Queuing Theory: from Markov Chains to Multi-Server Systems

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 3

• Characterize a queue, based on probabilistic assumptions about arrivals and service times, number of servers, buffer size and service discipline
• Describe the basics of discrete time and continuous time Markov chains
• Model simple queuing systems, e.g. M/M/1 or M/M/C/C queues, as continuous time Markov chains
• Compute key performance indicators, such as an average delay, a resource utilization rate, or a loss probability, in simple single-server or multi-server system
• Design queuing simulations with the Python language to analyze how systems with limited resources distribute them between customers

• Some knowledge of basic statistical theory and probability will be required for the course. Lab work will require some familiarity with Python 3.