Waiting is inherently related to many situations that we encounter in practice. Some examples of such practical situations are production systems, transportation and stocking systems, communication systems, and health care systems. Queuing models are particularly useful for the design of these systems in terms of layout, capacities and control. In this course, we focus on the mathematical analysis of a number of elementary queueing models. Specifically, as waiting primarily occurs due to randomness in the arrival and service processes of customers, queueing theory is embedded in the field of applied probability. We mainly pay attention to methods for the analysis of queueing models, but also to its applications.

Basic knowledge of probability at the level:
- S.M. Ross, Introduction to probability models, 9th edition, Academic Press, 2007 (chapters 1-3).

Aim of the course
In this course, you will learn the theory of queueing models with one queue. The main focus will be on the methods for solving queueing models, whereas model formulation and insights will also be addressed. More specifically, the following subjects will be treated:

  • Fundamental queueing relations (Little's law, PASTA property)
  • Markovian queues (M/M/1 queue, M/M/c queue, M/E_r/1 queue)
  • M/G/1 queue and G/M/1 queue
  • Mean value technique
  • Priority queues
  • Variations of the M/G/1 queue
  • Insensitive queues (M/G/c/c queue and M/G/infinity queue)

Jacques Resing, Department of Mathematics and Computer Science, Eindhoven University of Technology
René Bekker, Department of Mathematics, Vrije Universiteit Amsterdam