How do I generate a Poisson Process?

Question

Original Question:

I want to generate a Poisson process. If the number of arrivals by time t is N(t) and I have a Poisson distribution with parameter

Answer 1

The discussion here has all the details about using inverse sampling to generate inter-arrivals, which is usually what people want to do for games.

https://stackoverflow.com/a/15307412/1650437