Variance and derivative estimation of virtual performance

Yujing Lin*, Barry L. Nelson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Virtual performance is a class of time-dependent performance measures conditional on a particular event occurring at time τ0 for a (possibly) nonstationary stochastic process; virtual waiting time of a customer arriving to a queue at time τ0 is one example. Virtual statistics are estimators of the virtual performance. In this article, we go beyond the mean to propose estimators for the variance, and for the derivative of the mean with respect to time, of virtual performance, examining both their small-sample and asymptotic properties. We also provide a modified K-fold cross validation method for tuning the parameter k for the differencebased variance estimator, and we evaluate the performance of both variance and derivative estimators via controlled studies and a realistic illustration. The variance and derivative provide useful information that is not apparent in the mean of virtual performance.

Original languageEnglish (US)
Article numberA17
JournalACM Transactions on Modeling and Computer Simulation
Issue number3
StatePublished - Aug 2018


  • Nearest-neighbor regression
  • Output analysis
  • Queueing simulation

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computer Science Applications


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