Estimation methods for stochastic Petri nets based on standardized time series

Abstract

When a computer, manufacturing, telecommunication, or transportation system is modeled as a stochastic Petri net, many long-run performance characteristics of interest can be represented as time-average limits of the underlying marking process. For nets with generally-distributed firing times, such limits typically cannot be computed analytically or numerically, but must be estimated using simulation. We provide conditions on the clock-setting distributions and new-marking probabilities of a stochastic Petri net under which the output process of the simulation obeys both a strong law of large numbers and a multivariate functional central limit theorem. It then follows from results of Glynn and Iglehart that strongly consistent point estimates and asymptotic confidence intervals for time-average limits can be obtained using methods based on standardized time series. In particular, the method of batch means (with the number of batches fixed) is applicable. Moreover, the methods of Munoz and Glynn can be used to obtain point estimates and confidence intervals for ratios of time-average limits. All of these estimation methods apply to stochastic Petri nets for which the regenerative method for analysis of simulation output is not applicable.