Generation of simulation input scenarios using bootstrap methods

Simulation modellers frequently face a choice between fidelity and variety in their input scenarios. Using an historical trace provides only one realistic scenario. Using the input modelling facilities in commercial simulation software may provide any number of unrealistic scenarios. We ease this dilemma by developing a way to use the moving blocks bootstrap to convert a single trace into an unlimited number of realistic input scenarios. We do this by setting the bootstrap block size to make the bootstrap samples mimic independent realizations in terms of the distribution of distance between pairs of inputs. We measure distance using a new statistic computed from zero crossings. We estimate the best block size by scaling up an estimate computed by analysing subseries of the trace.

[1]  P. Hall,et al.  On blocking rules for the bootstrap with dependent data , 1995 .

[2]  D. Freedman,et al.  Some Asymptotic Theory for the Bootstrap , 1981 .

[3]  Joseph P. Romano,et al.  Inference for Autocorrelations under Weak Assumptions , 1996 .

[4]  Upmanu Lall,et al.  A Nearest Neighbor Bootstrap For Resampling Hydrologic Time Series , 1996 .

[5]  E. Carlstein.  Resampling techniques for stationary time-series: Some recent developments , 1990 .

[6]  David G. Tarboton,et al.  Multivariate nonparametric resampling scheme for generation of daily weather variables , 1997 .

[7]  Barry L. Nelson,et al.  Input modeling when simple models fail , 1995, WSC '95.

[8]  Lori A. Thombs,et al.  Bootstrap Prediction Intervals for Autoregression , 1990 .

[9]  Joseph P. Romano,et al.  The stationary bootstrap , 1994 .

[10]  H. Künsch.  The Jackknife and the Bootstrap for General Stationary Observations , 1989 .

[11]  Hans R. Künsch,et al.  Matched-block bootstrap for dependent data , 1995 .

[12]  A. J. Lawrance,et al.  A new autoregressive time series model in exponential variables (NEAR(1)) , 1981, Advances in Applied Probability.

[13]  Russell C. H. Cheng.  Bootstrap methods in computer simulation experiments , 1995, WSC '95.

[14]  Jorge Haddock,et al.  The binary bootstrap: inference with autocorrelated binary data , 1993 .

[15]  Robert Tibshirani,et al.  Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy , 1986 .

[16]  D. P. Gaver,et al.  First-order autoregressive gamma sequences and point processes , 1980, Advances in Applied Probability.

[17]  T. Willemain,et al.  The threshold bootstrap and threshold jackknife , 1999 .

[18]  Benjamin Melamed,et al.  TES: A Class of Methods for Generating Autocorrelated Uniform Variates , 1991, INFORMS J. Comput..

[19]  E. Carlstein.  The Use of Subseries Values for Estimating the Variance of a General Statistic from a Stationary Sequence , 1986 .

[20]  Reinaldo Castro Souza,et al.  A bootstrap simulation study in ARMA (p, q) structures , 1996 .

[21]  Barry L. Nelson,et al.  Autoregressive to anything: Time-series input processes for simulation , 1996, Oper. Res. Lett..

[22]  David Goldsman,et al.  The TES methodology: modeling empirical stationary time series , 1992, WSC '92.

[23]  Yun B. Kim,et al.  Simulation output analysis using the threshold bootstrap , 2001, Eur. J. Oper. Res..

[24]  Lawrence Leemis.  Input modeling for discrete-event simulation , 1995, WSC '95.

[25]  Chong-wei Xu,et al.  Bootstrap confidence intervals for simulation outputs , 1993 .

[26]  A. J. Lawrance,et al.  The Exponential Autoregressive‐Moving Average Earma(P,Q) Process , 1980 .

[27]  Ed. McKenzie.  10. Time Series Analysis by Higher Order Crossings , 1996 .

[28]  Regina Y. Liu.  Moving blocks jackknife and bootstrap capture weak dependence , 1992 .

[29]  Chong-wei Xu,et al.  Applying Bootstrap Methods to Simulation Output Analysis , 1992 .

[30]  Bing-Yi Jing,et al.  On Sample Reuse Methods for Dependent Data , 1996 .

[31]  A. Alan B. Pritsker,et al.  Introduction to simulation and SLAM II , 1979 .

[32]  Marne C. Cario.  Modeling and simulating time series input processes with ARTAFACTS and ARTAGEN , 1996, Winter Simulation Conference.