# Module 19 Queueing Systems

by Ehssan Ghashim and Patrick Boily

Queuing theory is a branch of mathematics that studies and models the act of waiting in lines, or queues. As a topic in operational research, it combines elements of a variety of quantitative disciplines, but it is not often part of the data analyst’s toolbox. In this module, we introduce the terminology and basic framework of queueing models (including Kendall-Lee notation, birth-death processes, and Little’s formula), as well as the most commonly-used queueing system: $$M/M/c$$.

### Contents

19.1 Background

19.2 Terminology
19.2.1 Input/Arrival Process
19.2.2 Output/Service Process
19.2.3 Queue Discipline
19.2.4 Method Used by Arrivals to Join Queue

19.3 Queueing Theory Framework
19.3.1 Kendall-Lee Notation
19.3.2 Birth-Death Processes
19.3.3 Little’s Queuing Formula

19.4 $$M/M/1$$ Queueing Systems
19.4.1 Basics
19.4.2 Limited Capacity

19.5 $$M/M/c$$ Queueing Systems

19.6 Exercises