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The mathematics behind finding the fastest check-out line at the supermarket

You’re at the supermarket, you’ve made your way past the maze of aisles, you’ve overcome the shopping carts blocking your path, you’re about to reach the finish line, when suddenly… A stack of long lines at the check-out greets you. The question now is: which line do you choose?

Mathematics can help you with that. There’s a specific field in mathematics made to address issues in waiting lines. It’s called queuing theory and it was pioneered by Danish engineer and mathematician Agner Krarup Erlang in the early 20th century.

It all began with Erlang trying to determine the minimum circuits Copenhagen needed to ensure the phone lines would be working.

(Note: phone lines in this era required an operator who would plug a jack into a cork board to connect calls. Too few lines meant network traffic, too many lines meant the telephone company was forking out for superfluous equipment.)

Erlang created theories and studies that made telecommunication more efficient, and even got a unit of measurement named after him – an erlang – because he was so awesome. His work also influenced fields like traffic engineering, factory design, the internet, and queuing.

Going back to the check-out, queuing theorists believe that the fastest line will always be a serpentine line. It’s basically a single line that sends the person at the front to the next available cashier. You can see examples of this at the bank, where clients wait for their number to be called.

In serpentine lines, delays are lessened and movement is more efficient. While a traditional line can be delayed by a slow bagger, a malfunctioning register or a customer fumbling with their coupons, a serpentine line makes sure that the next person will be directed to other open cashiers.

If your local supermarket doesn’t have that kind of system, simply opt to choose lines to the left rather than the right. According to some studies, right-handed people, who are the vast majority, almost always head right. So the right decision is to go left!

Via Boing Boing

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Comments (1)


    Monday 15 June 2015

    just choose the one with the most few customers. it’s not the amount of groceries that makes the line take longer, the act of payment and handeling receipts (and coupons, collectables etc.) is what takes the longest and can cause additional delays