Dan Meyer writes about his research on which line is faster at the store? Awesome. One quick tidbit is the minimum time for one person is about 50 seconds, but an average item adds about 3 seconds. So it's faster to pick a line with up to 17 more items vs a line with one more person that has only one item.
The comments are interesting too, pointing out "invisible" effects like will the person use coupons, or want to buy a lotto ticket? The commenters note that you could assign weighted probabilities, which leads to another interesting series of questions. For example, based on probabilities suppose you have the following estimates to get to the head of each line:
|Estimate based on
|Line 1||3 min||5 min||11 min|
|Line 2||4 min||6 min||10 min|
|Line 3||5 min||7 min||9 min|
Now which line would you pick? Line 3 is predictable, but Line 1 could finish really fast; or take a really long time.