Regenerative stochastic Petri nets
Performance Evaluation
Estimating time averages via randomly-spaced observations
SIAM Journal on Applied Mathematics
Sufficient conditions for functional-limit-theorem versions of L=λW
Queueing Systems: Theory and Applications
Simulation methods for queues: an overview
Queueing Systems: Theory and Applications
Ordinary CLT and WLLN versions of L=λW
Mathematics of Operations Research
Properties of standardized time series weighted area variance estimators
Management Science
Simulation output analysis using standardized time series
Mathematics of Operations Research
Likelihood ratio gradient estimation for stochastic systems
Communications of the ACM - Special issue on simulation
Notes: conditions for the applicability of the regenerative method
Management Science
Markov regenerative stochastic Petri nets
Performance '93 Proceedings of the 16th IFIP Working Group 7.3 international symposium on Computer performance modeling measurement and evaluation
Petri Net Theory and the Modeling of Systems
Petri Net Theory and the Modeling of Systems
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Estimation of delays in non-regenerative discrete-event stochastic systems
ACM SIGMETRICS Performance Evaluation Review
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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.