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Estimation Methods for Nonregenerative Stochastic Petri Nets
March/April 1999 (vol. 25 no. 2)
pp. 218-236

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 SPNs 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 SPNs 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 [9] 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 Muñoz 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.

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Index Terms:
Stochastic Petri nets, stochastic simulation, discrete-event stochastic systems, standardized time series, batch means, modeling power, video on demand, Harris recurrence, Markov chains, generalized semi-Markov processes, stability.
Peter J. Haas, "Estimation Methods for Nonregenerative Stochastic Petri Nets," IEEE Transactions on Software Engineering, vol. 25, no. 2, pp. 218-236, March-April 1999, doi:10.1109/32.761447
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