Introduction to simulation input modeling

In this tutorial we first review introductory techniques for simulation input modeling. We then identify situations in which the standard input models fail to adequately represent the available input data. In particular, we consider the cases where the input process may (i) have marginal characteristics that are not captured by standard distributions; (ii) exhibit dependence; and (iii) change over time. For case (i), we review flexible distribution systems, while we review two widely used multivariate input models for case (ii). Finally, we review nonhomogeneous Poisson processes for the last case. We focus our discussion around continuous random variables; however, when appropriate references are provided for discrete random variables. Detailed examples will be illustrated in the tutorial presentation.

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

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

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

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

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

[6]  Linus Schrage,et al.  A guide to simulation , 1983 .

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

[8]  Wolfgang Härdle,et al.  Applied Multivariate Statistical Analysis: third edition , 2006 .

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

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

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

[12]  Barry L. Nelson,et al.  Answers to the top ten input modeling questions , 2002, Proceedings of the Winter Simulation Conference.

[13]  T. Sargent,et al.  The multivariate normal distribution , 1989 .

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

[15]  Barry L. Nelson,et al.  Input modeling tools for complex problems , 1998, 1998 Winter Simulation Conference. Proceedings (Cat. No.98CH36274).

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

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

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

[19]  Bahar Biller,et al.  Chapter 5 Multivariate Input Processes , 2006, Simulation.

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

[21]  Emily K. Lada,et al.  Multivariate Input Models for Stochastic Simulation , 2005 .

[22]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[23]  Paul Bratley,et al.  A guide to simulation (2nd ed.) , 1986 .

[24]  S. Vincent Input Data Analysis , 2007 .

[25]  J. Banks,et al.  Discrete-Event System Simulation , 1995 .

[26]  Paul Bratley,et al.  A guide to simulation , 1983 .

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

[28]  Lawrence Leemis,et al.  Building credible input models , 2004, Proceedings of the 2004 Winter Simulation Conference, 2004..

[29]  Richard A. Johnson,et al.  Applied Multivariate Statistical Analysis , 1983 .

[30]  William H. Press,et al.  Numerical Recipes 3rd Edition: The Art of Scientific Computing , 2007 .

[31]  S. Shapiro,et al.  THE JOHNSON SYSTEM: SELECTION AND PARAMETER ESTIMATION , 1980 .

[32]  K. Pearson Contributions to the Mathematical Theory of Evolution. II. Skew Variation in Homogeneous Material , 1895 .

[33]  Stuart Jay Deutsch,et al.  A Versatile Four Parameter Family of Probability Distributions Suitable for Simulation , 1977 .

[34]  Mark E. Johnson,et al.  Multivariate Statistical Simulation , 1989, International Encyclopedia of Statistical Science.

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

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

[37]  K. Pearson Contributions to the Mathematical Theory of Evolution , 1894 .