# Queueing theory

 related topics {math, number, function} {system, computer, user} {theory, work, human} {company, market, business} {rate, high, increase} {day, year, event} {service, military, aircraft} {math, energy, light}

Queueing theory is the mathematical study of waiting lines, or queues. The theory enables mathematical analysis of several related processes, including arriving at the (back of the) queue, waiting in the queue (essentially a storage process), and being served at the front of the queue. The theory permits the derivation and calculation of several performance measures including the average waiting time in the queue or the system, the expected number waiting or receiving service, and the probability of encountering the system in certain states, such as empty, full, having an available server or having to wait a certain time to be served.

Queueing theory has applications in diverse fields,[1] including telecommunications[2], traffic engineering, computing[3] and the design of factories, shops, offices and hospitals.[4]

## Contents

### Overview

The word queue comes, via French, from the Latin cauda, meaning tail. The spelling "queueing" over "queuing" is typically encountered in the academic research field. In fact, one of the flagship journals of the profession is named "Queueing Systems".

Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide service. It is applicable in a wide variety of situations that may be encountered in business, commerce, industry, healthcare,[5] public service and engineering. Applications are frequently encountered in customer service situations as well as transport and telecommunication. Queueing theory is directly applicable to intelligent transportation systems, call centers, PABXs, networks, telecommunications, server queueing, mainframe computer queueing of telecommunications terminals, advanced telecommunications systems, and traffic flow.