Death by Queue

They infuriate us. They disrupt our daily schedules. They pervade our lives. Queues. We are all too familiar with them but most of us fail to understand them. In our new ‘COVID-19’ world, queues will be all that more prevelant.

Standing in line at the amusement park or waiting to board that flight home are common experiences of queueing but there are many more. That movie that takes forever to download or the 10 minute wait for your morning coffee are more examples of when queues “have us”.

So what is a queue? Beyond our everyday understanding there are mathematical models that explain why they form and how they behave.

Queues are born when someone or something needs to wait for a resource or service. They grow as demand outpaces delivery and only die once that demand is satisfied or those waiting, depart in disappointment.

Life in the queue is about waiting. Waiting until you reach the front of the queue to be served and once there, waiting for the server to service your request. So the total time you spend in the queue is the sum of these:

Total Wait Time = Queueing Time + Service Time.

These concepts are important because they provide insights into how best to control a queue. There are two common approaches to reducing a queue — making the server faster or adding more servers.

Consider waiting for your morning coffee. Imagine nine people arrive at the same time each after their particular latte or cappuccino. Now imagine a single barista serving each one, who takes the order, prepares it and takes payment. Assuming this takes 3 minutes per order, the 9th person must wait 24 minutes before their order is taken and another 3 minutes before receiving their “cup of joe”.

So what can be done to improve this situation? You could start by having more baristas. What happens when we employ two additional people, giving us three servers in total? First, customers one, two and three can be served immediately. Customer one notices no difference in her experience, it still takes 3 minutes to get her coffee but customer three gets his coffee in 3 minutes also, instead of waiting 9 minutes — a big improvement. If we look at customer nine, they are now served in 6 minutes and get their coffee in 9 minutes, rather than waiting for almost half-an-hour.

But this isn’t the only alternative. Assume instead we can encourage our single barista to make and serve coffee of the same quality in just 1 minute? Now customer one is out of the store in just one minute and customer three is out 2 minutes later. Even customer nine gets a much better experience, now only having to wait a total of 9 minutes.

So which alternative is better? More baristas or a faster barista? At first the faster barista looks better. Customers one and two get served faster than they would have with three slower baristas. But what happens when our ‘super barista’ needs to take a break or their coffee machine needs to be cleaned. At these times there is no one two service the queue, the queue grows and customers will turn away in disappointment yet again.

So it is a trade off between have alternate baristas available and service time. These are the types of problems traffic engineers and network programmers deal with every day, but they are also the sorts of problems business owners must grapple with when satisfying their customers’ demand for products and services.

So the next time you see that queue of people out your door, think about what you could do to improve the situation. Don’t leave them waiting.