15-849b Theory of Performance Modeling (FALL 03)

Starting 9/03/03, MW 10:30 - 12, WEAN 4601

Extra-theoretical version of the traditional Performance Modeling Course. Offered only every 2 or 3 years!

Class lecture notes are here: Lecture notes and Homeworks

Queueing theory is an old area of mathematics which has recently become very hot. The goal of queueing theory has always been to improve the design/performance of systems, e.g. networks, servers, memory, distributed systems, etc., by finding smarter schemes for allocating resources to jobs. In this class we will study the beautiful mathematical techniques used in queueing theory, including stochastic analysis, discrete-time and continuous-time Markov chains, renewal theory, product-form, Laplace transforms, supplementary random variables, fluid theory, scheduling theory, matrix-geometric techniques, and more. Throughout the class we will emphasize realistic workloads, in particular heavy-tailed workloads. The techniques studied in this class are useful to students in Computer Science, Mathematics, ACO, GSIA, Statistics, and Engineering. This course is packed with open problems -- problems which if solved are not just interesting theoretically, but which have huge applicability to the design of computer systems today. Class Reviews


Monday and Wednesday 10:30-12, Wean Hall 4601


Recommended only for those comfortable with probability. Highly recommended for CS theory students, ACO students, GSIA students. Ph.D. students only. Assumes knowledge of continuous and discrete distributions, conditional probability, conditional expectation, moments, and some previous exposure to Markov Chains. Assumed material can be found in: "Introduction to Probability Models" by Sheldon M. Ross, Chapters 1-3. You can borrow this book from my office. No auditors allowed.




I will pass out my own course notes and some supplementary handouts and papers at the end of each class. Some good reference texts are listed here: BOOK LIST. You can borrow most of these books from my office.



You will receive one homework every week or 10 days. These will be difficult. Start immediately so that you can take full advantage of office hours. You will find office hours very helpful! Some of these homework problems will be repeated from previous years. The reason is that I have made up all the problems myself and it takes a very long time to think up good problems. Do not ask people who took this course in previous years to help you with the homeworks. This is considered cheating and will be reported to the dean. On the other hand, I strongly encourage you to collaborate with your current classmates to solve the homework problems after you have tried solving them by yourself. Each person must turn in a separate writeup. You should note on your homework specifically which problems were a collaborative effort and with whom.


PART I: Introduction, Operational Laws (laws that hold independent of any assumptions), Back-of-the-Envelope Bounds, and Modification Analysis.

PART II: Traditional Queueing Theory (with all the usual assumptions: Exponential Service, Poisson Arrivals, FCFS Scheduling). Strong emphasis on applications/case studies.

PART III: "MODERN" Applied Queueing Theory: Measured Heavy-tailed Workloads, Corrolated Arrivals, Preemptive Service Disciplines. (Applications include: Load Balancing in NOWs, Task Assignment in Super-Computing Centers, Scheduling in a Web Server, Scheduling in a Distributed Web Server.)