A Quick Guide to Queuing Theory

Businesses and organizations that serve customers in a physical location have many operational needs, including a way for those customers to wait for service.

However, queues are more than just a requirement. They can affect—positively or negatively—many parts of the organization. A badly designed queue can drive customers away; an efficient queue can increase sales.

Therefore, understanding the mechanics of the queue is important for overall success. Queuing theory becomes more than just a theory—it must be a guiding operational principle.

What Is Queuing Theory?

When you’re standing in a line or waiting in a queue, your most immediate concern might be how long until you reach the front. Sometimes you get lucky and the wait is short; sometimes it feels like you’re waiting forever.

The truth is, what you think is good or bad luck has concrete math and science behind it. This is queuing theory, which uses math to measure, model, and predict how a queue works. It looks at hard data as well as the behavior of the people waiting in and serving the queue to arrive at conclusions about how the queue is operating. Based on the results, decisions and adjustments can be made to achieve better efficiency or, in a less-than-optimal scenario, to determine what kind of wait time can you and your customers tolerate.

Queuing Theory in Practice

In practice, queues affect—and are affected by—how floor space is used, hours of operation, staffing, sales strategy, and anything else that might require people to wait. Consider these places that benefit from queuing theory:

Airports

Airport security changed forever after 9/11. Quick jaunts through metal detectors became a thing of the past. Queues now had to account for passengers having their IDs checked, needing to take off their shoes, collecting all their belongings after being scanned, and other measures necessary to guarantee safety. Airports adjusted their queuing systems to help the process along.

The TSA checkpoint isn’t the only part of the airport that benefits from queue management. For example, ticket counters must ensure passengers are efficiently checking in. Moreover, airport employees must be screened before entering the facility, and without an efficient queuing process, they might be forced to wait a long time before starting their shifts.

Customer Service Counters

The dread people feel about going to the DMV comes from decades of experiences with long, slow lines. But queuing theory has helped the DMV experience seem not so bad anymore—particularly when it’s driving virtual queuing technology.

Customer service counters at retail stores, repair shops, and other government facilities have queues that are just as notorious as those at the DMV. By applying science and the right tools, many organizations have figured out how to minimize lines so that the experience doesn’t feel so painful for customers.

Amusement Park Queues

Over the years, you may have seen signs at amusement parks’ more popular roller coasters that say things like “45 minutes from this point in line.” That’s queuing theory in action—the park knows how many people the line can hold ahead of the sign, as well as how long the ride takes and how many people ride a single train.

Those signs aren’t just for the benefit of guests. If you’re stuck in line for an hour, that’s time during which you’re not buying food and drink, paying for go-kart and slingshot rides, playing carnival games on the midway, and so on. Some amusement parks have adopted some form of digital queuing that allows people to reserve a place in a virtual line, then return when it’s their time to enjoy the ride.

Urgent Care

For several years now, emergency rooms and urgent care facilities have been using queuing principles to advertise—on electronic billboards or their websites—how long their waits are before patients show up. If your health emergency is serious enough, you just go to the nearest ER, but for crises that aren’t as desperate, patients can decide which facility they want to visit based on wait times and their needs.

This general queuing idea has trickled down to animal hospitals, which often will tell callers how long they can expect to wait to bring a pet in for treatment. Veterinary clinics are suffering through a nationwide shortage of workers—coinciding with the pet boom that occurred during the COVID-19 pandemic. Long wait times are common, but by applying queuing theory principles, clinics can inform pet owners, in advance, how long their waits might be.

Queuing Variables

In 1953, David G. Kendall proposed base models for measuring queuing. In queuing theory (which dates back more than a century), this is known as Kendall’s Notation and is still used today. The math behind the model can get a little heavy, but Kendall’s Notation basically relies on six variables:

• The arrival process (A): This measures how people enter the queue and at what time.
• Service time (S): This represents a mathematical distribution on how long service might take.
• Number of servers (c): Essentially, this is how many employees are serving customers.
• Queue capacity (K): Although not always a factor, this represents how many people the queue can hold.
• Number of possible customers (N): This also may not be a factor, but when it is, it shows the potential volume of customers a queue might receive.
• The queue’s discipline (D): Basically, this is the rules governing how people are served after being in the queue. Most queues are first in, first out, but some might pick out people to be served ahead of others, no matter when they arrived. A good example of an exception is an amusement park queue when an employee might call out for single riders not at the front to board immediately.

In Kendall’s Notation, A, S, and c comprise the core of the queuing model (the last three variables were added years after his original paper). As an extremely simple example, if 10 people arrive (A) in the queue at the same time, and it takes 15 minutes (S) for one employee to serve one customer, and two employees (c) are working the counter, the last customer will wait 60 minutes to be served.

Add an employee to this example and the time drops to 45 minutes. Shave three minutes off each service and the time drops some more, to 36 minutes. Of course, there’s much more that can influence these variables (e.g., time of day, skill level of employees), but our scenario shows that queue characteristics are often anything but random.

Why Queuing Theory Matters

You may be wondering why you should bother with queuing theory. After all, if people want and need your service, won’t they be willing to wait? And doesn’t a long line mean you’re getting plenty of business?

Today’s queue impacts more than just today’s results. Efficient queuing offers a variety of long-term benefits, including:

• Increased sales: Customers who aren’t stuck in line are able to shop more and buy more.
• Customer experience: Similarly, customers who don’t feel trapped by a long queue generally come away feeling better about their visit. A better customer experience leads to not only more sales but also better online reviews, better treatment of your employees, and repeat business.
• Staffing: Queuing theory can help you pinpoint the ideal number of employees you need on hand at any given time, as well as the skills they should be taught and how to adjust if the line becomes unexpectedly busy or quiet.
• Productivity: Serving more customers in less time should be a priority with your queuing strategy. With the right intel and tools, employees can be more prepared for customers, who can be more prepared when they reach the point of service. Saving just a minute off 60 customers’ interactions can not only make the queue go faster, but also free up an hour of staffing that could be used somewhere else.
• Floor space: If you have a massive physical queue but don’t get many customers who need to wait, you’re wasting floor space. Alternately, if your queue is too small and people are spilling over into another area of the store, the traffic jam might hurt the customer experience. Queuing theory gives you the information to right-size your physical queue and intel on whether you should consider a virtual queuing solution.
• Marketing: As mentioned in the ER example, you can market short waiting times as a reason for people to visit your location—but only if you can back it up with data that queuing theory can provide.

Virtual queuing has taken queuing theory to a new, exciting level, and Qtrac’s platform is at the forefront of this evolution. Qtrac is part of Lavi Industries, a leader in the queuing space for decades. We understand queues because we’re experts in the science behind it—all so you don’t have to be.

Using virtual queuing with Qtrac also makes financial sense—and that’s the sort of math we’re sure you’ll embrace. Read our guide, Why Virtually Queued Customers Buy More, to learn how a queue management system can help your customers as well as your bottom line.