On a little waiting

Besides fried chicken, another prevalent phenomenon in summer in Japan is long queues everywhere: in banks, ice cream shops, Disneyland and most women's public toilets. Ever noticed how there are signs for estimated waiting times in certain queues? Ever wondered how the waiting time was calculated, and whether it's actually accurate or just cooked up randomly by a ride operator? Ever wanted to know how to calculate your own estimated waiting time? If you haven't, you're going to find out the answer anyway.

And the answer is.... Little's Law! A quite clever and neat-looking theorem developed by an American academic named John Little (who did not, however, develop any department stores), which Japanese Afternoon TV summarised, applied and simplified to the following:

No. of people in front of you in the queue ÷ No. of people who join the queue behind you after 1 minute = No. of minutes of waiting time

To test this wonderfully simple theory, JAT sent a young man out to stand in the snaking queues for Cold Stone, a popular ice cream store developed by an American couple. The young man duly started his stopwatch upon entering the queue, counted 22 people in front of him, waited a minute, and counted 2 people queuing behind him in that time. Using his mental mathematical powers, he concluded that his waiting time should be 11 minutes. And indeed, it was.... 10 minutes and 20 seconds till the moment when the cheery singing staff handed him his ice cream. That, for the home audience, is an impressive discrepancy of just 40 seconds. Amazing!

So this summer, why not spend the 2 hours in line for a ride at Disneysea putting Little's Law to the test? Distract yourself and the kids for at least 2 minutes! That's the power of mathematics.

Ijyou desu!