If you frequently commute via public transit, you may be frustrated with bus arrivals not aligning with the schedule. The waiting time paradox asserts that even if buses are scheduled every 10 minutes, on average, riders wait 10 minutes between buses. This concept is part of the inspection paradox, where the probability of observing a value is related to the value itself. A simulation of bus arrivals confirmed this paradox. While real-world bus arrivals might not fit a Poisson process perfectly, analyzing arrival data from Seattle buses in 2016 showed that buses do not follow uniform schedules, leading to varied arrival intervals and departure times.
https://jakevdp.github.io/blog/2018/09/13/waiting-time-paradox/