Queuing Theory and How Ombori Is Improving the Customer Experience

Blog post author
Andreas Hassellöf
May 5, 2021

Queueing refers to someone waiting in line. It can involve waiting in line to check out at a grocery store, waiting in line to be seated at a restaurant, and even waiting online in a virtual waiting room to purchase tickets. 

The idea of queueing was first introduced in the twelfth century and has been extensively studied since. Today, queuing theory is the most popular way to study waiting lines or queues.

What is Queueing Theory?

Queuing theory was first introduced in 1901 when Agner Krarup Erland, a Danish mathematician, statistician, and engineer, published a paper titled “The Theory of Probabilities and Telephone Conversations.” Erland, who at the time was working for the Copenhagen Telephone Company, was studying how many circuits were needed to provide enough service so that customers would not have to wait too long for a circuit to become available. During his research, he identified a problem that keeps appearing in various aspects of life – waiting in line. From there, he introduced the concept of queueing theory. 

By definition, queueing theory is a branch of “mathematics that studies and models the act of waiting in line.” Researchers construct queueing models to predict queue lengths and wait times. In 1953, D. G. Kendall proposed the standard system used today to describe and classify a queueing node. It looks at six different elements of queuing, using the notation A/S/c/K/N/D:

  • A is the arrival process.
  • S is the mathematical distribution of the service time.
  • c is the number of servers.
  • K is the capacity of the queue, omitted if unlimited.
  • N is the number of possible customers, omitted if unlimited.
  • D is the queuing discipline, assumed first-in-first-out if omitted.


Why is Queueing Theory Important?

Waiting in line is an inevitable part of life, and queueing theory has transformed the customer experience. As consumer demand has increased, companies, including Ombori, have introduced queue management systems to help them adapt to the changes. These systems review different types of queues and offer potential solutions to various scenarios. Here are the most commonly recognized types of queues:

  • First In, First Out: The most common type of queue, first in, first out, refers to the act of lining up and waiting your turn as servicers help the next person in line. 
  • Last In, First Out: This is the opposite of first in, first out and is rarely used to enhance the customer experience. Instead, it is common in organizations when determining who will be let go first – the last hired is often the first to go. 
  • Priority: Customers or tasks are ranked by priority and serviced accordingly. For example, in healthcare systems, emergency cases are often prioritized. 
  • Processor Sharing: Individuals are all helped simultaneously. In this case, queuing does not occur; all customers enter simultaneously and receive an equal fraction of the service’s capacity. 

Consumer response shifts depending on the perceived line experience. Balking occurs when a customer immediately leaves because the service time appears to be long. Reneging occurs when a customer leaves after already entering a line – often because they are annoyed by the experience, and jockeying occurs when a customer jumps lines, looking for the shortest wait time. 

Queueing theory helps us develop an in-depth understanding of the types of queues that exist and provides direction on how to improve efficiencies through a mathematical understanding of queues. 

What are the Benefits of an Effective Queue Management System?

To retain current customers and attract new ones, companies must rely on effective queue management systems. Such systems are used in numerous industries, including retailers, office spaces, healthcare locations, and many more. When executed correctly, they provide many benefits.

Queue Management Systems Improve Customer Experience

Wait times are one of the biggest deterrents for consumers. For example, some customers who enter a retail store and see a long line will immediately leave. Or, customers who visit a doctor and have to wait for an extended period of time may choose to find another doctor. In both scenarios, the associated entity loses a customer and a profit opportunity. 

With queue management systems such as Ombori, the customer wait time is often reduced – either actually through greater efficiency or theoretically through customer perception. Here’s what we mean. 

Actual wait time can be reduced by optimizing solutions found in queueing theory. For example, queue management systems can identify traffic patterns and times when more staff are required at a checkout lane. Another way to reduce wait time is to reduce perceived wait time – often done by utilizing a virtual queue. Virtual queues offer guests the ability to check-in online, then be notified when it is their time to be next. Instead of waiting in a physical line, guests can continue their business until their name is called. 

Improving Internal Efficiencies

Queue management systems not only promote a better customer experience but also improve internal efficiencies by offering innovative solutions to back-house issues. The also increase employee satisfaction. 

As the study of queueing theory continues, new business solutions emerge. What started as a simple theory looking strictly at in-person lines has now expanded to improve the functions of all business operations. Furthermore, as technology has continued to evolve and e-commerce platforms have gained popularity, queue management systems have improved organizations’ ability to adapt. Systems such as Ombori have created solutions for many of the urgent problems today’s businesses face. These systems are designed to enhance the following services:

  • Queue Management: Management of mobile, paper, and pre-booked virtual ticket solutions
  • Self-Checkout: A quicker and easier way for customers to pay for purchases
  • Staffed Checkout: Reduced checkout lines with improved customer service
  • Curbside Pick-Up: A more straightforward solution for shoppers to collect their purchases 
  • BOPIS: Buy online, pick up in-store
  • Omnichannel and Unified Commerce: Bridging the divide between the physical and digital world
  • Customer Experience: Surprising and delighting customers with an improved experience
  • Guided Selling: A system to help customers find things they didn’t know they wanted
  • Store Occupancy: A system to monitor store occupancy and ensure compliance
  • Increased Sales: The implementation of smart technology to increase revenues

An Ongoing Shift in Technology

Just like any other aspect of life, queue demands and systems are continuously changing. Queuing theory provides businesses, including retailers, the opportunity to leverage scientific research and data to improve their operations, ultimately improving their bottom line.

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