ezyang’s blog

the arc of software bends towards understanding

Little’s law

A short thought from standing in line at the World Expo: Little’s law is a remarkable result that relates the number of people in a queue, the arrival rate of people to the queue, and the time spent waiting in the queue. It seems that it could be easily applied to a most universal feature of theme parks: waiting queues. Instead of such unreliable methods as giving visitors tokens to test how long it takes to traverse some portion of the line and then eyeballing the wait time from there, it would be a simple matter to install two gates: one to count incoming visitors and one to count outgoing visitors, and with this data derive an instantaneous “wait time in queue” figure based on a smoothed running average of queue size and arrival rate. Added benefit for being electronic, which means you can easily beam it to information boards across the park!

It occurs to me that I don’t have any evidence that theme parks aren’t already using this technique, except maybe for the fact that their posted wait times are wildly inaccurate.

2 Responses to “Little’s law”

  1. Brian Sniffen says:

    It’s far from clear that theme park operators have incentive to give honest estimates. They win by maximizing customer-perceived customer happiness. Customers want to do all the rides, but don’t gain much happiness from repeats. Customers enjoy getting a “bargain” when a line is shorter than expected, hate spending longer than expected, but don’t know how long any line without waiting in it.

    So theme park operators can steer crowds around by setting signs alternately a little low, high enough to induce a feeling of discount, and high enough to scare most people away, producing waves of people instead of a uniform densite.

  2. That’s definitely true. I usually notice the my time spent waiting in line to be much shorter than what is claimed on the signs, which is doubtless in an effort to make me feel better about spending half an hour instead of an hour.

    I’ve never heard of theme park operators steering crowds around by manipulating wait times though!

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