15-857: Analytical Performance Modeling & Design of Computer Systems
Cross-listed with Tepper: 47-774 & 47-775. 12 Units.
Satisfies THEORY CORE requirement for CSD PhDs.
Classes: M,W,F 2:00 p.m. - 3:20 p.m., Room: GHC 4307
CLASS STARTS AUGUST 28, 2023
This class meets 3x per week, although a few classes will be canceled due to travel. There is no recitation.
- Monday 5:30 p.m. - 7 p.m. in GHC 5th floor, Carrel 2, with Anup Agarwal email@example.com
- Tuesday 3:30 p.m. - 5 p.m. in GHC 5007, with Jalani Williams firstname.lastname@example.org
- Wednesday 5:30 p.m. - 7 p.m. in GHC 7207 with Mor Harchol-Balter email@example.com
- Thursday 7 p.m. - 8:30 p.m. in GHC 5th floor, Carrel 4, with Andrew Park firstname.lastname@example.org
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:
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.
- 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,
- Queueing Theory: open systems, closed systems, M/M/1, M/M/k, M/M/k/k, M/G/1 full analysis,
M/G/k, G/G/1, transform analysis (Laplace and z-transforms).
- Queueing Theory: Networks of Queues. Jackson and class-Jackson networks.
- Simulations: time averages versus ensemble averages,
generating random variables for simulation, Inspection
- Modeling Empirical Workloads: heavy-tailed property,
Pareto distributions, heavy-tailed distributions, understanding variability and
- 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, plus the latest scheduling research: SOAP.
- Applications to Today's Datacenters:
Scheduling for multiserver system, resource allocation for multi-dimensional jobs, c-mu rule for maximizing value, parallel jobs with different speedup functions.
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.
We assume a reasonable background in probability, such as that covered in an Undergraduate Probability class.
Specifically, we assume a knowledge of continuous and discrete
distributions, conditional probability, conditional expectation, and higher moments.
Chapter 3 of our textbook summarizes most of the assumed material. Alternatively, you can get a much better feel for the assumed material by reading Chapters 1 through 9 of the Undergraduate PnC Probability Book: "Introduction to Probability for Computing" textbook that was mailed to you.
We also expect you to know basic calculus and nested integrals (3D integration). 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 and calculus.
If math is not your cup of tea, there's an alternate offering of this course that is taught with "zero math," called 15-829 .
- Weekly Homeworks -- worth 40% total. (We drop the lowest homework score)
- Midterm 1 -- 25% Tentatively: Evening Oct 12.
- Midterm 2 -- 25% Tentatively: Evening Dec 7.
- NO FINAL EXAM (go home early!)
- ONE mandatory grading meeting during semester -- 5% . Will take place over the weekend. Includes free dinner!
- ONE 30-minute individual (or pair) meeting with Jalani or Mor where you present an example of queueing in your research or your life. Best to run this by a TA first! Super informal. No slides. -- 5% .
- Standard grading scale: 90%- 100% is A; 80% - 89% is B; 70%- 79% is C; and so on, often with curve at end.
HOMEWORK POLICY and LATENESS:
There is a large emphasis on homework. This is how you learn. Homeworks are released on Friday morning. Please start the homeworks early and get help in office hours!
Homeworks are due at the start of Friday's class ( 2 p.m. sharp ). Please turn in a physical copy of your homework, because that's easier for us to grade. Homeworks can be hand-written if that's easier for you, but you need to keep your writing legible. The homework is graded over the weekend, and you will receive your graded homework back in Monday's class, as well as a full solution.
If you cannot be in class on Friday, then it is your responsibility to email your homework to the TAs by 2 p.m. Friday. If you are going to be late, you need to coordinate with your TAs. They might or might not give you an extension until the time when the homework grading session happens (typically Saturday). Keep in mind that your TAs are busy, so don't make a habit of asking for such extensions. Your TAs will not grade your homework if they don't have it by the time they start their weekend grading, so, whatever you do, make sure the TAs have your homework in time to grade.
We will drop your lowest homework grade, so as to cover emergencies like illness and last-minute paper deadlines. Please save up your drop for a real emergency.
COLLABORATING vs. CHEATING and other RULES:
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 we have made up
all the problems ourselves 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, we 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 write-up. You should
note on your homework specifically which problems were a collaborative
effort and with whom.
Please, no laptops during class.
PRIOR COURSE EVALUATIONS:
Prior course evaluations average 4.8/5.0. To see all FCEs for the instructors Click Here .