# Waiting for the bus

### 4 Responses

1. Artur Adib says:

Ha, very neat Esteban. I have to think a bit more about this, but the presentation is very clear. I’ve never really thought about this problem as (a) in Brazil buses never really promise to arrive with a given frequency, and (b) the trains I take in the US are pretty much on time always!

2. admin says:

Thank you Artur. I came accross the paradox when reading about response time in emails. In fact is the same kind of thing…

3. Mario Konschake says:

Hi Esteban,

in traffic science I have learned that this is called “bus bunching” and is simply caused by any small delay self-amplifying. If a bus has a delay it has to pick up more people, because there is more waiting time available at the next station. The station after, even more people are waiting plus more people want to get off the bus, and so on…. The good thing about this is, that in the very end you have two buses following each other. If you know this you can let the crowded one pass and get your free seat in the next one. Of course buses can overtake each other and therefore this works more reliable with trains.

*just noted that is a very old post, but someone found it intersting enough to tweet…

4. admin says:

Thank you Mario
(and thanks to the one that tweeted it!)

Indeed what you mention is my experience when I was in Oxford. Bus bunching was always a problem specially during rush hours. However, the waiting time paradox is not due to bus bunching. It has to do with different times between buses. Actually, bus bunching is a way produce a high heterogeneous distribution of times between buses and thus the variance sigma is large and thus we have larger waiting times. But one can have the paradox without bus bunching.

Best