A generalized semi-Markov process provides a stochastic process model for a discrete-event simulation. This representation is particularly useful for non-Markovian systems where it is nontrivial to obtain recurrence properties of the underlying stochastic processes. We develop "geometric trials" arguments which can be used to obtain results on recurrence and regeneration in this setting. Such properties are needed to establish estimation procedures based on regenerative processes. Applications to modeling and simulation of ring and bus networks are discussed.