  We study long run average behavior of generalized semi-Markov processes with
both fixed-delay events as well as variable-delay events. We show that allowing
two fixed-delay events and one variable-delay event may cause an unstable
behavior of a GSMP. In particular, we show that a frequency of a given state
may not be defined for almost all runs (or more generally, an invariant measure
may not exist). We use this observation to disprove several results from
literature. Next we study GSMP with at most one fixed-delay event combined with
an arbitrary number of variable-delay events. We prove that such a GSMP always
possesses an invariant measure which means that the frequencies of states are
always well defined and we provide algorithms for approximation of these
frequencies. Additionally, we show that the positive results remain valid even
if we allow an arbitrary number of reasonably restricted fixed-delay events.
