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The waiting time paradox: why is my bus always late? (2018)

(jakevdp.github.io)
219 points skadamat | 3 comments | 20 Aug 24 13:55 UTC | HN request time: 0.44s | source
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stonemetal12 ◴[20 Aug 24 17:02 UTC] No.41301771[source]▶
>when the average span between arrivals is N minutes, the average span experienced by riders is 2N minutes.

Who is arriving in the first part of the sentence? At first I thought he meant the bus arrival, thus N = 10, and 2N would be 20. But then he says

>The average wait time is also close to 10 minutes, just as the waiting time paradox predicted.

10 isn't 20 so ???

replies(1): >>41304238 #
1. outop ◴[20 Aug 24 21:25 UTC] No.41304238[source]▶
The average time between two buses (based on the Poisson model used in TFA) is N minutes. But you are more likely to arrive in a long interval than a short one. So if you turn up to the station at a random time, the average time between the last bus that departed before you got there and the next departure, is 2N minutes.
replies(1): >>41310398 #
2. stonemetal12 ◴[21 Aug 24 14:01 UTC] No.41310398[source]▶
Doesn't change the fact that N is 10 and evidently 5 in the same sentence. Does author think only 'N' can be used for variables and readers are left to figure out which 'N's are the same and which are different?
replies(1): >>41317524 #
3. outop ◴[22 Aug 24 06:52 UTC] No.41317524[source]▶
No, N means 10 in both parts of the sentence you quoted.

> when the average span between arrivals is [10] minutes, the average span experienced by riders is [20] minutes.

>The average wait time is also close to 10 minutes, just as the waiting time paradox predicted.

The average wait time is half the 'average span experienced by riders', since the rider arrives, on average, halfway through the average span.