Abstract
Over the last decade an important new direction has developed in the performance evaluation of computer systems: the study of heavy-tailed distributions. Loosely speaking, these are distributions whose tails follow a power-law with low exponent, in contrast to traditional distributions (e.g., Gaussian, Exponential, Poisson) whose tails decline exponentially (or faster). In the late ’80s and early ’90s experimental evidence began to accumulate that some properties of computer systems and networks showed distributions with very long tails [7],[28],[29], and attention turned to heavy-tailed distributions in particular in the mid ’90s [3],[9],[23],[36],[44].
This is a revised version of a paper originally appearing in Lecture Notes in Computer Science 1786, pp. 1–9, March 2000.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Réka Albert, Hawoong Jeong, and Albert-László Barabási. Diameter of the world wide web. Nature, 401:130–131, 1999.
Virgílio Almeida, Azer Bestavros, Mark Crovella, and Adriana de Oliveira. Characterizing reference locality in the WWW. In Proceedings of 1996 International Conference on Parallel and Distributed Information Systems (PDIS’ 96), pages 92–103, December 1996.
Martin F. Arlitt and Carey L. Williamson. Internet web servers: Workload characterization and performance implications. IEEE/ACM Transactions on Networking, 5(5):631–645, 1997.
Paul Barford and Mark E. Crovella. Generating representative Web workloads for network and server performance evaluation. In Proceedings of Performance’ 98/SIGMETRICS’ 98, pages 151–160, July 1998.
Lee Breslau, Pei Cao, Li Fan, Graham Phillips, and Scott Shenker. Web caching and zipf-like distributions: Evidence and implications. In Proceedings of INFOCOM’ 99, pages 126–134, 1999.
Andrei Broder, Ravi Kumar, Farzin Maghoul, Prabhakar Raghavan, Sridhar Rajagopalan, Raymie Stata, Andrew Tomkins, and Janet Wiener. Graph structure in the web: experiments and models. In Proceedings the Ninth World Wide Web Conference (WWW9), 2000.
R. Cáceres, P. B. Danzig, S. Jamin, and D. J. Mitzel. Characteristics of wide-area TCP/IP conversations. Computer Communication Review, 21, 1991.
M. E. Crovella, M. Harchol-Balter, and C. D. Murta. Task assignment in a distributed system: Improving performance by unbalancing load. Technical Report TR-97-018, Boston University Department of Computer Science, October 31 1997.
Mark E. Crovella and Azer Bestavros. Self-similarity in World Wide Web trafic: Evidence and possible causes. IEEE/ACM Transactions on Networking, 5(6):835–846, December 1997.
Mark E. Crovella, Robert Frangioso, and Mor Harchol-Balter. Connection scheduling in Web servers. In 1999 USENIX Symposium on Internet Technologies and Systems (USITS’ 99), 1999.
Mark E. Crovella, Mor Harchol-Balter, and Cristina Duarte Murta. Task assignment in a distributed system: Improving performance by unbalancing load. In Proceedings of SIGMETRICS’ 98 (poster paper), July 1998.
Mark E. Crovella and Lester Lipsky. Simulations with heavy-tailed workloads. In Kihong Park and Walter Willinger, editors, Self-Similar Network Trafic and Performance Evaluation. Wiley / Wiley Interscience, New York, 1999.
Carlos A. Cunha, Azer Bestavros, and Mark E. Crovella. Characteristics of WWW client-based traces. Technical Report TR-95-010, Boston University Department of Computer Science, April1995.
Michalis Faloutsos, Petros Faloutsos, and Christos Faloutsos. On power-law relationships of the internet topology. In Proceedings of SIGCOMM’ 99, 1999.
Anja Feldmann, Jennifer Rexford, and Ramon Caceres. Eficient policies for carrying web trafic over flow-switched networks. IEEE/ACM Transactions on Networking, December 1998.
Anja Feldmann and Ward Whitt. Fitting mixtures of exponentials to long-tail distributions to analyze network performance models. In Proceedings of IEEE INFOCOM’97, pages 1098–1116, April 1997.
Sharad Garg, Lester Lipsky, and Maryann Robbert. The effect of power-taildistributions on the behavior of time sharing computer systems. In 1992 ACM Symposium on Applied Computing, Kansas City, MO, March 1992.
Steven Glassman. A caching relay for the World Wide Web. In Proceedings of the First International World Wide Web Conference, pages 69–76, 1994.
Charles M. Goldie and Claudia Kluppelberg. Subexponential distributions. In Robert J. Adler, Raisa E. Feldman, and Murad S. Taqqu, editors, A Practical Guide To Heavy Tails, pages 435–460. Chapman & Hall, New York, 1998.
Michael Greiner, Manfred Jobmann, and Lester Lipsky. The importance of powertail distributions for telecommunication tra.c models. Operations Research, 41, 1999.
S. D. Gribble, G. S. Manku, D. Roselli, E. A. Brewer, T. J. Gibson, and E. L. Miller. Self-similarity in file systems. In Proceedings of SIGMETRICS’ 98, pages 141–150, 1998.
M. Harchol-Balter, M. E. Crovella, and S. Park. The case for SRPT scheduling in Web servers. Technical Report MIT-LCS-TR-767, MIT Lab for Computer Science, October 1998.
M. Harchol-Balter and A. Downey. Exploiting process lifetime distributions for dynamic load balancing. ACM Transactions on Computer Systems, 15(3):253–285, 1997.
Mor Harchol-Balter, Mark E. Crovella, and Cristina D. Murta. On choosing a task assignment policy for a distributed server system. Journal of Parallel and Distributed Computing, SpecialIssue on Software Support for Distributed Computing, September 1999.
Gordon Irlam. Unix file size survey-1993. Available at http://www.base.com-/gordoni/ufs93.html, September 1994.
Cheng Jin, Qian Chen, and Sugih Jamin. Inet: internet topology generator. Technical Report CSE-TR-433-00, U. Michigan Computer Science, 2000.
Butler W. Lampson. Hints for computer system design. Proceedings of the Ninth SOSP, in Operating Systems Review, 17(5):33–48, October 1983.
W. E. Leland and T. J. Ott. Load-balancing heuristics and process behavior. In Proceedings of Performance and ACM Sigmetrics, pages 54–69, 1986.
W. E. Leland and D. V. Wilson. High time-resolution measurement and analysis of LAN trafic: Implications for LAN interconnection. In Proceeedings of IEEE Infocomm’ 91, pages 1360–1366, Bal Harbour, FL, 1991.
W.E. Leland, M.S. Taqqu, W. Willinger, and D.V. Wilson. On the self-similar nature of Ethernet tra.c (extended version). IEEE/ACM Transactions on Networking, 2:1–15, 1994.
Benoit B. Mandelbrot. The Fractal Geometry of Nature. W. H. Freedman and Co., New York, 1983.
Alberto Medina, Ibrahim Matta, and John Byers. BRITE: a flexible generator of internet topologies. Technical Report BU-CS-TR-2000-05, Boston University Computer Science, January 2000.
Norifumi Nishikawa, Takafumi Hosokawa, Yasuhide Mori, Kenichi Yoshida, and Hiroshi Tsuji. Memory-based architecture for distributed WWW caching proxy. Computer Networks and ISDN Systems, 30:205–214, 1998.
I. Norros. A storage model with self-similar input. Queueing Systems, 16:387–396, 1994.
Kihong Park, Gi Tae Kim, and Mark E. Crovella. On the relationship between file sizes, transport protocols, and self-similar network trafic. In Proceedings of the Fourth International Conference on Network Protocols (ICNP’96), pages 171–180, October 1996.
Vern Paxson. Empirically-derived analytic models of wide-area tcp connections. IEEE/ACM Transactions on Networking, 2(4):316–336, August 1994.
Vern Paxson and Sally Floyd. Wide-area trafic: The failure of poisson modeling. IEEE/ACM Transactions on Networking, pages 226–244, June 1995.
D. Peterson and R. Grossman. Power laws in large shop DASD I/O activity. In CMG Proceedings, pages 822–833, December 1995.
David L. Peterson. Data center I/O patterns and power laws. In CMG Proceedings, December 1996.
David L. Peterson and David B. Adams. Fractalpatterns in DASD I/O trafic. In CMG Proceedings, December 1996.
Matthew Roughan, Darryl Veitch, and Michael Rumsewicz. Computing queuelength distributions for power-law queues. In Proceedings of INFOCOM’ 98, pages 356–363, 1998.
Anees Shaikh, Jennifer Rexford, and Kang Shin. Load-sensitive routing of longlived IP flows. In Proceedings of ACM SIGCOMM’ 99, pages 215–226, September 1999.
R. W. Weber. On the optimal assignment of customers to parallel servers. Journal of Applied Probability, 15:406–413, 1978.
Walter Willinger, Murad S. Taqqu, Robert Sherman, and Daniel V. Wilson. Selfsimilarity through high-variability: Statistical analysis of Ethernet LAN trafic at the source level. IEEE/ACM Transactions on Networking, 5(1):71–86, February 1997.
G. K. Zipf. Human Behavior and the Principle of Least-Effort. Addison-Wesley, Cambridge, MA, 1949.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Crovella, M.E. (2001). Performance Evaluation with Heavy Tailed Distributions. In: Feitelson, D.G., Rudolph, L. (eds) Job Scheduling Strategies for Parallel Processing. JSSPP 2001. Lecture Notes in Computer Science, vol 2221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45540-X_1
Download citation
DOI: https://doi.org/10.1007/3-540-45540-X_1
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42817-6
Online ISBN: 978-3-540-45540-0
eBook Packages: Springer Book Archive