Fractal Network Traffic Analysis with Applications

iii To my parents iv ACKNOWLEDGEMENTS This thesis is dedicated to my parents for their compassionate support and encouragement. Although we are thousands of miles apart, they are with me everyday. This thesis is also partially theirs. The work helps us understand each other better. I am greatly indebt to my advisor Prof. John Copeland for his patience, his financial support, and the advice he gave his students personally, and in every group meeting for more than seven years. Vidakovic for their instruction on solving math problems. I also want to thank the engineers from Scientific Atlanta that I had coordinated with in my research projects on broadband networks in the past few years. They are Dr. Dennis of MIT, with whom I worked and learned about Gigabit network processor processing and designs in Acorn Networks; and also Mike Coffee, CEO of Commetrex, with whom I worked on media network processing. Last but not least, I thank many of my colleagues and friends from the research groups of CSC, CSIP, the CS networking group, and the ISYE statistical group. I was fortunate to work with you and to learn from you. Particularly, I would like to mention Ms. Kathy Cheek, my administrator in CSC, who has helped me with tedious paper work and has done a wonderful job, and my friend Jonathan Atteberry, who helped me with my English, which I am still learning. Finally, the completion of a thesis is not an end of anything but a beginning of everything. For years ahead, I believe there are many engineering and scientific problems to be solved using fractals, which motivates me to continue this work.

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