Introduction to Modeling and Generating Probabilistic Input Processes for Simulation

Techniques are presented for modeling and generating the univariate and multivariate probabilistic input processes that drive many simulation experiments. Among univariate input models, emphasis is given to the generalized beta distribution family, the Johnson translation system of distributions, and the Bezier distribution family. Among bivariate and higher-dimensional input models, emphasis is given to computationally tractable extensions of univariate Johnson distributions. Also discussed are nonparametric techniques for modeling and simulating time-dependent arrival streams using nonhomogeneous Poisson processes

[1]  James R. Wilson,et al.  Using Univariate Bezier Distributions to Model Simulation Input Processes , 1996, Proceedings of 1993 Winter Simulation Conference - (WSC '93).

[2]  M. E. Johnson,et al.  Bounds on the Sample Skewness and Kurtosis , 1979 .

[3]  N. Cox.  Statistical Models in Engineering , 1970 .

[4]  Melba M. Crawford,et al.  Modeling and simulation of a nonhomogeneous poisson process having cyclic behavior , 1991 .

[5]  Robert S. Sullivan,et al.  A simulation model for welfare policy analysis , 1988 .

[6]  Simaan M. AbouRizk,et al.  FITTING BETA DISTRIBUTIONS BASED ON SAMPLE DATA , 1994 .

[7]  J. J. Swain,et al.  Least-squares estimation of distribution functions in johnson's translation system , 1988 .

[8]  Peter A. W. Lewis,et al.  Statistical Analysis of Non-Stationary Series of Events in a Data Base System , 1976, IBM J. Res. Dev..

[9]  M. A. Johnson,et al.  Estimating and simulating Poisson processes having trends or multiple periodicities , 1997 .

[10]  J. R. Wilson,et al.  Flexible modelling of correlated operation times with application in product-reuse facilities , 2004 .

[11]  Jennie P. Psihogios,et al.  Multivariate input modeling with Johnson distributions , 1996, Winter Simulation Conference.

[12]  B. Melamed,et al.  The transition and autocorrelation structure of tes processes: Part II: Special Cases , 1992 .

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

[14]  L. Leemis,et al.  Nonparametric Estimation of the Cumulative Intensity Function for a Nonhomogeneous Poisson Process from Overlapping Realizations , 2000 .

[15]  William J. Mcbride,et al.  PERT and the beta distribution , 1967 .

[16]  Kanti V. Mardia,et al.  Families of Bivariate Distributions , 1970 .

[17]  Ward Whitt,et al.  Estimating the parameters of a nonhomogeneous Poisson process with linear rate , 1996, Telecommun. Syst..

[18]  James R. Wilson,et al.  Graphical interactive simulation input modeling with bivariate Bézier distributions , 1995, TOMC.

[19]  Donald J. Leo,et al.  Monte Carlo simulation of a solvated ionic polymer with cluster morphology , 2006 .

[20]  James R. Wilson,et al.  Estimating and simulating Poisson processes with trends or asymmetric cyclic effects , 1997, WSC '97.

[21]  James R. Wilson,et al.  Modeling and simulating Poisson processes having trends or nontrigonometric cyclic effects , 2001, Eur. J. Oper. Res..

[22]  J. R. Wilson,et al.  Modeling input processes with Johnson distributions , 1989, WSC '89.

[23]  James R. Wilson,et al.  Recent developments in input modeling with Bézier distributions , 1996, WSC.

[24]  Lawrence M. Leemis,et al.  Nonparametric Estimation of the Cumulative Intensity Function for a Nonhomogeneous Poisson Process from Overlapping Realizations , 2000 .

[25]  Ayman Baklizi,et al.  Nonparametric estimation of P(X , 2006 .

[26]  Seong-Hee Kim,et al.  A discussion on ‘Detection of intrusions in information systems by sequential change-point methods’ by Tartakovsky, Rozovskii, Blažek, and Kim , 2006 .

[27]  James R. Wilson,et al.  Least squares estimation of nonhomogeneous Poisson processes , 1998, 1998 Winter Simulation Conference. Proceedings (Cat. No.98CH36274).

[28]  N L JOHNSON,et al.  Bivariate distributions based on simple translation systems. , 1949, Biometrika.

[29]  Averill Law,et al.  Simulation Modeling and Analysis (McGraw-Hill Series in Industrial Engineering and Management) , 2006 .

[30]  Nathan White,et al.  Distribution Selection with No Data Using VBA and Excel , 2004 .

[31]  James R. Wilson.  Modeling dependencies in stochastic simulation inputs , 1997, WSC '97.

[32]  Moshe Pollak,et al.  A discussion on ‘Detection of intrusions in information systems by sequential change-point methods’ by Tartakovsky, Rozovskii, Blažek, and Kim , 2006 .

[33]  Edward P. C. Kao,et al.  Modeling time-dependent arrivals to service systems: a case in using a piecewise-polynomial rate function in a nonhomogeneous Poisson process , 1988 .

[34]  Lawrence M. Leemis,et al.  TECHNICAL NOTE: Nonparametric estimation and variate generation for a nonhomogeneous Poisson process from event count data , 2004 .

[35]  Yongro Park.  A statistical process control approach for network intrusion detection , 2005 .

[36]  W. Press,et al.  Numerical Recipes: The Art of Scientific Computing , 1987 .

[37]  Stephen E. Chick,et al.  Input Distribution Selection for Simulation Experiments: Accounting for Input Uncertainty , 2001, Oper. Res..

[38]  N. L. Johnson,et al.  Systems of frequency curves generated by methods of translation. , 1949, Biometrika.

[39]  James R. Wilson,et al.  Using univariate Be´zier distributions to model simulation input processes , 1993, WSC '93.

[40]  James R. Wilson,et al.  Analysis of Space Shuttle ground operations , 1982 .

[41]  I. D. Hill,et al.  Fitting Johnson Curves by Moments , 1976 .

[42]  Janet S. Reust,et al.  Organ transplantation policy evaluation , 1995, Winter Simulation Conference Proceedings, 1995..

[43]  James R. Wilson,et al.  Visual interactive fitting of bounded Johnson distributions , 1989, Simul..

[44]  James R. Wilson,et al.  Clinic: correlated inputs in an automotive paint shop fire risk simulation , 2007, 2007 Winter Simulation Conference.

[45]  Faker Zouaoui,et al.  Accounting for input-model and input-parameter uncertainties in simulation , 2004 .

[46]  Averill M. Law,et al.  Simulation Modeling and Analysis , 1982 .

[47]  Donald J. Leo,et al.  Application of Rotational Isomeric State Theory to Ionic Polymer Stiffness Predictions , 2005 .

[48]  Stephen E. Chick.  Steps to implement Bayesian input distribution selection , 1999, WSC '99.

[49]  Simaan M. AbouRizk,et al.  Visual Interactive Fitting of Beta Distributions , 1991 .

[50]  Nitis Mukhopadhyay.  A discussion on ‘Detection of intrusions in information systems by sequential change-point methods’ by Tartakovsky, Rozovskii, Blažek, and Kim , 2006 .

[51]  Barry L. Nelson,et al.  Numerical Methods for Fitting and Simulating Autoregressive-to-Anything Processes , 1998, INFORMS J. Comput..

[52]  James R. Wilson,et al.  Accounting for parameter uncertainty in simulation input modeling , 2001, Proceeding of the 2001 Winter Simulation Conference (Cat. No.01CH37304).

[53]  R. Strawderman.  Continuous Multivariate Distributions, Volume 1: Models and Applications , 2001 .

[54]  Mark E. Johnson.  Multivariate Statistical Simulation: Johnson/Multivariate , 1987 .

[55]  J. E. Glynn,et al.  Numerical Recipes: The Art of Scientific Computing , 1989 .

[56]  James R. Wilson,et al.  An Automated Multiresolution Procedure for Modeling Complex Arrival Processes , 2006, INFORMS J. Comput..

[57]  Sarah E. Taranto,et al.  An update on a successful simulation project: the UNOS Liver Allocation Model , 2000, Winter simulation conference : proceedings.

[58]  James R. Wilson,et al.  Smooth flexible models of nonhomogeneous poisson processes using one or more process realizations , 2008, 2008 Winter Simulation Conference.

[59]  B. Melamed,et al.  The transition and autocorrelation structure of tes processes , 1992 .