How waiting in line is like war

A defense researcher analyzes (1) customer satisfaction in a shopping scenario and (2) the efficient use of warplanes in battle. He comes up with a mathematical model common to both—in which “[the] parameter of principal interest is the expected customer-survival rate.”  Here’s his paper on how the two relate:

Queuing with Impatient Customers and Indifferent Clerks,” D.Y. Barrer, Operations Research, Vol. 5 (5), Oct. 1957, pp. 644-9.  The author, at the Institute for Defense Analyses, Washington, DC, explains:

“In certain queuing processes a potential customer is considered ‘lost’ if the system is busy at the time service is demanded.  The telephone subscriber hangs up when he gets a busy signal.  A man trying to get a haircut during his lunch hour does not wait unless a chair is immediately available.  Another form of this general situation is that in who customers wait for service, but wait for a limited time only.  If not served during this time, the customer leaves the system and is considered lost.  Such situations occur in the processing or merchandising of perishable goods.  Many types of military engagements are similarly characterized.  An attacking airplane engaged by antiaircraft or guided missiles is available for ‘service,’ i.e., is within range, for only a limited time.  It is of interest to relate the expected rate at which aircraft are shot down to the firing rate and accuracy of the defensive weapons, the rate at which aircraft come within range, and the time that each airplane would remain within range if not shot down.”

BONUS: At some point Barrer also turned his attention to the mathematics of fly-fishing.