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Copyright 1999 Gary McGraw and Edward Felten. All rights reserved. Published by John Wiley & Sons, Inc.

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We have shown that a dif cult problem arises when simulating systems with heavytailed workloads. In such systems, steady-state behavior can be elusive, because

average-case behavior depends on the presence of many small observations as well as a few large observations. This problem has two implications. First, since a number of large but rare observations must occur before average-case behavior is evident, convergence of a simulation to steady state may be slow. It may not be possible in any reasonable time to achieve steady state. Second, since many small observations must occur to balance the presence of large observations, large observations can have a dominating effect on performance results even at steady state. Simulations may still behave erratically even at steady state. ACKNOWLEDGMENTS This research was supported in part by NSF grant CCR-9501822 and by a grant from Hewlett-Packard Company. REFERENCES

CHAPTER SECTIONS: 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13

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1. M. F. Arlitt and C. L. Williamson. Web server workload characterization: the search for invariants. IEEE=ACM Trans. Networking, 5(5):631 645, 1997. 2. S. Asmussen and K. Binswanger. Simulation of ruin probabilities for subexponential claims. Preprint, 1995. 3. M. E. Crovella and A. Bestavros. Self-similarity in World Wide Web traf c: evidence and possible causes. IEEE=ACM Trans. Networking, 5(6):835 846, December 1997. 4. W. Feller. An Introduction to Probability Theory and Its Applications, Vol. II, 2nd ed. Wiley, New York, 1971. 5. M. Garrett and W. Willinger. Analysis, modeling, and generation of self-similar VBR video traf c. In Proc. ACM SIGCOMM '94, September 1994. 6. C. M. Goldie and C. Kluppelberg. Subexponential distributions. In R. J. Adler, R. E. Feldman, and M. S. Taqqu, eds., A Practical Guide to Heavy Tails, pp. 435 460. Chapman and Hall, New York, 1998. 7. M. Harchol-Balter and A. Downey. Exploiting process lifetime distributions for dynamic load balancing. ACM Trans. Comput. Syst., 15(3):253 285, 1997. 8. P. Heidelberger. Fast simulation of rare events in queueing and reliability models. Lecture Notes Comput. Sci., 729:165 202, 1993. 9. W. E. Leland and T. J. Ott. Load-balancing heuristics and process behavior. In Proceedings of Performance and ACM Sigmetrics, pp. 54 69, 1986. 10. W. E. Leland, M. S. Taqqu, W. Willinger, and D. V. Wilson. On the self-similar nature of Ethernet traf c (extended version). IEEE=ACM Trans. Networking, 2:1 15, 1994. 11. K. Park, G. T. Kim, and M. E. Crovella. On the relationship between le sizes, transport protocols, and self-similar network traf c. In Proceedings of the Fourth International Conference on Network Protocols (ICNP'96), pp. 171 180, October 1996. 12. V. Paxson. Fast approximation of self-similar network traf c. Technical Report LBL36750, Lawrence Berkely National Laboratory, April 30 1995.

13. D. L. Peterson, Data center I=O patterns and power laws. In CMG Proceedings, December 1996. 14. R. Y. Rubinstein and B. Melamed. Ef cient Simulation and Monte Carlo Methods, Wiley, New York, 1997. 15. G. Samorodnitsky and M. S. Taqqu. Stable Non-Gaussian Random Processes. Stochastic Modeling. Chapman and Hall, New York, 1994.

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Self-Similar Network Traf c and Performance Evaluation, Edited by Kihong Park and Walter Willinger Copyright # 2000 by John Wiley & Sons, Inc. Print ISBN 0-471-31974-0 Electronic ISBN 0-471-20644-X

The Java language is designed to enforce type safety. This means that programs are prevented from accessing memory in inappropriate ways. More specifically, every piece of memory is part of some Java object. Each object has some class. For example, a calendar-management applet might use classes like Date, Appointment, Alarm, and GroupCalendar. Each class defines both a set of objects and operations to be performed on the objects of that class. In our calendar management example, the Alarm class might define a turnOn operation, but the Date class would neither need nor allow turnOn. Type safety means that a program cannot perform an operation on an object unless that operation is valid for that object.

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