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Two tills, one line, and my arithmetic broke

The shop opened a second till halfway through my hour. My wait dropped by more than half, which I did not expect.

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ArithmeticAnswered389 views

Counted 14 in the line, arrivals about 3 a minute, wait around 4 minutes and 40 seconds. That matched the stopwatch, which was satisfying.

Then they opened a second till onto the same line. Same arrivals. Line length dropped to 5 and my measured wait dropped to about 1 minute 20.

I expected half. I got a quarter. Have I made an arithmetic mistake or is this a real thing?

3 replies

  1. Marked as the answer

    That is the pooling result and you found it a week early. Doubling servers on one line does more than halve the wait, because the second server also removes the case where one slow customer blocks everybody behind them. Week 8 is this whole lecture. Bring the numbers.

  2. Mine did the opposite. They opened a second till with its own line and the wait barely moved, because half of us were stuck behind the person doing a return.

  3. Two queues is not two servers. Ravi has just described the difference better than my slides do, so I am stealing it.

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