Course Info

This is a new course that covers topics in the performance analysis of computer systems. The contents of the course should prove very helpful for computer science students who wish to analyze computer systems and learn more about how to improve the performance of systems. Existing courses do not cover this material.
The course is targeted primarily at PhD and Masters students in the Computer Science Department, however upper-level undergraduates can take the course as well. In addition, students from AMS, Math, and ECE would also benefit from the course contents.
Students are expected to voice their opinions on the papers to make the class more interactive (=fun).

Grading will be based on assignments, exams, and class participation.

Syllabus & Schedule

Date	Topic	Readings	Notes
Jan 27 (Tuesday)	No class	-	Snow day :-)
Jan 29 (Thursday)	Introduction, Class logistics 1. Class logistics 2. Overview of syllabus	-	-
Feb 03 (Tuesday)	Probs & Stats 1 1. Probability basics 2. Random variables 3. Discrete: Bernoulli, Binomial, Geometric 4. Continuous: Uniform	MHB, Ch. 3.1 - 3.9. Ross, Probability book.	-
Feb 05 (Thursday)	Probs & Stats 2 1. Exponential distribution 2. Joint RVs 3. L.O.E., P.O.E., independent RVs 4. Conditional probability	MHB, Ch. 3.8 - 3.11.	-
Feb 10 (Tuesday)	DTMC - 1 1. Probs & Stats - sum of RV number of RVs 2. DTMC basics and definitions 3. Clear/Snowy example 4. Powers of one-step probability matrix, P	MHB, Ch. 8.1 - 8.4.	-
Feb 12 (Thursday)	DTMC - 2 1. Limiting probability and stationary probability 2. Guessing a solution to the DTMC 3. Solving DTMCs	MHB, Ch. 8.5 - 8.10.	Assignment 1 out. Due in class, 2/26.
Feb 17 (Tuesday)	DTMC - 3 1. C-states management 2. PageRank 3. Irreducible and Aperiodic DTMCs 4. Existence of limiting probability for finite DTMCs 5. Single server with unbounded queue	MHB, Ch. 8.10, 9.1-9.2, 10.1.	-
Feb 19 (Thursday)	No class	-	Assignment 2 out. Due in class, 3/05. Career Fair
Feb 24 (Tuesday)	DTMC - 4 1. Positive recurrence 2. Tii for M/M/1 3. Tii for successive failures	-	-
Feb 26 (Thursday)	CTMC - 1 1. Memoryless property 2. Exponential distribution 3. Ordering property for exp 4. Distribution of min of exp 5. Multi-server queue example	MHB, Ch. 12.1 - 12.4.	-
March 03 (Tuesday)	CTMC - 2 1. Poisson distribution 2. Relationship between Poisson and exp 3. Merging property for Poisson 4. Splitting property for Poisson	MHB, Ch. 12.5 - 12.7.	-
March 05 (Thursday)	No class	-	Snow day
March 10 (Tuesday)	CTMC - 3 1. Relationship between geometric and exp 2. CTMC as a DTMC 3. Solving a CTMC 4. M/M/1 example	MHB, Ch. 13, 14.1.	Assignment 3 out. Due in class, 4/2.
March 12 (Thursday)	Mid-term 1	-	-
March 24 (Tuesday)	No class	-	Travel
March 26 (Thursday)	CTMC - 4 1. Service time and service rate 2. Utilization 3. First-step analysis and Tii 4. Little's Law	MHB, Ch. 2.2, 2.5, 6.1-6.2.	-
March 31 (Tuesday)	M/M/1 1. Proof and applications of Little's Law 2. M/M/1 analysis 3. D/D/1 4. Network of parallel M/M/1 systems 5. Network of M/M/1 systems in series	MHB, Ch. 6.4, 14.1-14.2.	-
April 02 (Thursday)	M/M/1 variants and M/M/k 1. PASTA 2. H2, E2, Coefficient of variation (C2) 3. M/H2/1 4. E2/M/1 5. Mt/M/1 6. M/M/k	MHB, Ch. 14.3, 22.1-22.2, 15.3.	Assignment 4 out. Due in class, 4/16.
April 07 (Tuesday)	M/M/k and variants 1. M/M/k 2. M/M/k/k 3. M/M/∞ 4. PQ, PBlock 5. Physical interpretations	MHB, Ch. 15.2-15.3, 16.1-16.2.	-
April 09 (Thursday)	Applications of M/M/k 1. Modeling multi-core, hyperthreading, DBs 2. Load-dependent service rates 3. Comparison of M/M/1 and M/M/k 4. Capacity provisioning 5. Modeling power consumption	MHB, Ch. 15.4, 16.2, 28.1.	-
April 14 (Tuesday)	M/M/1/Setup, RC, TR 1. M/M/1/Setup 2. Comparison between M/M/1 and M/M/1/Setup 3. Sleep states, Delaying sleep 4. Rate Conservation 5. Time Reversibility	MHB, Ch. 16.2.	-
April 16 (Thursday)	Burke's Theorem 1. Burke's Theorem statements 1 and 2 2. Poisson(λ) departures 3. M/M/1 in series 4. Partial CTMC for M/M/1 series 5. Acyclic networks 6. Extension to M/M/k in series	MHB, Ch. 16.3-16.6.	Assignment 5 out. Due in class, 4/30.
April 21 (Tuesday)	More on Burke's Theorem 1. Proof sketch of statement 1 of Burke's Theorem 2. Product form for Burke's 3. Applications of Burke's Theorem 4. Description of Jackson Networks	MHB, Ch. 16.4-16.6, 17.1.	-
April 23 (Thursday)	Jackson Networks 1. Arrival rate in Jackson Networks 2. Rate Conservation revisited 3. Setting up state equations 4. Solving balance equations 5. Interpreting the limiting probabilities	MHB, Ch. 17.1-17.4.	-
April 28 (Tuesday)	More on Jackson Networks 1. Product form for Jackson Networks 2. Applications of Jackson Networks 3. Description of Jackson Networks	MHB, Ch. 17.4.	-
April 30 (Thursday)	M/G/1 1. Description of M/G/1 2. Tagged-job analysis of M/G/1 3. Example distributions for G 4. Inspection Paradox	MHB, Ch. 23.1-23.2.	Assignment 5 due.
May 05 (Tuesday)	Renewal-Reward Theory 1. Inspection Paradox explained 2. Renewal-Reward Theorem 3. Example applications of Renewal-Reward	MHB, Ch. 23.3-23.5.	-
May 07 (Thursday)	Renewal-Reward and M/G/1 1. Train station problem 2. Recursive Renewal Reward application 3. E[Se] 4. E[T] for M/G/1	MHB, Ch. 23.3-23.6.	-

Resources

• Recommended text: "Performance Modeling and Design of Computer Systems: Queueing Theory in Action" by Mor Harchol-Balter (MHB).
• There is copy placed on reserve in the library. The instructor also has a few personal copies that you can borrow.


• Others:
• S.M. Ross, Introduction to Probability Models, Academic Press
• L. Kleinrock: Queueing Systems, Vol. I and II, Wiley
• R.W. Wolff: Stochastic Modeling and the Theory of Queues, Prentice Hall
• R. Jain: The Art of Computer System Performance Analysis, Wiley
• S.M. Ross, Stochastic Processes, Wiley

Grading (tentative)

• Assignments: 45%
• Roughly 1 assignment every 2 weeks. Expect 5-8 questions per assignment.
• Collaboration is allowed (max group size 3). Submit one solution per group.
• Assignments are due in class. No late submissions allowed. Hard-copies only, please.


• Exams: 45%
• Two in-class exams.
• Mid-term 1: 20%.
• Mid-term 2: 25%.
• Roughly as difficult as the assignments.


• Class interaction: 10%
• The basic idea is to get you to talk in the class and contribute to discussions.
• By the end of the semester, if I can recognize you based on your contributions to the class discussion, you should get a good score on this.
• Very helpful for bumping your grade if you are on the border.