Format

Course Organization at-a-Glance

Although the course Syllabus is organized at a traditional "lecture" granularity, the course consists 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 the "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 review session, either synchronous or asynchronous, that goes over the material that was covered in the preceding "information push" for each unit and is intended to offer students the opportunity to go over the material one more time and make sure the underlying concepts are clear.
• 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 [~1.5 weeks – 3 lectures]
  • This unit builds on Unit 3 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

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;
• Occasional in-class problems that will be used to supplement the preview problems and/or offer a different perspective on the material covered in the preview problems;
• lecture component that will be used to expand on or clarify concepts covered in the reading assignment and illustrated in the preview problems.

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 may be (randomly) selected to provide a brief overview of their solution to the preview problems.

Grading

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. Note that as grading is not based on correctness, there will also be no feedback on graded review questions. Students are expected to check the solutions that will be posted in the Assignment section of the course's Canvas site and ask questions if they are unsure about the solution.

In addition to reading assignments and preview problems, homeworks will also be assigned (typically one every two weeks). There will be six (6) 30 minutes quizzes (one for each unit, except the last unit that will have two) spread out over the semester. Each quiz will be available to be taken online over a period of 72 hours, starting at 5:30pm on the day shown on the tentative schedule and/or Canvas. The lowest quiz score will be dropped when computing your overall grade (alternatively, this allows students to miss one quiz for personal reasons). The relative weights of these different components in determining a student's overall grade is as follows:

Preview problems	10%
Homeworks	45%
Quizzes*	45%

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 THROUGH CANVAS ASSIGNMENT PAGE. QUIZZES WILL ALSO BE ADMINISTERED THROUGH CANVAS AND SHOULD BE SUBMITTED THROUGH THE CANVAS QUIZZES PAGE.

* 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 ~30 minutes long, spending time searching for material in the book or your notes will typically not be a good idea.
Computer access is also allowed, though using the Internet to find or ask how to solve a quiz or homework problem will be considered an Academic Integrity violation. For homeworks, you can discuss them with the instructor and TAs as well as, to a limited extent, other students provided that the final solution is your own. In other words, you can discuss general concepts 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 (or of a solution you found on the Internet) will be considered an Academic Integrity violation. 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 the Canvas Assignments page) before the start of the corresponding lecture. As an incentive to completing them, they count for a certain percentage (see Overview & Grading) of your final grade. Their grading will be "binary" (0 or 1) and based on whether you have meaningfully attempted to do them rather than correctness of your results. One or more students may 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.

Solutions to preview problems will be accessible through Canvas. If you have problems accessing the page, first login to Canvas and then try again. The reason for making those solutions only accessible through Canvas, is that many/most of them come from the textbook and are not meant to be publicly distributed. As a result, please do not post any of them on public repositories and similarly do not forward them to students outside the class. If you do and are caught, this will be considered a violation of the the course's Academic Integrity policy and will earn you an immediate F for the class.

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 first lecture for the first quiz), and up to and including the lecture immediately preceding the date posted for the quiz on the Syllabus & schedule page. So, if the period during which you can start taking a quiz begins on, say, a Wednesday after class, then the quiz will cover everything from the point where the previous quiz left off (or the first lecture for the first quiz), up to and including the material covered in the preceding Monday class. Quizzes are open book, open notes, and open computer (though you are expected not to use the Internet to look for solutions), but given their short duration, there won't be much time available to search for answers in the books or your notes.

There will be six (6) quizzes and the quiz with the lowest score will be dropped when computing a student's final grade. Note that all past quizzes are available on the course's Past Exams & quizzes page, so that students can use them to become familiar with the format and practice completing a problem within the limited amount of time assigned to quizzes.

For all students, whether taking the class in-person or remotely, quizzes will be available on Canvas for a period of 72 hours, starting at the end of the class on the day indicated on the course Syllabus & schedule and with a "due date/deadline" set to 72 hours later. For example, if quiz 1 becomes available at 5:30pm on September 14 after the end of class on that day, it must then be submitted before 6:05pm on September 17. Students will be able to take their quiz any time during that 72 hours time period, but will only be allowed one attempt. Quizzes are time-limited to 30 minutes with an additional 5 minutes to allow students to take a picture of their completed quiz and upload it into Canvas. Canvas has been setup to only allow a single submission within that time window once you start your quiz, so you will need to make sure that you are ready and have stable Internet connectivity prior to starting. A test/practice quiz is available on Canvas to allow you to try this out and make sure you can complete your uploads within 5 minutes (it may take a few rounds of practice, but 5 minutes should be plenty of time).

Homeworks

Homeworks are assigned approximately every two weeks (there will be a total of 6 homeworks). 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) and uploaded into Canvas.

See the Formatting page for instructions on how to prepare the document you need to upload in the Canvas Assignment page for each homework.

Practice Problems

A number of practice problems are available on the Practice Problems Canvas page together with their solution. If you have problems accessing the page, first login to Canvas and then try again. The reason for making those problems and their solutions only accessible through Canvas, is that many/most of them come from the textbook and are not meant to be publicly distributed. As a result, please do not post any of them on public repositories. If you do and are caught, this will be considered a violation of the the course's Academic Integrity policy and will earn you an immediate F for the class.

Late and Make-Up Policies

Preview problems: They are expected to be turned in before 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: As preview problems, they are expected to be turned in before the start of class on their due date. There will 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 - Please Read Very Carefully

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 WashU's academic integrity policy and the process followed for alleged violations is available on the Academic Integrity webpage of the Office of the Provost with additional information for undergraduate students available here.

Violations of the Academic Integrity policy, be they in the form of cheating during a quiz (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, or generated by an external tool such as ChatGPT or Bard) will result in the filing of a report with Academic Integrity in the Office of the Provost for formal investigation. The process that will follow the filing of such a report is detailed here.

• 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.

In addition, many/most of the problems and their solutions come from the textbook and are not meant to be publicly distributed. As a result, please do not post any of them on public repositories and similarly do not forward them to students outside the class. If you do and are caught, this will be considered a violation of the the course's Academic Integrity policy and will earn you an immediate F for the class.

• Quizzes: Collaboration is obviously not allowed, and any attempt to "share" problems or their answers with others will be considered an academic integrity violation and treated as such, as will be any attempt to solicit help from others, whether in-person or over the Internet. 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.

• Practice Problems: You are entirely free to discuss any of those problems with other students. However, for practice problems available from the Practice Problems Canvas page together with their solution, it is explicitly forbidden for you to post them on any publicly available forum or to forward them to someone outside the course. Many of problems and their solutions come from the textbook and are not meant to be publicly distributed. In case you violate this rule and are caught, you will be considered in violation of the course's Academic Integrity policy which will earn you an immediate F for the class. Note that this does not apply to practice problem associated with exams and quizzes from previous years, as those are already publicly accessible on the course wiki.