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## Estimation Methods for Stochastic Petri Nets Based on Standardized Time Series.

Haas, Peter J.
In:
*Proceedings of the Seventh International Workshop on Petri Nets and Performance Models, June 3-6, 1997, Saint Malo, France*, pages 194-204.
Los Alamitos, California: IEEE Computer Society,
June 1997.

Abstract:
When a computer, manufacturing, telecommunication, or transportation
system is modeled as a stochastic Petri net, many long-run performance
characterisics 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. Morever, 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.

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