Queue Theory vs Reality: Why Traditional Models Break Down in Online Queuing

Picture this: You're in a virtual queue for concert tickets. The system shows you're number 45,000 in line. Do you stay? Leave? Come back later? 

Wait time is important, but your final decision will also be affected by a combination of human psychology, perceived value, and available information. 

When managing large online queues (and keeping customer satisfaction in mind), websites must consider not only your potential decision but every other person waiting, too. Sometimes, this can be upwards of a million people. 

Queue theory has much to say about idealised service times but little about the psychology of the people in the queue and the feedback mechanisms it causes. 

Understanding Classical Queue Theory

Queue theory, or queuing theory, was invented by the Danish engineer Agner Krarup Erlang in the early 1900s while studying Copenhagen's telephone exchanges. It was a strictly mathematical approach originally used to explain the system of incoming calls at the Copenhagen Telephone Exchange Company. 

However, the mathematical foundations underpinning this approach still work in modern-day understandings of queue systems. 

Classical queue theory focuses on the following:

• The rate at which new customers enter the queue (arrival rate)

• The rate at which customers are served (service rate)

• How many parallel service points exist (number of servers)

• How well the queue sticks to the “rules” (queue discipline)

These principles help us understand how queues work, like how fast things come in, how quickly they get handled, and how many people can help at once.

One key idea in queue theory is Little’s Law, which helps explain the relationship between the number of people in a queue, how fast they arrive, and how long they stay in the system. 

Simply put, Little’s Law says that if you know how fast people are joining the queue and how long they stay, you can figure out how many people are in the system on average. 

There’s another helpful concept called the "leaky bucket" theory. It’s a way of controlling the flow of requests, making sure the system doesn’t get overloaded. 

Think of it like a bucket with a hole at the bottom — requests are like water being poured into the bucket, and the hole allows water to leak out at a steady rate.

In modern systems, the "leaky bucket" algorithm works like this:

• There's a bucket that can hold a limited number of tokens (like a finite amount of water).

• Tokens are added to the bucket at a constant rate.

• Each time a service request comes in, it uses up one token.

• If the bucket runs out of tokens (it’s empty), new requests have to wait until more tokens are available.

This approach helps avoid overload, but it makes a few assumptions that aren't always true:

• Customers will wait as long as needed.

• Service times are predictable.

• Arrivals aren't affected by the queue length.

So, how do organisations put this model into practice? 

The Disney Revolution: Queue Psychology in Practice

Disney theme parks revolutionised queue management by recognising that the psychology of waiting is just as important, if not more so, than the actual wait time. 

Like many of their films, Disney structures their queues like a three-act story:

1. The Opening Act: Setting expectations with posted wait times

2. The Experience: Interactive elements and storytelling within the queue

3. The Finale: Building anticipation as guests near the attraction

Why does this approach work? Well, it’s based on a few key principles: 

• Occupied time feels shorter: Disney includes interactive elements and storytelling in the queue to keep guests engaged, making the wait feel faster.

• Anxiety makes waits feel longer: By setting clear expectations with posted wait times, Disney reduces uncertainty and prevents guests from feeling anxious.

• Not knowing how long the wait is feels worse than knowing it’s short: With accurate wait times displayed, guests can mentally prepare, making the wait feel more manageable.

• Explaining the wait makes it more acceptable: Disney uses storytelling throughout the queue, which makes the wait feel more purposeful and enjoyable.

• Fair waits are easier to handle: Disney ensures the wait feels fair by keeping guests informed and maintaining queue discipline.

• Waiting with others is better: The queue is designed to create shared experiences, so guests feel the time passes faster when they’re enjoying the environment together.

This is fine for theme park attractions, but can these principles be applied in online queues? 

The Self-Regulating Nature of Online Queues

In the digital world, managing queues gets a lot trickier. At CrowdHandler, we've noticed some interesting patterns in how online queues tend to regulate themselves based on user behaviour.

The Ghost User Problem

The Ghost User Problem refers to when users hold their spot in a queue but aren’t actually active or engaged anymore. This typically occurs when someone abandons the session or stops interacting, but their spot in the queue remains used up.

Think of it as “hold my place”. 

However, this causes problems. When queue positions are held indefinitely:

• Abandoned sessions remain in the queue

• Active users face artificially longer wait times

• System efficiency decreases

• User satisfaction drops

There is, however, a solution: session expiration. 

By allowing sessions to expire when users leave:

• Queue length naturally optimises

• Active users move forward faster

• System resources are used more efficiently

• Wait time estimates become more accurate

Queue expiries make sense: it’s how the real world works. Could you imagine queuing for a ride at Disney World and half of the “queue” isn’t even there? It wouldn’t make sense in person, so why should it make sense online? 

The Mathematics of Queue Psychology

It isn’t just the logistical differences between online and offline – it’s the role of human psychology, too. 

Real-world queue behaviour often deviates from theoretical models due to psychological factors:

One major factor is the abandonment rate—the chance that someone will leave the queue before they reach the front. This rate isn’t random; it’s influenced by three things:

• Where the person is in the line: If they're near the back, they're more likely to give up.

• How long they've been waiting: The longer the wait, the more likely people are to lose patience.

• How valuable the wait feels: If people think what they’re waiting for is worth it, they’ll stick around.

The optimal queue length must balance:

• System capacity: The maximum number of people the system can handle at once without overcrowding.

• User patience: How long people are willing to wait before they start losing interest or give up.

• What users expect: Setting realistic expectations about the value of the wait.

• Transparency: Making sure people know how long the wait will be and why they’re waiting.

By balancing these factors, queues can be managed in a way that keeps both the system running efficiently and the people waiting satisfied.

The Transparency Paradox

The question is, then, how transparent should you be? 

Hiding queue information typically worsens outcomes:

It may seem like keeping queue information hidden would reduce frustration, but in reality, it often makes things worse. Here's why:

When users don’t know what to expect, it increases their anxiety and leaves them unable to make informed decisions. Without information, people might abandon the queue for reasons that feel random, which makes the whole system less predictable. Plus, the queue can’t regulate itself effectively without clear data on wait times.

On the other hand, providing transparency actually helps the system. When users have clear wait time information, they can decide for themselves whether to stay or leave based on how long they’re willing to wait. This manages expectations, reduces anxiety, and helps the queue optimise naturally as people self-select based on their tolerance (so long as the sessions can expire, as previously touched upon). 

Practical Implementation Guidelines

At Crowdhandler, we’ve been doing queues for over a decade. Based on our experience, here’s what we recommend to make classical queue theory work online: 

Provide clear, accurate information:

Make sure users always have the most up-to-date details to manage their expectations. This includes:

• Their current queue position so they know where they stand.

• The estimated wait time so they can decide how long they’re willing to wait.

• Progress indicators that show how far they’ve already come. 

Implement effective session management:

Ensure sessions are managed in a way that optimises the flow of users:

• Set reasonable expiry times to ensure inactive users don’t take up space in the queue.

• Communicate session rules clearly so users know how long they can stay in the queue and when they might be removed.

Monitor and adjust based on data:

Keep track of queue performance and user behaviour to fine-tune your system:

• Analyse user behaviour patterns to identify trends and pain points in the waiting experience.

• Regularly adjust parameters like estimated wait time or session expiration based on real-time data to improve efficiency.

Conclusion

Effective queue management takes more than just maths - it needs to consider human psychology, too. Transparency and self-regulation create systems that are both efficient and satisfying for users, proving that the best solutions prioritise humans as well as pure numbers.

Crowdhandler specialises in queuing software that enables this so that you can provide the best experience for your customers. 

Sign up today for a free trial.