A semi-Markov point process is defined for which the intervals of time between successive events have phase-type distribution. The distribution of the number of events in an interval is examined, and it is shown how the expected number of events in an interval may be efficiently computed. A stationary version of the process is analyzed. In particular, a necessary and sufficient condition, and simple sufficient conditions under which the new process is a renewal process, are determined.
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Guy Latouche (1982) studied this question.
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