The Waiting Time Paradox, Or, Why Is My Bus Always Late?
> a Poisson process is a memoryless process that assumes the probability of an arrival is entirely independent of the time since the previous arrival. In reality, a well-run bus system will have schedules deliberately structured to avoid this kind of behavior: buses don't begin their routes at random times throughout the day, but rather begin their routes on a schedule chosen to best serve the transit-riding public.<p>I've never really understood any example involving a poisson process. They always seem to involve bus arrivals or light bulbs burning out, and I can't understand why the memory less property would ever make any sense for these.<p>Even if the bus system was poorly run, why would it make sense to assume that the expected value of time to arrival doesn't change based on how long you've been waiting?<p>What is an actual phenomenon that is well modeled by a poisson process?