I think this is the correct way to model it. In particular you can model it as a markov chain (commonly studied in queueing theory): https://en.wikipedia.org/w

I think this is the correct way to model it. In particular you can model it as a markov chain (commonly studied in queueing theory): https://en.wikipedia.org/wiki/Birth%E2%80%93death_process#/media/File:BD-proces.png https://en.wikipedia.org/wiki/Birth%E2%80%93death_process#/m...