One-dependent cycles and passage times in stochastic Petri nets

It is demonstrated that whenever the marking process of a stochastic Petri net has a recurrent single-state, the sample paths of any sequence of delays can be decomposed into one-dependent, identically distributed cycles. It is then shown that an extension of the regenerative method for analysis of simulation output can be used to obtain meaningful point estimated and confidence intervals for time-average limits. This estimation procedure is valid not only when there are no ongoing passage times at any regeneration point but, unlike previous method, also when the sequence of delays does not inherit regenerative structure. Application of these methods to simulation of a manufacturing flow-line with a shunt bank is discussed.