# Queuing Theory Definition, Elements, and Example

## What Is Queuing Theory?

Queuing theory is a branch of mathematics that studies how lines form, how they function, and why they malfunction. Queuing theory examines every component of waiting in line, including the arrival process, service process, number of servers, number of system places, and the number of customers—which might be people, data packets, cars, or anything else.

Real-life applications of queuing theory cover a wide range of businesses. Its findings may be used to provide faster customer service, increase traffic flow, improve order shipments from a warehouse, or design data networks and call centers.

As a branch of operations research, queuing theory can help inform business decisions on how to build more efficient and cost-effective workflow systems.

• Queuing theory is the study of the movement of people, objects, or information through a line.
• Studying congestion and its causes in a process is used to help create more efficient and cost-effective services and systems.
• Often used as an operations management tool, queuing theory can address staffing, scheduling, and customer service shortfalls.
• Some queuing is acceptable in business. If there's never a queue, it's a sign of overcapacity.
• Queuing theory aims to achieve a balance that is efficient and affordable.

## How Queuing Theory Works

Queues can occur whenever resources are limited. Some queuing is tolerable in any business since a total absence of a queue would suggest a costly overcapacity.

Queuing theory aims to design balanced systems that serve customers quickly and efficiently but do not cost too much to be sustainable.

At its most basic level, queuing theory involves an analysis of arrivals at a facility, such as a bank or a fast-food restaurant, and an analysis of the processes currently in place to serve them. The end result is a set of conclusions that aim to identify any flaws in the system and suggest how they can be ameliorated.

The origin of queuing theory can be traced to the early 1900s in a study of the Copenhagen telephone exchange by Agner Krarup Erlang, a Danish engineer, statistician, and mathematician. His work led to the Erlang theory of efficient networks and the field of telephone network analysis.

To this day, the fundamental unit of telecommunications traffic in voice systems is called an "erlang."

### The Parameters of a Queue

In queuing theory, the process being studied is broken down into six distinct parameters. These include the arrival process, the service and departure process, the number of servers, the queuing discipline (such as first-in, first-out), the queue capacity, and the size of the client population.

Queues are not necessarily a negative aspect of a business, as their absence suggests overcapacity.

## Benefits of Queuing Theory

Queuing theory as an operations management technique is commonly used to determine and streamline staffing needs, scheduling, and inventory in order to improve overall customer service. It is often used by Six Sigma practitioners to improve processes.

### The Psychology of Queuing

The psychology of queuing is related to queuing theory. This is the component of queuing that deals with the natural irritation felt by many people who are forced to queue for service, whether they're waiting to check out at the supermarket or waiting for a website to load.

A call-back option while waiting to speak to a customer representative by phone is one example of a solution to customer impatience. A more old-fashioned example is the system used by many delis, which issue customer service numbers to allow people to track their progress to the front of the queue.

Supositorio offers free online queuing theory calculators with a choice of queuing models.

## Example of Queuing Theory

A paper by Stanford Graduate School of Business Professor Lawrence Wein et al. used queuing theory to analyze a variety of possible emergency responses to an airborne bioterrorism attack in a public place. The model pointed to specific actions that could be taken to reduce the wait time for emergency care, thus decreasing the potential number of deaths.

Queuing theory is useful, if not quite so urgent, in guiding the logistics of many businesses. The operations department for a delivery company, for example, is likely to use queuing theory to help it smooth out the kinks in its systems for moving packages from a warehouse to a customer. In this case, the "line" being studied is comprised of boxes of goods waiting to be delivered to customers.

By applying queuing theory, a business can develop more efficient systems, processes, pricing mechanisms, staffing solutions, and arrival management strategies to reduce customer wait times and increase the number of customers that can be served.

## How Do You Use Queuing Theory?

Queuing theory is used to identify and correct points of congestion in a process. The queue may consist of people, things, or information. In any case, they are being forced to wait for service. That is inefficient, bad for business, and annoying (when the queue consists of people).

Queuing theory is used to analyze the existing process and map out alternatives with a better result.

## Who Invented Queuing Theory?

Agner Krarup Erlang, a Danish mathematician, statistician, and engineer, is credited with creating not only queuing theory but the entire field of telephone traffic engineering.

In the early 20th century, Erlang was head of a technical laboratory at the Copenhagen Telephone Co. His extensive studies of wait time in automated telephone services and his proposals for more efficient networks were widely adopted by telephone companies.

## What Are the Basic Elements of Queuing Theory?

A study of a line using queuing theory would break it down into six elements: the arrival process, the service and departure process, the number of servers available, the queuing discipline (such as first-in, first-out), the queue capacity, and the numbers being served. Creating a model of the entire process from start to finish allows the cause or causes of congestion to be identified and addressed.

## What Does It Mean to Be Queued?

Americans stand in line for service (except for New Yorkers, who stand "on line"). British people queue. The word queue comes from an old French noun for an animal's tail.

The computer age has introduced a new usage. An email provider may indicate that your message has been "queued." This means that there is a delay in delivering it but it will be sent ASAP.

Queuing and queueing are both acceptable spellings of the word.

Article Sources
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1. Erlang, A.K. “The Theory of Probabilities and Telephone Conversations.” Nyt Tidsskrift for Matematik B, 1909, Page 20, 33.

2. Supositorio.com. "Queueing Theory Calculator."

3. Wein Lawerence, Craft David, Kaplan Edward, "Emergency Response to Anthrax Attack," National Academy of Sciences of the United States of America, Vol. 100 Issue 7, April 2003, Pages 4346–4351.