Queueing Definitions

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This file contains definitions of queues and queueing theory taken from some of the standard texts in the field.

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If you would like to make corrections or add information, please e-mail Dr. Hlynka at hlynka@uwindsor.ca
URL is http://web2.uwindsor.ca/math/hlynka/queue.html
Last update: May 4, 2006.

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DEFINITIONS

(Kleinrock) "We study the phenomena of standing, waiting, and serving, and we call this study Queueing Theory. " "Any system in which arrivals place demands upon a finite capacity resource may be termed a queueing system."

(Cooper) "The term Queueing Theory is often used to describe the more specialized mathematical theory of waiting lines.

(Gross and Harris) "A Queueing System can be described as customers arriving for service, waiting for service if it is not immediate, and if having waited for service, leaving the system after being served."

(Jain, Mohanty, Bohm) "Lining up for some form of service is a common phenomenon, be it visible of invisible, be it human beings or inanimate objects. [...] Whenever the available resource is not sufficient to satify the demands, then the demanding units have to wait and are subjected to queueing analysis."

(Wolff) "The primary tool for studying these problems [of congestions] is known as queueing theory."

(Prabhu) "A queue or waiting line is formed when customers arrive at a counter offering certain facilities and demand service."

(Saaty) "A queue, or a waiting line, involves arriving items that wait to be served at the facility which provides the service they seek."

(Kashyap and Chaudhry) "In queueing theory, we study situations where units of some kind arrive at a service facility for receiving service of some description, some of the units have to wait for service, and depart after service."

(Cox and Smith) "The thing common to all the [queueing] systems that we consider a flow of customers requiring service, there being some restriction on the service that can be provided."

(Takacs) "...the theory of queues deals with the investigation of the stochastic law of different processes arising in connection with mass servicing in cases where random fluctuations occur."

(Lipsky) "... a queue is a line of customers waiting to be served."

(Bose) "the basic phenomenon of queueing arises whenever a shared facility needs to be accessed for service by a large number of jobs or customers."

(Takagi) "A queue is formed when service requests arrive at a service facility and are forced to wait while the server is busy working on other requests."

Finally, we have this gem from "Communicating the Bible in the Context of Religious Pluralism in Indonesia" by E. G. Singgih.
"When people see arrows, they think of “queueing”, and in turn, queueing means “scarcity”. In other countries such as Singapore and Malays, queueing means that you are sure to get what you want, even if you have to wait for some time. In Indonesia, queueing means “quick, for there will be nothing left soon”. And so you will witness that kind of queueing where people are pressed hard against one another, and where no kind word is heard, and where people sometimes get into blows with one another. Even if they do not relate queueing with scarcity, for many queueing is not a normal way of doing things. They will queue only at the last moment, and feel that this is a regulation which is forced upon them by those who are in power. Arrows that direct people to stand in line, are representatives of the powers that be. But surely arrows are there to help you? And what is queueing except a cultured way of life? Yes, for some, but not for all."