# Understanding Queuing Theory: Definition, Key Elements, and Real-World Examples

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## What Is Queuing Theory?

Queuing theory is a branch of mathematics that focuses on understanding and optimizing queue efficiency. It examines how lines form, function, and sometimes malfunction. Queuing theory examines every component of waiting in line, including the arrival process and the number of [customers](https://www.investopedia.com/terms/c/customer.asp) among others, which might be people, data packets, cars, or telecommunications.

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. It helps create efficient workflows and to minimize wait times. The concept of queuing theory is credited to Agner Krarup Erlang, a Danish engineer and statistician.

### Key Takeaways

*   Queuing theory studies the dynamics of lines, focusing on efficiency to manage customer wait times and improve service systems.
*   It applies broadly in fields like logistics, telecommunications, and emergency services to optimize processes.
*   Originating from early 20th-century telephone traffic analysis, queuing theory helps streamline operations management.
*   Some queuing is efficient for businesses to avoid costly overcapacity, balancing customer flow and resource allocation.
*   A major challenge in queuing theory is its reliance on assumptions about arrivals and service times, which may not align with real-world scenarios.

## Understanding the Mechanics of Queuing Theory

Queuing theory aims to design balanced systems that serve customers quickly and efficiently but do not cost too much to be sustainable. It aids business decisions to create efficient and cost-effective [workflow](https://www.investopedia.com/terms/w/workflow.asp) systems.

Queuing theory began in the early 1900s with Agner Krarup Erlang's study of the Copenhagen telephone exchange. His work led to the Erlang theory of efficient networks and the field of telephone network analysis.

At its most basic level, queuing theory involves the analysis of arrivals at a facility, such as a bank or a fast-food [restaurant](https://www.investopedia.com/articles/markets/012516/worlds-top-10-restaurant-companies-mcdsbux.asp), and analyzing the processes currently in place to serve them. The result is a set of conclusions that aim to identify any flaws in the system and suggest how they can be alleviated. The Erlang is the fundamental unit for measuring telecommunications traffic in voice systems.

Queuing theory as an operations management technique is commonly used to determine and streamline staffing needs, scheduling, and inventory to improve overall customer service. [Six Sigma](https://www.investopedia.com/terms/s/six-sigma.asp) practitioners often use it to improve processes.

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

In queuing theory, the process being studied is broken down into six distinct parameters. These include the following:

## Key Factors Influencing Queuing Efficiency

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](https://www.investopedia.com/terms/e/excesscapacity.asp).

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 issues customer service numbers to allow people to track their progress to the front of the queue.  

## Practical Applications of Queuing Theory Across Industries

Queuing theory applies to many situations, such as:

*   Business logistics
*   Banking and finance
*   Telecommunications
*   Project management
*   Emergency services, such as fire, police, and ambulance

How it works and how involved it may be depends on the complexity of the case involved.

## Challenges and Limitations in Queuing Theory

One major limitation of queuing theory is its reliance on specific assumptions. Many queuing models assume that arrivals follow a [Poisson process](https://www.investopedia.com/terms/p/poisson-distribution.asp) and that service times are exponentially distributed. While this helps simplify the mathematical model, this isn't always how things work in real systems. For example, customer arrivals may occur in bursts rather than at regular intervals, or service times might vary significantly depending on the complexity of each request.

Unpredictable customer behavior can complicate systems beyond the reach of standard queuing theory. For instance, some customers may abandon the queue after waiting for too long, while others may decide not to join a long queue at all. These two functions may depend on an individual's unique preferences.

A challenge is that most queuing models are static. Queuing theory often relies on steady-state conditions. However, in reality, many environments are dynamic. For example, a retail store may experience sudden surges in customer traffic during holiday seasons, though queuing theory may be more useful in steadier, more predictable periods like the non-holiday windows.

## Real-World Examples: Queuing Theory in Action

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](https://www.investopedia.com/terms/l/logistics.asp) 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.

Businesses can use queuing theory to improve efficiency, reduce wait times, and serve more customers.

## 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 queue or service capacity, the number of servers available, the size of the client population, the queuing discipline (such as first-in, first-out), and the departure process. Creating a model of the entire process from start to finish allows the cause or causes of congestion to be identified and addressed.

## The Bottom Line

Queuing theory is a mathematic discipline that looks at line formation, operation, and dysfunction in various contexts: specifically, how they form, how they work, and why they sometimes don't work. It's linked to Agner Krarup Erlang and evolved in telephone network analysis to ensure context and depth.

Queuing is an unavoidable facet of doing business and the theory helps improve customer service, enhance traffic flow, and optimize order shipments and inventory. It has an impact on manufacturing, inventory, shipping, and distributions and it impacts profits and revenues. Queuing theory balances efficiency and cost-effectiveness in business operations, ensuring neither overcapacity nor excessive wait times.

It nonetheless has some limitations, including reliance on specific assumptions like the Poisson process, which may not always reflect real-world scenarios.

> **Article Sources**
>
> 1.  University of Houston. "[Erlang](https://engines.egr.uh.edu/episode/2972)."
>     
> 2.  Erlang, A. K. “[The Theory of Probabilities and Telephone Conversations](http://www.medicine.mcgill.ca/epidemiology/hanley/statbook/Erlang1909.pdf).” _Nyt Tidsskrift for Matematik B_, vol 20, 1909, p. 133.
>     
> 3.  Wein, Lawerence M., David Craft, and Edward Kaplan. "[Emergency Response to Anthrax Attack](https://www.gsb.stanford.edu/faculty-research/publications/emergency-response-anthrax-attack)." _Proceedings of the National Academy of Sciences of the United States of America,_ vol. 100, no. 7, April 2003, pp. 4346–4351.