How queuing theory informs Waitwhile's queue management practices

Americans spend 37 billions hours a year waiting in lines. This is time spent away from their family and friends, their jobs, and their hobbies. This is why waiting in line is associated with a variety of negative emotions, from frustration to impatience, and if things get extreme, even anger!

Making queues faster and more pleasant isn't just a necessity for businesses, but it is a branch of science that's studied in universities and applied in Fortune 500 companies. It is called queuing theory, and it is what underpins and informs our approach to Waitwhile's queue management software!

This article aims to help business owners and industry leaders get an overview of queuing theory. Its origins, its practical applications, and its relevance to your business! Read on and find out more about the fascinating world of queue management!

The history of queueing theory

Queuing Theory arose in the early 20th century as a direct result of new technology - the telephone. Around 1908, the Copenhagen Telephone Company (CTC) was trying to resolve issues connected with phone systems, getting overwhelmed by demand - humans do, after all, like to talk.

At the time, phone calls were routed manually by human operators who would connect the caller to the call receiver by means of jack plugs and cord boards. The challenge lay in determining the number of circuits needed to provide an acceptable level of telephone service - basically to keep phone users from waiting “on hold” for too long before being connected. In addition to the number of circuits, CTC also wanted to know what volume of calls a single telephone operator could process in a given period of time. Though they might manifest differently, optimizing service delivery and making the waiting experience more comfortable for clients are still core questions businesses ask themselves to this day.

Finally, in 1920, Elang, the chief engineer at CTC, published "Telephone waiting times," based on his team's experience in optimizing the phone lines at CTC. This Danish engineer virtually invented queuing theory, and his book became the foundational work that is studied to this day!

The psychology of queuing

Of course, there’s a second aspect to queuing theory that’s equally important, which is the psychological side – how people experience waiting. Qiuping Yu, an assistant professor of Operations Management and Business Analytics at the Georgia Institute of Technology, has done extensive research on the subject, resulting in some remarkable findings.

• First, she found that providing wait time estimates actually reduces wait times. Why? Because inevitably, once they know how long it’s going to take, some people don’t want to wait. Once they leave, the wait times get shorter for everyone else.
• Another finding, which Disney theme parks are known for, is that under-promising and over-delivering by telling people waits are longer than they actually are, leads to a better customer experience. Interestingly, while getting to the front of the line sooner than expected only makes people slightly happier, having to wait longer than was promised makes people significantly more unhappy. As Yu writes, “The penalty for under-delivery, in fact, was up to seven times larger than the reward for over-delivery.”
• Finally, and perhaps most interestingly, is the discovery that people who end up waiting longer than expected will take more time when it’s their turn. A study was conducted where calls were made to a bank call center. Callers had some say over how long they spent on a call. Those who waited longer ended up taking more time once they got through. The researchers theorized that customers who waited longer than anticipated spent more time on calls either because they were complaining or felt like they’d earned more time by waiting. This made them feel justified in asking for additional services.

These are just a few examples of the psychology of queuing and how it is relevant for businesses. Being aware of the quirks of the human mind and leveraging them to provide a better experience for your customers has become an increasingly larger part of queue management.

The basic elements of the queuing discipline

Queuing theory, just like any other scientific field, is built on a number of fundamentals. Understanding these fundamentals is key to properly contextualizing queuing theory and what it means for your business.

• The arrival process: The arrival process refers to everything that happens between the time the customer sets foot in your store to the time they start waiting in line. Though not explicitly part of the queuing process, it is still an important part of how businesses manage customers. An effective arrival process increases conversion rates and customer satisfaction.
• The arrival rate: The arrival rate refers to the rate at which customers enter your store. The arrival rate varies depending on time of day, day of the week, and even the season. A business with a successful queue system handles accounts for a large variance in the arrival rate, reliably managing to service clients regardless of the size of customer traffic.
• The waiting line: When queues are formed, there needs to be a way to keep track of customers/items/products in that queue, and this is called the waiting line. Traditionally, this has been a literal definition, with most businesses having physical queue lines and a waiting area where they organize customers. Increasingly, however, this definition no longer holds true as virtual lines, which keep track of customers electronically, without any need to stand or wait in a physical line, have become ubiquitous.
• The waiting time: The waiting time is the average time spent in a queue before a customer is serviced. It is the fundamental unit that businesses use to determine the viability of how they process customers. Long wait times lead to lost revenues and an unhappy customer base, which can be catastrophic. So, when the average wait time gets longer, businesses either need to hire more employees, open new branches, adopt a new queuing model, or, in extreme cases, change key business processes altogether!
• System throughput: A technical term, throughput refers to the average number of customers a queue can handle in a specific period of time. As an example, if your business can only service 60 customers in an hour, your company's hourly throughput would be 60 customers/hour. Throughput is one of the most vital key performance indicators (KPIs) that companies need to increase to improve productivity and expand their business.
• System capacity: The system capacity is the theoretical maximum throughput your business can achieve. On paper, your business can service a customer every five minutes, for example, but due to a variety of factors like an unorganized queue, a distracted employee, or any other unforeseen factor, your business's throughput will never reach the system capacity.
• Queuing model: The term "queuing model" can refer to two things. In academia, it is a mathematical model that is designed to represent a queue and its properties. In commercial spaces, it largely refers to a piece of software that models and keeps track of the status of queues and waiting lines in your business.
• Queuing system: Queuing system is an all-encompassing term that refers to everything related to organizing and managing a queue. It includes the employees who service customers, the assemblers who manage inputs in a factory, and much more. Though it might not neatly map into reality, thinking of operations related to customer management and queueing can help businesses take more efficient steps to optimize business processes.

Real-life applications of queuing theory

Queuing theory is considered a branch of operations research, a branch of mathematics that uses applied models to improve management and decision-making, both of which are vital for the functioning of our societies. So, naturally, queueing theory has been used in a variety of fields, and to great success no less:

Commercial applications of queuing theory

Queuing theory is fundamental to how every business organizes bookings and services customers, even if they don't know about it. From calculating how many customers each employee can handle to determining and accommodating peak hours, these are all part of queuing theory.

While mom and pop shops are likely not picking up the textbook when running their business, queuing theory is a fundamental part of business decision-making in larger enterprises. Whether to expand in a specific city, how many new employees to hire, what needs changing in business processes to reduce wait times, and where to place stands to make possible customers more comfortable: These are all questions businesses answer by using queuing theory.

Industrial applications of queuing theory

Though it might not look like it at first glance, queuing theory is fundamental to organizing and running industrial plants efficiently. This is why industrial engineers take courses on both operations research, in general, and queuing theory, in particular.

Managing assembly lines is not that different from managing customers. From determining system capacity and throughput to prioritizing specific production lines and accommodating demand, all the core principles of queuing theory are relevant, even if optimizing industrial queues needs an entirely different approach from commercial, customer-centric ones.

Technological applications

Queues are fundamental to the operation of every electronic device you own. From your phone to your computer and smart watch, they'd all break down and stop functioning if you remove all the functions responsible for queuing in these devices.

The CPU needs queues to learn which tasks to prioritize. The RAM relies on queues to regulate memory access. The hard drive uses queues to regulate reads and writes. And these are just a few examples of how queues are used to regulate the inner workings of electronics.

How Waitwhile incorporates queuing theory to deliver a better experience

Our queue management system draws heavily from cutting-edge queuing theory to provide up-to-date models and effective tools to help our clients manage customer flow more effectively:

Providing accurate and up-to-date waiting time estimates

In order to accurately estimate wait times, Waitwhile collects wait time data from each and every guest’s visit. We can also feed in other variables that affect wait times – such as staff member, guest service, and party size.

The goal is to determine the average time it takes for one guest to move up one spot in line, taking into account the type of service they’re receiving, the size of their party, and other relevant factors. Once we know this, we can estimate wait times for anyone, no matter their place in line. The more data we gather, the more accurate our estimates become.

Keeping track of productivity

Let's say you are managing a hair salon that employs two hairstylists. Hair stylist #1, we’ll call her Joi, is faster with her snippers than hair stylist #2, we’ll call her Leanne. So if both stylists are offering the same service, Joi will finish faster and thus have an open chair sooner.

Waitwhile keeps track of the productivity of each employee and incorporates this information into its wait time estimate models. This gives businesses a better overview of the entire process and their company's service capacity, and it helps them make more informed decisions when optimizing their business processes.

Handling uncertainty

Not every business will have access to key inputs. For instance, at a hair salon, you usually know that the person is coming in for a coloring as opposed to a beard trim, which makes the wait estimation easier to predict.

Waitwhile can help you handle this uncertainty better by using cutting-edge mathematical analysis to create an accurate queuing model for your business. By keeping track of the properties of different types of bookings across a large time scale, our software can give you data-based estimates on how long each appointment will take. Though these figures remain rough estimates due to the inherent uncertainty of running a business, they'll help you make more informed decisions.