Waiting in line is one of life's most frustrating tasks. In fact, we spend approximately 18 months of our lives standing in line.
When choosing the right line to stand in it seems obvious... the shorter one, of course!
Have you ever stood in the shorter line only to find out that the line with more people is actually moving faster than you so you consider jumping lines?
Turns out joining the shorter line isn't always advantageous. But what is?
Enter the concept of the 'service time distribution.' The service time distribution is a random variable that helps you measure how long it will take for a customer to be served.
According to one study posted on DailyMail.co.uk you can guess the fastest cue by relying on good ol human psychology. Joining the leftmost line queue might be more advantageous because most people are right handed and therefore automatically default to going right.
The inspection paradox works like this: Suppose a bank offers two services.
One service takes either zero or five minutes, with equal probability. The other service takes either ten or 20 minutes, again with equal probability.
It is equally likely for a customer to choose either service and so the bank’s average service time is 8.75 minutes.
If you join the queue when a customer is in the middle of being served then their service can’t take zero minutes.
They must be using either the five, ten or 20 minute service.
This pushes the time that customer will take to be served to more than 11 minutes on average, more than the true average for the of 8.75 minutes.
In fact, two out of three times you encounter the same situation, the customer will want either the 10 or 20 minute service.
This will make it seem like the line is moving more slowly than it should, all because a customer is already there and you have extra information.
So while you can use maths to try to determine the fastest queue, in the absence of accurate data – and for your own peace of mind – you’re often better just taking a gamble and not looking at the other options once you’ve made your mind up.