# 15-857: Analytical Performance Modeling & Design of Computer Systems

## 12 Units. Cross-listed with Tepper: 47-774 and 47-775.

## Classes: M,W 1:30 p.m. - 2:50 p.m., Room: GHC 4307

#

## Recitation: F 1:30 p.m. - 2:50 p.m., Room: GHC 4307

## STARTS: WED SEPTEMBER 6, 2017

#### INSTRUCTORS:

#### 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 our textbook.
Please read through all of Chapter 3 before the start of class. Make sure that you can solve all the exercises in Chapter 3. You can come see me or your TAs for help!
There is an assessment provided on the first day of class to make it clear to you if you have the prerequisites with respect to undergraduate probability.

#### GRADING:

- Weekly Homeworks -- worth 50% total.
- Midterm 1 -- 20% (somewhere after Chpt 14)
- Midterm 2 -- 25% (near the very end -- instead of a "final exam")
- One mandatory grading meeting during semester -- 5%.
- Standard grading scale: 90%- 100% is A; 80% - 89% is B; 70%- 79% is C; and so on.
- Bonus points available at the discretion of the professor. Typically bonus points are given for either solving an open queueing theory problem, or applying class material towards solving an applied 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 4.8/5.0 for "Course Overall" and 4.9/5.0 for "Instructor Overall."
To see all FCEs for the instructor ** Click Here ** .