I'll quote from the conclusion of that article, because the frequent assumptions that bus arrivals are a poisson process peeve me and this article did a good jo

I'll quote from the conclusion of that article, because the frequent assumptions that bus arrivals are a poisson process peeve me and this article did a good job of actually testing that assumption: > Even without a statistical test, it's clear by eye that the actual arrival intervals are definitely not exponentially distributed, which is the basic assumption on which the waiting time paradox rests. > The average waiting times are are perhaps a minute or two longer than half the scheduled interval, but not equal to the scheduled interval as the waiting time paradox implied. In other words, the inspection paradox is confirmed, but the waiting time paradox does not appear to match reality. > the above analysis shows pretty definitively that the core assumption behind the waiting time paradox — that the arrival of buses follows the statistics of a Poisson process — is not well-founded.