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

## CLASS STARTS AUGUST 30, 2021

### INSTRUCTORS:

 Prof. Mor Harchol-Balter Prof. Weina Wang TA Jalani Williams TA Mik Zlatin

### 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 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).
• 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.
• 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.
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.

### PREREQUISITES:

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 2 through 10 of the Undergraduate Probability Notes, in the "Probability for Computer Scientists" text that was mailed to you. We also expect you to know basic calculus and nested integrals, as are covered in Chapter 2 of the "Probability for Computer Scientists" text. 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 40% total. (We drop the lowest homework score)
• Midterm 1 -- 25% (somewhere after Chpt 14)
• Midterm 2 -- 25% (near the very end -- instead of a "final exam")
• ONE mandatory grading meeting during semester -- 5%. Will take place Friday or Saturday. Includes free dinner!
• Participation -- 5%.
• Standard grading scale: 90%- 100% is A; 80% - 89% is B; 70%- 79% is C; and so on, typically with curve at end.
• Note the large emphasis on homework. Homeworks are due Friday at the start of recitation and are graded over the weekend. It is your responsibility to get the homework to the TAs on time! If you cannot be in recitation, then email the homework to the TAs by the start of recitation. Any further issues should be handled through the TAs. Keep in mind that your TAs are busy. Your TAs will not grade your homework if they don't have it by the time they start grading.

### 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 writeup. You should note on your homework specifically which problems were a collaborative effort and with whom.

Please, no laptops during class. You will get a handout on which you can write your notes. Also, please no eating/drinking during class until COVID-19 improves. There will be a 3-minute break during most classes, to give you a chance to eat a quick snack or get a drink of water.

### PRIOR COURSE EVALUATIONS:

Prior course evaluations average 4.8/5.0. To see all FCEs for the instructors