Format

Course Organization at-a-Glance

Although the course Syllabus is organized at a traditional "lecture" granularity, the course can be seen to consist of five (5) broad, logical units. Each unit is organized more or less the same way:

• Preparatory preamble. This is material, mostly in the form of reading assignments (see Syllabus) and Preview problems that need to be completed before each module/lecture of the unit.
• Information push. This is the equivalent of "lecture" component in a traditional course and will mirror it relatively closely, though possibly with a different granularity. It is in the form of either synchronous lectures or asynchronous recordings that cover essentially the same material.
• Assimilation. A session, either synchronous or asynchronous, that goes over possible applications of the material that was covered in the preceding "information push".
• Assessment. This is meant to determine how well students have absorbed the material from a given unit. It will be in the form of a short quiz and/or a set of "homework" problems. Quizzes will be administered in a time-limited fashion, while homework problems do not have time limits. Homeworks need to be completed without any outside help, and for each homework every student will be asked to explain and justify their solution for a randomly selected problem.

The five course units are as follows:

• Unit 1: Probability Refresher & Basic Principles [1.5 weeks – 3 lectures]
  • This unit is meant to reintroduce students to basic concepts and tools from probability that will be essential to the rest of the course. It also offers a first glimpse into how to apply those tools to obtain simple but useful characterization of system performance in a variety of settings. Basic performance metrics or interest are also introduced in this unit.
  • The unit is also used to introduce the students to the use of preview problems that they need to complete ahead of each session.
• Unit 2: Discrete time Markov chains (DTMC) [2 weeks – 4 lectures]
  • This unit introduces the concept of Markov chains and their use in modeling various basic systems to obtain performance metrics of interest. Students are also introduced to the concept of time reversibility that will be subsequently used to study more complex systems.
  • The goal of this unit is to help students understand what systems can be represented using discrete time Markov chains, and how to use them to extract performance metrics of interest.
• Unit 3: Continuous time Markov chains (CTMC) [2 weeks – 4 lectures]
  • This unit exposes the limitations of discrete time models and introduces continuous time processes and their use in developing a continuous time version of Markov chains, which are then applied to study a number of basic (single queue) systems. Applications leveraging those techniques to answer “provisioning” questions (how big or fast should my system be to meet certain performance levels) are also covered.
  • After completing this unit, students should understand both similarities and differences between discrete time and continuous time Markov chains, and be able to choose which one to rely on to model different types of systems. They will also be exposed to using results from CMTC analysis to evaluate and approximate some basic non-Markovian systems, and in the process become awareness of the limitations of the Markovian assumption.
• Unit 4: Queueing Networks [2 weeks – 4 lectures]
  • This unit builds on Unit 4 to consider more complex systems that can still be modeled using CTMC, namely, networks of queues. Those have applications in communication, computer, and manufacturing systems, and more generally systems that consist of sequences of connected “service” facilities. Students will gain awareness of the fact that what is gained in model sophistication is to a large extent lost in system intuition. In other words, while the models give answers, they don’t always give insight. The two are, however, useful in different contexts and this unit seeks to impart students with an appreciation for those differences.
  • This unit introduces students to models applicable to more complex interconnected systems, while also making them aware of

their limitations and the assumptions on which they rely.

• Unit 5: Advanced Modeling techniques and Applications [4 weeks – 8 lectures]
  • This is the last and most demanding unit of the class. It exposes students to more advanced modeling techniques, both numerical and analytical, that overcome the limitations inherent to Markov chains. The unit also includes several applications of those techniques to a set of questions of relevance to the design of computer systems. It alternates between exposure to new tools and illustrations of how to apply them to problems of relevance.
  • After this unit students will either hate or love the class ;-), but hopefully will have acquired a set of powerful modeling tools and an understanding of how they can be used to not just evaluate system performance, but also design systems that aim to optimize different performance metrics.

Course Structure

Overview & Grading

The class will follow a semi-flipped format. Specifically, a typical lecture will include:

• reading assignment and preview problems that will need to be completed AHEAD of the lecture;
• in-class problems that will build on the preview problems and be used to explore the material covered in the preview problems;
• lecture component that will be used to expand on or clarify material from the reading assignment.

This format works ONLY if students have completed the reading assignment and preview problems ahead of the class where they will be covered. As a result, students are expected to turn-in (using Canvas) their preview problem at the beginning of each class, and a student will be (randomly) selected to provide a brief overview of their solution to the preview problems. Preview problems will NOT be graded based on correctness of the solution, but based on whether or not there has been a genuine attempt at solving them using the material from the reading assignment, i.e., solutions that demonstrate an honest effort will get a grade of 1, while solutions that don't will receive a grade of 0.

In addition to reading assignments and preview problems, homeworks will also be assigned (typically one every two weeks). There will be six (6) 15 minutes quizzes (one for each unit, except the last unit that will have two) spread out over the semester that will be held at the beginning of class with the lowest score being dropped (alternatively, this allows to miss one quiz for personal reasons). The relative weights of these different components in determining a student's overall grade will be as follows:

Preview problems	15%
Homeworks	45%
Quizzes*	40%

NOTE: I WILL NOT GRADE ANYTHING THAT IS NOT LEGIBLE. IT IS YOUR RESPONSIBILITY TO ENSURE I CAN DECIPHER WHAT YOU SUBMIT. PREVIEW PROBLEMS AND HOMEWORKS ARE AVAILABLE IN SOFT COPIES, AND MUST BE SUBMITTED ELECTRONICALLY USING CANVAS. QUIZZES WILL ALSO BE ADMINISTERED THROUGH CANVAS.

* There are 6 quizzes with the lowest score being dropped (alternatively, this allows you to miss one quiz for personal reasons).

Preview problems, homeworks, and quizzes are open-book and access to personal notes, homework solutions, and other related material will be allowed. Note though that because quizzes are only ~15 minutes long, spending time searching for material in the book or your notes will typically not be a good idea.
Computer access will also be allowed during quizzes (and homeworks), though NOT INTERNET QUERIES. Students found issuing Internet queries for additional information during a quiz will be considered to be committing an Academic Integrity violation. Similarly, it is forbidden to solicit external help for homeworks, though you can discuss them with the instructors as well as, to some extent, other students provided that the final solution is your own. In other words, it is fine to discuss general concept and directions with other students, but you need to be the one ultimately responsible for developing your solution. In particular, copying even just parts of another student's solution will be considered to be a violation of the course's academic integrity rules. Penalties for violations are as described below in the #Collaboration Policy and Academic Integrity Violations section. There will be NO exception.

Reading Assignments

Reading assignments are intended to get you ready for the next class, so that you can participate during the discussions and ask questions aimed at clarifying what you may not have understood in the material. Reading assignments will typically be from the textbook itself, though additional material, e.g., from some of the online textbooks and notes in Online resources may also be used.

Preview Problems

They are assigned ahead of each lecture and meant to test your understanding of the material covered in the reading assignment for the lecture. You will be expected to turn them in (using Canvas) before the start of the corresponding lecture. One or more students will be selected at the beginning of a class and asked to describe how they have approached solving each preview problem. Student selection will be random but without replacement to ensure that students go through approximately the same number of turns. Successfully completing the preview problems will require reading the assigned material, as well as in most cases being proactive by asking questions on Piazza. Generic questions of the form "How do I solve Problem X" won't be entertained, but otherwise students will be provided with as much help as necessary to successfully complete preview problems.

Quizzes

Quizzes will consist of one or two very short problems/questions meant to test students' understanding of material covered since the previous quiz (or the start of the class for the first quiz). They will be open book, open notes, and open computer (though not Internet access), but given their short duration, there won't be much time available to search for answers in the books or your notes.

Homeworks

Homeworks will be assigned approximately every two weeks. They are meant to offer a more in-depth assessment of students' mastery of the course material than quizzes. Homeworks will consist of multiple problems, often from the textbook, which will target material covered since the previous homework was assigned. Like preview problems, homeworks are expected to be turned in on their due date before the start of class (see #Late and Make-Up Policies for possible exceptions to this rule).

Late and Make-Up Policies

Due date policy: Homeworks and preview problems are expected to be turned in at the start of class on their due date, by uploading an electronic copy in Canvas.

Quizzes: There will be no make-ups or adjustments for missed quizzes except for duly documented medical emergency or family emergency reasons. Note though that since your lowest quiz score will be discarded, you are equivalently allowed to miss one quiz.

Homeworks: There will typically be no extensions for homeworks, as it will only make it harder for you to complete the next assignment. However, because emergencies and/or special circumstances can arise, a single 48 hours extension will be granted to students who ask for it at least 48 hours before the homework's due date.
In addition, if you have already used your one-time 48 hours extension or failed to ask for it 48 hours in advance, you will also be allowed a one-time 48 hours extension but with a 50% grade penalty. In other words, if you ask for an extension at the last minute, you will be allowed this once, and if your point total on the homework is, say, 90/100, your actual grade for the homework will be 45/100.

Collaboration Policy and Academic Integrity Violations

A copy of the McKelvey School of Engineering Academic Integrity Policy is available here, and it applies in its entirety to this course. Make sure you are familiar with it. A more comprehensive description of the policy and the process followed for alleged violations is described here, as it pertains to undergraduate students.

Violations of the Academic Integrity policy, be they in the form of cheating during a quiz or an exam (e.g., copying another student's answer or seeking to find it on the Internet) or submitting material that is not your own (e.g., by reusing solutions found on the Internet, or from previous years, or copied from another student) will result in an immediate referral to the registrar's office for formal investigation. Students found in violation will have it entered in their record, and receive a penalty commensurate with the severity of the violation. It can range from a negative score for the assignment, or exam, or lab in question (it will cost you more than not turn anything in), to a grade of F for the course. Instances of a second confirmed violation will automatically result in an F for the course.

• Preview Problems & Homeworks: You should complete them on your own, but you are not prohibited from discussing them with others. Turning in a verbatim copy of someone else work is, however, not acceptable and will be considered an academic integrity violation. The minimum penalty if you are found guilty of such a violation is an automatic grade of -5 points for a violation affecting a preview problem and -x/2, for violations affecting homeworks, where x is the maximum possible grade for the homework. A higher penalty may be levied, including an F for the class, depending on the severity of the violation. Those decisions are at the discretion of the instructor. Note also, that besides being counter to the principles laid out in the School's Academic Integrity Policy, submitting work that is not your own, be it for preview problems or homeworks, will only make it harder for you to assimilate the class' material and subsequently apply it, including in the context of quizzes and exams.

• Quizzes: Collaboration is obviously not allowed, and any attempt to "share" answers with others will be considered an academic integrity violation and treated as such. In particular, if found guilty, it will result in at least an automatic grade of -x for a quiz (where x is the quiz maximum grade). Alternatively, depending on the severity of the violation, the instructor reserves the right to assign an overall class grade of F.