What kind of physical processes are well modeled as poisson processes? For instance, it is easy to understand how Brownian motions appear: when an object receives many small shocks that are roughly i.i.d., the resulting path will look like Brownian motions.
What type of physical processes give rise to Poisson processes?
For instance, with one dimension thought of as time: what kind of physically processes would naturally have the "memoryless property" between spikes?

The Poisson distribution is appropriate for modeling the number of time an event has happened in a specific time interval. In the transportation safety field the Poisson distribution is widely used for the analysis of crashes at individual sites. For instance, imagine having data on the monthly number of crashes at an intersection for 10 years; the distribution of the data will follow the Poisson distribution.
