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# Queuing Theory: from Markov Chains to Multi-Server Systems

### Overview

Situations where resources are shared among users appear in a wide variety of domains, from lines at stores and toll booths to queues in telecommunication networks. The management of these shared resourcescan have direct consequences on users,whether it be waiting times or blocking probabilities.

In this course, you'll learn how to describe a queuing system statistically, how to model the random evolution of queue lengths over time and calculate key performance indicators, such as an average delay or a loss probability.

This course is aimed at engineers, students and teachers interested in network planning.

Practical coursework will be carried out using ipython notebooks on a Jupyterhub server which you will be given access to.

Student testimonial
"Great MOOC ! The videos, which are relatively short, provide a good recap on Markov chains and how they apply to queues. The quizzes work well to check if you've understood." Loïc, beta-tester

"The best MOOC on edX! I'm finishing week 2 and I've never seen that much care put in a course lab! And I love these little gotchas you put into quizzes here and there! Thank you!" rka444, learner from Session 1, February - March 2018

### Syllabus

This is a five week course :

• Week 1 is an introduction to queuing theory. We will introduce basic notions such as arrivals and departures. Particular attention will be paid to the Poisson process and to exponential distribution, two important particular cases of arrivals and service times.
• During week 2 we will analyze a first simple example of a no-loss queue , the so called M/M/1 queue, and we will compute its average performance metrics.
• Week 3 will be dedicated to a basic course in discrete time Markov chains. We will learn how they are characterized and how to compute their steady-state distribution.
• Then in week 4 we will move on to continuous time Markov chains. Again we will learn how to characterize them and how to analyze their steady-state distribution. Equipped with these tools we will then analyze the M/M/1 queue.
• In week 5 we will study multiserver and finite capacity queues and study how to dimension a loss network.

Each week of the course will include five or six video lectures, a quiz to test your understanding of the main concepts introduced during that week and a lab using python.

### Taught by

Sandrine Vaton, Isabel Amigo, Hind Castel and Patrick Maillé

## Reviews

4.8 rating, based on 13 Class Central reviews

Start your review of Queuing Theory: from Markov Chains to Multi-Server Systems

• Anonymous
This opinion is based on the early 2018 run of the course.
The only flaws in this course are a thin mathematical treatment of more advanced subjects (Continuous-time Markov Chains, Erlang formulas), too easy/short programming assignments, and limited real life examples. Other than this, the course is very well organized, with all materials released upfront, informative explanations provided to the quiz/homework answers, immediate availability of the instructors on the forum, and high quality jupyter notebooks.
• Gian Marino Di Gregorio
Excellent introductory course for Queuing Systems and Markov processes. This course is structured so as to provide a theoretical intro followed by a practical section. In the latter you will requiere some python but overall, it's a couple of lines o…
• Provided you have studied some probability theory (previous exposure to Markov chains wouldn't hurt), this course can give you a fast-paced introduction to some more advanced ideas related to stochastic processes and queueing theory.

It is hard to overemphasise how important queueing theory is, apart from technical applications also, for instance, for the management of knowledge work (Principles of Product Development Flow by Don Reinertsen). This course offers a rare opportunity to get a solid foundation.

The material includes lecture slides and carefully prepared labs with Jupyter notebooks.
• Anonymous
Knew of the subject before taking the course but never had time to study it. Finally took the plunge; and albeit introductory, the material / modelling is fascinating. The course motivated me to start working through M. Harchol Balter's book, "Performance Modelling and Design of Computer Systems: Queueing Theory In Action". Hoping to eventually apply some of this at work. Staff was very supportive!

• Anonymous
Very nicely packaged short course with some mildly challenging exercises on a topic I've found difficult to learn from books.

Good pace - short lectures with good animation and quizzes and the material gets progressively harder. I first used the archive material last year but thought it was worth paying for, so signed up for a certificated course to give the presenters their due.

• Anonymous
I think this course is very good. The staff clearly put up a lot of effort on the preparation and follow up. They created very helpful and high-quality slides, interesting material to learn the basics and resources to find extensions. The course is not very hard to follow, but it does require an effort. I think they found just the right balance. Congratulations and thank you!
• Anonymous
The course is a good introduction to queuing theory and Markov chains. Lecture videos are short, helping to focus on one aspect at a time, and the instructors are great at explaining the basics. Labs are fairly easy, especially if you are familiar with python. Discussion forums are also good, and the instructors respond promptly.
• Jinhua Guo
This course is very well designed. The topics are extremely interesting with applications in Queuing Delay analysis in computer networks, which is my primary interest. The Quizzes and Labs are very helpful to reinforce the theory we learned in lectures.

I had a great time. Thanks a lot.
• Anonymous
The programming labs required some fiddling, but were a feature not available in most classes of this type. I found some of the queueing better explained than in a supply chain course I just took from a university of native English speakers.
• Anonymous
Really enjoyed this course. It was clear and well organised. I thought some of the assignments could have been more challenging, with more use made of simulation, but overall it provided an excellent introduction to queueing theory. James
• Jose Antonio
A very interesting and well exposed introduction to queueing theory. Better if you have some previous knowledge in statistics and stochastic processes because it pass too quickly over some related mathematical concepts.
• Anonymous
The best MOOC that I've taken because they mix theory and practice in an amazing way. Markov chains, a complex subject, is explained so well that I learn a great deal, more than I did in university. Thanks guys.
• Anonymous
I really enjoyed this course. It is very well organized, and programming exercises are very interesting. To resume, it is a great introduction to queuing systems.

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