Queuing theory is the fundamental tool to evaluate and dimension resource sharing systems. It is used to quantifying the service quality of wired and wireless communication networks, cloud computing architectures, parallel computing systems, but even road traffic systems. This course treats classical theory of Markov chains, queuing systems, and queuing networks. The theory is illustrated by practical system design problems.

Topics include: Basic terminology, Kendall’s notation and Little’s theorem. Discrete and continuous time Markov chains, birth-death processes, and the Poisson process. Markovian waiting systems with one or more servers, and systems with infinite as well as finite buffers and finite user populations (M/M/). Systems with general service distributions (M/G/1): the method of stages, Pollaczek-Khinchin mean-value formula and and systems with priority and interrupted service. Loss systems according to Erlang, Engset and Bernoulli. Open and closed queuing networks, Jackson networks.

The theory is illustrated by examples on the design of data communication networks, such as call blocking in mobile networks, end-to-end delay in the internet, as well as examples on the performance of distributed computing systems.

Examination: the course consists of two moments, homework assignments and small project (1.5 ECTS) and written exam (6 ECTS). You pass the course if you pass both of these moments. You get your grade based on the written exam.