The Other Line Always Moves Faster

This is a nice introductory video on elementary queuing theory from Bill Hammack, the engineer guy.

http://www.youtube.com/watch?v=F5Ri_HhziI0

Hammack poses a classic queuing theory conundrum:  people in a town use phone lines at an average rate of two per hour; how many phone lines should the town have?  The naive answer of two lines is far from optimal, because of bunching.

In addition to exploring this basic idea, Hammack also discusses the efficiency of the single-line system (everyone waits in one line for the next available cashier) versus the multiple-line system (each cashier has a separate line).  Assuming that delays are distributed randomly among the cashiers, the single-line system minimizes the overall impact of a delay at any one cashier, and so, is more efficient.

And if every individual line has an equal chance of experiencing a delay, it stands to reason that every line has an equal chance of being the fastest.  This explains why the other line always seems to move faster:  if there are ten lines, you’ve got a 1 in 10 chance of choosing the fastest one, which means 9 times out of 10 a different line is moving faster!