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## Estimation Methods for Non-Regenerative Stochastic Petri Nets.

Haas, Peter J.
In:
*IEEE Trans. Software Engrg.*, pages 218-236.
1999.
Expanded version of PNPM'97 paper.

Abstract:
When a computer, manufacturing, telecommunication, or transportation
system is modeled as a stochastic Petri net (SPN), many long-run
performance characteristics of interest can be expressed as time-average
limits of the associated marking process. For nets with
generally-distributed firing times, such limits often cannot be computed
analytically or numerically, but must be estimated using simulation.
Previous work on estimation methods for SPN's has focused on the case in
which there exists a sequence of regeneration points for the marking
process of the net, so that point estimates and confidence intervals for
time-average limits can be obtained using the regenerative method for
analysis of simulation output. This paper is concerned with SPN's for
which the regenerative method is not applicable. We provide conditions on
the clock-setting distributions and new-marking probabilities of an SPN
under which time-average limits are well defined and the output process of
the simulation obeys a multivariate functional central limit theorem. It
then follows from results of Glynn and Iglehart that methods based on
standardized time series can be used to obtain strongly consistent point
estimates and asymptotic confidence intervals for time-average limits. In
particular, the method of batch means 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. We illustrate our results
using an SPN model of an interactive video-on-demand system.

Keywords:
Stochastic Petri nets, stochastic simulation, discrete-event stochastic.

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