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

## STARTS: WED SEPTEMBER 6, 2017

### We will closely follow my textbook Performance Modeling and Design of Computer Systems .

#### INSTRUCTORS:

Please use OFFICE HOURS to ask technical questions, rather than asking these via email.

## Click here: ANNOUNCEMENTS, HANDOUTS, and HOMEWORKS

#### 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! Outside of probability, you are also expected to know basic calculus. There are some warmup sheets available to help you practice your calculus. Click here for calculus warmup sheets. 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.

• Weekly Homeworks -- worth 60% total.
• Midterm 1 -- 15% (somewhere after Chpt 14)
• Midterm 2 -- 20% (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, with curve if needed.
• Note the HUGE emphasis on homework. If you do well on your homework, you cannot fail this class. Homeworks are generally due Friday in recitation (with a few exceptions) and are graded over the weekend. It is your responsibility to get the homework to the TAs on time. Any issues should be handled through the TAs.

#### 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.