Compound Cycle of a Renewal Process and Applications

This paper presents a generic framework that is common to many stochastic models. For the virtual wait process in an M/G/1 queueing system, we obtain the expected number of events during a sojourn time above or below a state‐space level. Similar quantities are derived for the ‘extended age’ process in a standard G/M/1 queue. These results generalize the expected number of events in a busy period. We also apply the framework to a renewal model with a barrier. We obtain the expected number of renewals required to exceed the barrier.