Week 3 Field session: The long tail

Plotting your own service times and discovering that the average was hiding most of what matters.

10 March 2027

By now you should have a mean service time of your own. This session is about how remarkably little that one number tells you, and we work it through using your data rather than a textbook’s, which tends to make the point land harder.

What happens#

First half hour, hands on paper. Everybody plots their own service times as a histogram, by hand, on graph paper. Doing it by hand is deliberate. A plotting library will draw you something smooth and you will not look at it.

Next half hour. We put them all on the wall in a row. Twenty histograms from twenty queues is the fastest way to see that service time distributions are not all one shape, and some of them are nothing like the bell curve people expect.

Last hour. The coefficient of variation, computed for your own queue, and then Kingman applied to your own numbers. Most people get a predicted wait that is wrong. We spend the rest of the session on why, and the reasons are interesting.

The thing to watch for#

Watch for a queue with a bimodal service time. A counter that does two different jobs, one taking forty seconds and the other six minutes, produces a mean that nobody standing in it has ever experienced. If your histogram has two humps you have found the single best thing to write about in The Measured Queue.

Bring#

• Your observation sheets, with at least sixty service times on them. If you do not have sixty, come anyway and use somebody else’s while you arrange to collect more.
• A calculator or a laptop. Either is fine here.
• Graph paper is provided.

What leaves the room#

A hand-drawn histogram of your queue’s service times, a coefficient of variation, and a Kingman estimate of your mean wait with a note on how far it is from what you measured.