Have you ever waited in a line at the grocery store or bank? The British term for a line is a queue. Queuing theory is the mathematical study of waiting in line. Let’s learn more about this.

The British refer to a line as a queue. Queuing theory is the mathematical study of people, objects and information waiting in a line. The purpose is to identify ways to reduce the length of the queue and time in line to increase the flow through the process. You, like most other people, will get aggravated if you must wait in line too long and may even leave or abandon the line. Or you may not even get in line if you perceive it will take up too much of your time.

Overview: What is queuing theory? 

The concept of queuing theory is simple. The basic elements of queuing theory consist of:

1. The arrival time of people, objects, or information. This is expressed as the term lambda.

2. The service time or, on average, mean time it takes to do the required task.

3. The number of servers or resources available to provide the service.

4. The queuing discipline. For example; first-in, first-out or last-in, first-out.

5. The capacity of the queue. You don’t want people wrapping around the block or backed up in the parking lot.

6. The number of people that need to be served.

By using queuing theory, you can develop more efficient systems, processes, staffing solutions, and arrival management strategies. The goal is to reduce wait times and increase the number of customers you can serve.

An industry example of queuing theory 

Walt Disney World is known for long lines to get on their rides. By focusing on the components of a queue, they have utilized queuing theory to try and reduce the length of time their guests must wait in line. This is more important than most queuing issues, since many of the guests are young children.

How Disney can improve the queuing components:

  • Arrival rate of guests – balance arrival rate by using Disney Genie+ to balance the arrival times so people get in shorter lines and get on the rides quicker
  • Service times – unfortunately, unless they speed up a ride this may be a constraint
  • Number of servers – they can add boats, cars and other transportation within a ride but may be constrained by spacing requirements
  • Queuing discipline – they have gone away from the original first-in, first-out and now have a premium prioritization so guests who are willing to pay for the service can skip ahead of other guests
  • Capacity of the queue – on some rides, a guest goes through a queue and then is diverted to a holding area before getting on another queue to get on the ride.

Frequently Asked Questions (FAQ) about queuing theory

What does the word queue mean? 

It is the British term for a line of people, objects, or information.

What are the four key components of queuing theory? 

The four key elements are:

  • customer arrival rate
  • customer service rate
  • queuing discipline
  • number of servers 

What are three examples of where queuing theory would help? 

Here are three examples most people frequently experience which can cause stress and aggravation:

  1. Waiting on hold when calling an organization’s customer service number
  2. Waiting in the security line at the airport
  3. Waiting in line at the bank to cash a check
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