Queuing Theory: How It Works And Real-Life Examples

Article Summary:

Queuing theory is a branch of mathematics that analyzes the formation and functioning of lines, examining various components such as arrival processes, service processes, the number of servers, and more. It has real-life applications in improving customer service, traffic flow, order shipments, and business workflow efficiency. This article explores the key concepts of queuing theory, its parameters, benefits, and real-world applications. Discover how businesses can use queuing theory to enhance customer service and streamline operations.

What is queuing theory?

Queuing theory studies the formation and operation of queues or lines. It encompasses a wide range of factors, including how customers or entities arrive, the processes involved in serving them, the number of servers available, queuing discipline, queue capacity, and client population. These elements are critical for understanding how lines form, function, and, at times, malfunction.

Real-life applications

Queuing theory extends its reach into the real world, offering solutions for businesses in various sectors. It plays a pivotal role in enhancing customer service, optimizing traffic flow, streamlining order shipments, and designing efficient data networks and call centers. Businesses can harness the power of queuing theory to make informed decisions and create cost-effective workflow systems.

How queuing theory works

Queues are inevitable when resources are limited. A moderate level of queuing is acceptable, as its absence would imply overcapacity. Queuing theory aims to design systems that serve customers quickly and efficiently while maintaining sustainability.

The basic elements of queuing theory

When delving into the world of queuing theory, it becomes evident that a comprehensive understanding of its core elements is paramount. These fundamental components are the building blocks that allow businesses to analyze, optimize, and streamline their processes, ultimately leading to improved efficiency and customer satisfaction.

1. Arrival process

The arrival process is the gateway to any queue. It encompasses the method by which customers or entities arrive at a facility. Understanding how arrivals are distributed over time is crucial. This insight enables businesses to anticipate peak hours, allocate resources accordingly, and minimize wait times.

2. Service and departure process

Once customers enter the queue, they undergo a service and departure process. This stage involves the actual provision of service and the subsequent departure of customers. Analyzing this element allows businesses to fine-tune their service procedures, ensuring that each customer is served efficiently and departs satisfied.

3. The number of servers

Determining how many servers are available to serve customers is a critical factor. It directly affects the speed at which customers are served. Whether it’s checkout counters in a supermarket or customer service representatives in a call center, the number of servers plays a pivotal role in managing queues effectively.

4. Queuing discipline

Queuing discipline refers to the rules that govern the order in which customers are served. The most common approach is “first-in, first-out” (FIFO), but variations exist. Selecting the appropriate queuing discipline can significantly impact customer satisfaction and the overall flow of the queue.

5. Queue capacity

The maximum number of customers that a queue can hold at any given time is its capacity. Understanding this limit is essential to prevent overcrowding, which can lead to dissatisfaction among waiting customers. Businesses must strike a balance between efficient service and queue space management.

6. Client population size

The client population size refers to the number of customers or entities that the system serves. Whether it’s a retail store, a healthcare facility, or a data network, knowing the size of the client population helps businesses anticipate demand, allocate resources, and plan for growth.

By comprehensively analyzing these six fundamental elements, businesses can create a detailed model of their queuing process. This model serves as a valuable tool for identifying bottlenecks, congestion points, and areas that require improvement. Queuing theory empowers businesses to streamline their operations, reduce wait times, and enhance the overall customer experience.

Analyzing the arrival and service processes

At its core, queuing theory involves analyzing the arrival of customers or entities at a facility and assessing the existing processes used to serve them. The objective is to identify any inefficiencies in the system and propose improvements.

The history and origin

Queuing theory traces its roots back to the early 1900s when Agner Krarup Erlang, a Danish engineer, statistician, and mathematician, studied the Copenhagen telephone exchange. His groundbreaking work led to the Erlang theory, which laid the foundation for efficient network design.

The psychology of queuing: Dealing with customer impatience

Understanding the psychology of queuing is crucial for businesses aiming to provide a pleasant customer experience, even in situations where waiting is inevitable. One of the central elements of this field is managing customer impatience effectively.

1. Call-back options

One solution is offering customers a call-back option when they need to contact customer service. Rather than waiting on hold, customers can request a call-back at a more convenient time. This not only reduces their immediate frustration but also enhances the overall perception of the business’s commitment to customer service.

2. Customer service number systems

Many businesses, especially in service industries like healthcare and government offices, employ customer service number systems. Customers receive a number upon arrival, which allows them to track their progress and estimate how long they’ll need to wait. These systems make the waiting experience more manageable by providing a sense of order and transparency.

3. Distraction techniques

Some businesses deploy distraction techniques. For example, retail stores might place impulse-buy items near the checkout counters to encourage browsing and reduce the feeling of waiting time. In healthcare settings, waiting rooms are designed with TVs, magazines, and other distractions to keep patients occupied and less focused on waiting.

4. Effective communication

Transparent communication is key. Businesses that keep customers informed about their expected wait times, reasons for delays, and progress through the queue tend to receive better reviews. It’s essential to address uncertainties and maintain clear lines of communication with waiting customers.

By understanding customer impatience and adopting these strategies, businesses can mitigate the negative impact of queuing. The psychology of queuing is not only about making wait times feel shorter but also about leaving customers with a positive impression of the business.

Example of queuing theory

A notable application of queuing theory is demonstrated in a study by Stanford Graduate School of Business Professor Lawrence Wein. He used queuing theory to analyze emergency responses to an airborne bioterrorism attack, reducing wait times for emergency care and potentially saving lives.

The bottom line

Queuing theory is a fundamental mathematical discipline that investigates the dynamics of waiting. Queuing is an integral part of various industries, affecting customer service, traffic flow, and order shipments. By harnessing the insights of queuing theory, businesses can enhance their efficiency and customer satisfaction.


Here is a list of the benefits and drawbacks of applying queuing theory in businesses.

  • Improved customer service
  • Optimized traffic flow
  • Efficient order shipments
  • Enhanced operational efficiency
  • Implementation challenges
  • Resource-intensive
  • Complex for some businesses

Frequently asked questions

What is the primary focus of queuing theory?

Queuing theory primarily focuses on studying how lines form, function, and sometimes malfunction, encompassing various components such as arrival processes, service processes, and more.

How can queuing theory benefit businesses?

Businesses can benefit from queuing theory by improving customer service, optimizing traffic flow, streamlining order shipments, and designing efficient workflow systems.

Who is credited with inventing queuing theory?

Agner Krarup Erlang, a Danish mathematician and engineer, is credited with inventing queuing theory in the early 20th century.

What are the parameters considered in queuing theory?

Queuing theory breaks down the process into six key parameters: arrival process, service and departure process, number of servers, queuing discipline, queue capacity, and client population size.

Can queuing theory be applied to all types of businesses?

Queuing theory is a versatile concept that can be applied to a wide range of businesses to enhance efficiency, but its implementation may vary depending on the specific industry and context.

Key takeaways

  • Queuing theory is vital for understanding and optimizing waiting processes in various industries.
  • It helps businesses improve customer service, traffic flow, and overall operational efficiency.
  • The parameters of queuing theory include arrival processes, service processes, number of servers, queuing discipline, queue capacity, and client population size.
  • Agner Krarup Erlang is credited with inventing queuing theory, revolutionizing telephone traffic engineering.
  • Applying queuing theory can lead to improved efficiency and customer satisfaction in businesses.
View Article Sources
  1. Queueing Theory and Its Applications – Whitman College
  2. Queueing Theory, Part 1 – University of Washington
  3. Throughput: A Critical Measurement of Business Efficiency – SuperMoney