Fast, Approximate Synthesis of Fractional Gaussian Noise for Generating Self-Similar Network Traffic," Computer Comm. Rev., vol. 27, pp. 5-18, Oct. 1997.
[28] A. Parekh and R. Gallager, "A Generalized Processor Sharing Approach to Flow Control in Integrated Services Networks: The Single Node Case," IEEE/ACM Trans. Networking, vol. 1, no. 3, pp. 344-357, June 1993.
[29] R. Rajkumar, C. Lee, J. Lehoczky, and D. Siewiorek, "Practical Solutions for QoS-Based Resource Allocation Problems," Proc. Real-Time Systems Symp. (RTSS), 1998.
[30] T.G. Robertazzi, Computer Networks and Systems: Queueing Theory and Performance Evaluation. Springer-Verlag, 1990.
[31] K.W. Ross, M. Reisslein, and S. Rajagopal, "A Framework for Guaranteeing Statistical QoS," IEEE/ACM Trans. Networking, vol. 10, no. 1, pp. 27-42, Feb. 2002.
[32] V. Ribeiro, R. Riedi, M. Crouse, and R. Baraniuk, "Multiscale Queueing Analysis of Long-Range-Dependent Network Traffic," Proc. IEEE INFOCOM, 2000.
[33] O. Rose, "Statistical Properties of MPEG Video Traffic and Their Impact on Traffic Modeling in ATM Systems," Proc. Ann. Conf. Local Computer Networks (LCN), pp. 397-406, 1995.
[34] B. Schroeder and M. Harchol-Balter, "Web Servers under Overload: How Scheduling Can Help," ACM Trans. Internet Technologies, vol. 6, no. 1, pp. 20-52, Feb. 2006.
[35] M. Squillante, D. Yao, and L. Zhang, "Web Traffic Modeling and Web Server Performance Analysis," Proc. 38th IEEE Conf. Decision and Control, pp. 4432-4439, 1999.
[36] J. Wei and C.-Z. Xu, "eQoS: Provisioning of Client-Perceived End-to-End QoS Guarantees in Web Servers," IEEE Trans. Computers, vol. 55, no. 12, pp. 1543-1556, Dec. 2006.
[37] J. Wei and C.-Z. Xu, "sMonitor: A Non Intrusive Client-Perceived End-to-End Performance Monitor of Secured Internet Services," Proc. USENIX Ann. Technical Conf., May 2006.
[38] C. Xia and Z. Liu, "Queueing Systems with Long-Range Dependent Input Process and Subexponential Service Times," Proc. ACM SIGMETRICS, pp. 25-36, 2003.
[39] C.-Z. Xu, Scalable and Secure Internet Services and Architecture. Chapman Hill/CRC Press, 2005.
[40] C.-Z. Xu, J. Wei, and B. Liu, "Model Predictive Feedback Control for QoS Assurance in Web Servers," Computer, vol. 41, no. 3, pp. 66-72, Mar. 2008.
[41] M. Xu and C.-Z. Xu, "Decay Function Model for Resource Configuration and Adaptive Allocation on Internet Servers," Proc. Int'l Workshop Quality of Service (IWQoS), 2004.
[42] M. Xu and C.-Z. Xu, "Frequency Domain Filter Design and Analysis of Request Scheduling in Internet Servers," Proc. Int'l Conf. Distributed Computing Systems (ICDCS), 2008.
[43] Z.-L. Zhang, V. Ribeiro, S. Moon, and C. Diot, "Small-Time Scaling Behaviors of Internet Backbone Traffic: An Empirical Study," Proc. IEEE INFOCOM, pp. 1826-1836, 2003.
[44] X. Zhong, C.-Z. Xu, and M. Xu, "Optimal Time-Variant Resource Allocation for Internet Servers with Delay Constraints," Proc. Real-Time and Embedded Technology and Applications Symp (RTSA), 2005.
[45] X. Zhong and C.-Z. Xu, "Energy-Aware Modeling and Scheduling for Dynamic Voltage Scaling with Statistical Real-Time Guarantee," IEEE Trans. Computers, vol. 56, no. 3, pp. 358-372, Mar. 2007.
[46] X. Zhong and C.-Z. Xu, "Energy-Efficient Wireless Packet Scheduling with Quality of Service Control," IEEE Trans. Mobile Computing, vol. 6, no. 10, pp. 1158-1170, Oct. 2007.

Index Terms:
Scheduling, filter design, resource allocation, Internet server, frequency domain analysis.
Cheng-Zhong Xu, Minghua Xu, Le Yi Wang, George Yin, "Filter Design and Analysis in Frequency Domain for Server Scheduling and Optimization," IEEE Transactions on Parallel and Distributed Systems, vol. 21, no. 11, pp. 1573-1585, Nov. 2010, doi:10.1109/TPDS.2010.22
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