Science

How the maths of queuing can make lines more efficient

EDINBURGH, SCOTLAND - JUNE 06: Taylor Swift fans queue outside Murrayfield stadium ahead of tomorrow nights concert on June 06, 2024 in Edinburgh, Scotland. Taylor Swift's Eras World Tour plays 15 dates across Scotland, Wales and England this June and August. Her fans, known as Swifties, had made the superstar $200 million in Eras merchandise sales as of November 2023. (Photo by Jeff J Mitchell/Getty Images)

Taylor Swift fans queue outside Murrayfield stadium

Jeff J Mitchell/Getty Images

I imagine that you may, at some point in your life, have been in a queue that wasn’t run entirely efficiently. Despite allegedly loving to line up and wait for things, Brits like me have an array of stories about badly run queues.

Luckily, maths can give us insight into queues and answer questions like how many staff are needed to help them run efficiently. We can gather data on a real queue and use the average arrival rate to calculate the probability of someone joining. This is just…


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