15-359: Probability and Computing (SPRING 2013)

12 Units. Cross-listed with 15-659.

Classes: T,Th 10:30 - 12:00, Room: GHC 4307

Recitation A: F 10:30 Wean 5302

Recitation B: F 11:30 Wean 5302

HW1: Due 5 p.m. Wednesday Sept 19 under my door (GHC 7207): 2.2, 2.3, 3.8, 3.12, 3.13, 3.14, 3.23, 3.24, 3.25 (recommended for practice: 2.1, 3.6, 3.19, 3.22, 3.26, 5.1)
Recitation Notes from Sept 14 on Probability: pdf
HW2: Due 5 p.m. Thursday Sept 27 under my door (GHC 7207): 4.1, 6.2, 6.3, 6.4, 6.7, 7.1, 7.2, 7.3, 7.5.
Recitation Notes from Sept 21 on Generating RVs: pdf
HW3: Due IN CLASS WEDNESDAY Oct 10: 8.4, 8.6, 9.3, 9.4, 9.7, 9.8, 9.9, 9.12, 9.13, 9.14, 9.16, 10.3. (Optional problem: 7.6).
Recitation Notes from Sept 28 on Transforms: pdf
HW4: Due IN CLASS WEDNESDAY Oct 17: 10.1, 11.1, 11.4, 11.5, 11.6, 11.9, 11.12, 12.2, 25.2, 25.6. Extra Credit: 10.7 (Note: the extra credit may require reading Section 10.3).
HW5: Due IN CLASS WEDNESDAY Oct 24: 13.1, 13.5-13.7, 13.10, 13.11, 14.3 - 14.7, 25.9, 25.12.
MIDTERM: OCT 25, 5 p.m. - 7 p.m., in GHC 4303. You can bring one 3x5 index card with writing on one side.
HW6: Due IN CLASS FRIDAY Nov 2: 15.1 - 15.7, 15.10, 16.2, 17.1 - 17.3, 17.5.
HW7: Due IN CLASS FRIDAY Nov 9: 18.2 - 18.4, 18.6, 19.1, 19.3, 20.1 - 20.3.
HW8: Due IN CLASS MONDAY Nov 19: One of 21.3 or 21.8 ace; 21.2; 21.5; 21.6; 22.1; 23.3-23.5; 23.7; 23.9-23.11; 25.7; 25.8; 25.13; 25.14.
Recitation Notes from Nov 16 on Transforms: pdf
THERE WILL BE NO HOMEWORK FROM Nov 19 - Nov 25. Happy Thanksgiving!
HW9: Due IN CLASS MONDAY Dec 3: 24.2, 24.5, 24.6, 26.1, 26.3, 26.5, 27.1, 27.2 (see modification to 27.2 ), 27.3, 27.6, 29.2.
HW10: Due IN CLASS WEDNESDAY Dec 5: 30.1 and 30.3.
EXTRA OFFICE HOURS (MOR):

FRI, DEC 7: 3 p.m. - 4 p.m.
SAT, DEC 8: 4 p.m. - 5 p.m.
SUN, DEC 9: 4 p.m. - 5 p.m.
MON, DEC 10: 1 p.m. - 2 p.m.

EXAM: TUESDAY, Dec. 11 5:30p.m.- 8:30p.m., GHC 4215. You are allowed one 3x5 index card front and back for notes. Exam will cover only material from Chpt 14 onwards.

We will closely follow my textbook "Performance Modeling and Design of Computer Systems." This book is not yet available on Amazon.com, but will be made available as a spiral-bound soft-copy for students in the class. To get a copy, stop by my office (GHC 7207) any time after August 27th.
INSTRUCTORS:

Prof. Mor Harchol-Balter OFFICE HOURS: M,W 3-4:30 p.m. in Gates 7207, Phone: x8-7893.
TA: Sherwin Doroudi OFFICE HOURS: T,TH 4:30 - 5:30 p.m. in Gates 7th Floor Atrium

DESCRIPTION:

In designing computer systems one is usually constrained by certain performance requirements and limitations. For example, one might need to guarantee a response time SLA or certain throughput requirement, while at the same time staying within a power budget or cost budget. On the other hand, one often has many choices: One fast disk, or two slow ones? More memory, or a faster processor? A fair scheduler or one that minimizes mean response time? For multi-server systems, one can choose from a wide array of load balancing policies, a wide array of migration policies, capacity provisioning schemes, power management policies ... The possibilities are endless. The best choices are often counter-intuitive. Ideally, one would like to have answers to these questions before investing the time and money to build a system. This class will introduce students to analytic stochastic modeling with the aim of answering the above questions.

Topics covered include:

Operational Laws: Little's Law, response-time law, asymptotic bounds, modification analysis, performance metrics;
Markov Chain Theory: discrete-time Markov chains, continuous-time Markov chains, renewal theory, time-reversibility; Poisson Process: memorylessness, Bernoulli splitting, uniformity, PASTA;
Queueing Theory: open networks, closed networks, time-reversibility, Renewal-Reward, M/M/1, M/M/k, M/M/k/k, Burke's theorem, Jackson networks, classed networks, load-dependent servers, BCMP result and proof, M/G/1 full analysis, M/G/k, G/G/1, transform analysis (Laplace and z-transforms);
Simulations: time averages versus ensemble averages, generating random variables for simulation, Inspection Paradox;
Modeling Empirical Workloads: heavy-tailed property, Pareto distributions, heavy-tailed distributions, understanding variability and tail behavior, Matrix-analytic methods;
Management of Server Farms: capacity provisioning, dynamic power management, routing policies;
Analysis of Scheduling: FCFS, non-preemptive priorities, preemptive priorities, PS, LCFS, FB, SJF, PSJF, SRPT, etc.

Throughout, the theory developed will be applied to a wide array of computer systems design problems including the design of efficient data centers, web servers, DBMS, disks, call centers, routers, and supercomputer centers.

The techniques studied in this class are useful to students in Computer Science, ECE, Mathematics, ACO, Tepper, Statistics, MLD, 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.

For a more detailed description see the Table of Contents of the book.

PREREQUISITES:

We assume a reasonable background in probability, such as that covered in an Undergraduate Probability class. Specifically, we assumes a knowledge of continuous and discrete distributions, conditional probability, conditional expectation, and higher moments. All the assumed material can be found in Chapter 3 of my book. You can pick up a free copy of Chapter 3 of my book from my office (GHC 7207) at any time! Come over now! There is an entrance exam for this class. So make sure you've got the prerequisites.

GRADING:

Weekly Homeworks -- worth 45% total.
Midterm 1 -- 20% (somewhere after Chpt 14)
Midterm 2 -- 20% (near the very end)
One grading meeting during semester -- 5%.
Class participation -- 10%.
10% BONUS if you solve an Open Problem.

COLLABORATING vs. CHEATING:

You will receive regular homework problems. 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.

ADDITIONAL SOURCES:

In addition to the textbook for the class, there are additional sources available on this Booklist that you can borrow from my office: BOOK LIST.

PRIOR COURSE EVALUATIONS:

Prior course evaluations average 4.86/5.0 for "Course Overall" and 4.94/5.0 for "Instructor Overall." To see all FCEs for the instructor Click Here .