An empirical study of some branching processes with upper barrier

We consider discrete time branching processes with a reflecting upper barrier. The processes differ in their offspring distributions being either binary splitting or binomial one. Two important factors for the behavior of the processes characteristics are studied as follows: time to extinction and total progeny up to the n th generation. More specifically, we investigate the distribution and expected value of the time to extinction as well as the probability mass functions of the total progeny. The tools used are basic results for a finite state Markov chain