I visited my local hospital recently for a blood test. The test centre opened at 7am so I aimed to arrive at that time hoping to be seen straight away. There are often queues there. When I arrived, there was already a queue of around 10 people! We all had temperature checks, took a numbered ticket, and sat in the socially distanced waiting room. And I was impressed to see an information board that announced the next ticket number to go for the blood draw and also the average wait time. The average wait time was only a few minutes. As I sat there, the average wait time gradually crept up. In the end, I waited for 25 minutes before I was seen. But the average wait time still showed as only 15 minutes. What was going on?
When you learn French, there is a term “faux amis” (false friends). These are words that are the same, or similar, to English words but actually mean something different. For example attendre means to wait for rather than to attend to others, brasserie is not a type of lingerie but a bar, and pub is an advertisement. Metrics can be rather like this. Superficially, the average wait time in a queue is a really useful metric to know when you start queueing for something. After all, you would expect to be around the average wait time wouldn’t you? Time to run a simple Excel model to investigate further! Below you see the arrival times of patients at the hospital. I am highlighted as person 10. After 7am, there was a slow but steady stream of people so I have them arriving every 5 minutes. I estimated the time for each blood draw to be 3 minutes and so you can see when each blood draw took place and the wait time for each individual. But look at the average wait time. We don’t know how the hospital defined it exactly, but I’m guessing they took the previous patients that day and calculated the mean wait time – which is what I’ve done here. There are only 9 patients whose actual wait time is within 5 minutes of the average wait time (shown in green). And I’m shown as patient 10 with the longest wait time and the greatest difference to the average wait time. The average wait time is like a faux ami – it appears to tell you one thing but actually tells you something else. There may be a value to the metric. But not for those joining a queue.
When I join a queue, I’m interested in how long I might have to wait for. You can estimate that by knowing the time to process each person in the queue and multiplying by the number of people in front of you. In this case, the estimate would be 27 minutes for me rather than the few minutes that the average wait time metric told me. I am impressed that the hospital thought to include a metric. But perhaps they need to think more about the purpose of the metric and a better definition. The metric should try to answer the question “How long am I likely to have to wait for?”
Next time I go for a blood test, I’m going to arrive at the more civilised time of 8am and walk straight in!
Text: © 2020 Dorricott MPI Ltd. All rights reserved.
Picture – pixy.org CC0 Public Domain.