How the maths of queuing can make lines more efficient

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…