Urinal Protocol Vulnerability

The article examines the International Choice of Urinal Protocol, in which each arriving man takes the urinal furthest from others, and argues that the protocol packs people inefficiently for some urinal counts. It says a row of five urinals fills with three men, a row of seven fits only three before the fourth must use a stall or sink, and a row of eight packs better than seven. Packing efficiency, f(n)/n, peaks at 50% for certain counts such as 3, 5, 9, 17 and 33, and falls to about 33% for counts such as 4, 7, 13 and 25.