Estimation of Delays in Non-Regenerative Stochastic Petri Nets

Many long-run delay characteristics of computer, communication, manufacturing, and transportation systems can be specified as time-average limits of sequences of delays in stochastic Petri nets (SPN's). We consider SPN's with general firing times in which sequences of delays are determined
from the marking changes of the net using the method of start vectors. In this setting, time-average limits typically must be estimated using simulation. Previous work on estimation methods for delays has focused on SPN's in which there exists a sequence of regeneration points for the marking process. For such nets, point estimates and confidence intervals for time-average limits can be obtained using the regenerative method for simulation output analysis or recently proposed variants of the regenerative method. This paper is concerned with SPN's for which regenerative methods
are not applicable. We provide conditions on the building blocks of an SPN and start-vector mechanism under which the sequence of delays is an "od-regenerative" process with finite cycle-sum moments. Although the od-regeneration points usually cannot be determined explicitly, the
existence of these points implies that time-average limits are well defined and the sequence of delays obeys a multivariate functional central limit theorem. It then follows from results of Glynn, Iglehart, and Munoz that methods based on standardized time series can be used to obtain strongly
consistent point estimates and asymptotic confidence intervals for time-average limits and functions of time-average limits. In particular, the method of batch means is applicable.