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ABSTRACT
Techniques are presented for modeling and generating the univariate probabilistic input processes that drive many simulation experiments. Emphasis is on the generalized beta distribution family, the Johnson translation system of distributions, and the Bézier distribution family. Also discussed are nonparametric techniques for modeling and simulating time-dependent arrival streams using nonhomogeneous Poisson processes. Public-domain software implementations and current applications are presented for each input-modeling technique. Many of the references include live hyperlinks providing online access to the referenced material.
REFERENCES
Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.
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AbouRizk, S. M., D. W. Halpin, and J. R. Wilson. 1991. Visual interactive fitting of beta distributions. Journal of Construction Engineering and Management 117 (4): 589--605. Available online via <ftp.ncsu.edu/pub/eos/pub/jwilson/abourizk91jcem.pdf> {accessed July 13, 2007}.
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AbouRizk, S. M., D. W. Halpin, and J. R. Wilson. 1994. Fitting beta distributions based on sample data. Journal of Construction Engineering and Management 120 (2): 288--305. Available online via <ftp.ncsu.edu/pub/eos/pub/jwilson/abourizk94jcem.pdf> {accessed July 29, 2007}.
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Alexopoulos, C., D. Goldsman, J. Fontanesi, D. Kopald, and J. R. Wilson. 2008. Modeling patient arrival times in community clinics. Omega 36:33--43. Available online via <ftp.ncsu.edu/pub/eos/pub/jwilson/alex08omega.pdf> {accessed July 13, 2007}.
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D. J. DeBrota , R. S. Dittus , J. J. Swain , S. D. Roberts , J. R. Wilson, Modeling input processes with Johnson distributions, Proceedings of the 21st conference on Winter simulation, p.308-318, December 04-06, 1989, Washington, D.C., United States
[doi> 10.1145/76738.76777]
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DeBrota, D. J., R. S. Dittus, S. D. Roberts, and J. R. Wilson. 1989b. Visual interactive fitting of bounded Johnson distributions. SIMULATION 52 (5): 199--205. Available online via <ftp.ncsu.edu/pub/eos/pub/jwilson/debrota89sim.pdf> {accessed July 13, 2007}.
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Hill, I. D, R. Hill, and R. L. Holder. 1976. Algorithm AS99: Fitting Johnson curves by moments. Applied Statistics 25 (2): 180--189.
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Johnson, N. L. 1949. Systems of frequency curves generated by methods of translation. Biometrika 36:149--176.
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Kim, S.-H., and J. R. Wilson. 2006. A discussion on 'Detection of intrusions in information systems by sequential change-point methods' by Tartakovsky, Rozovskii, Blažek, and Kim. Statistical Methodology 3:315--319. Available online via <ftp.ncsu.edu/pub/eos/pub/jwilson/kim06statmeth.pdf> {accessed July 13, 2007}.
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Michael E. Kuhl , Halim Damerdji , James R. Wilson, Estimating and simulating Poisson processes with trends or asymmetric cyclic effects, Proceedings of the 29th conference on Winter simulation, p.287-295, December 07-10, 1997, Atlanta, Georgia, United States
[doi> 10.1145/268437.268493]
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Michael E. Kuhl , Emily K. Lada , Natalie M. Steiger , Mary Ann Wagner , James R. Wilson, Introduction to modeling and generating probabilistic input processes for simulation, Proceedings of the 38th conference on Winter simulation, December 03-06, 2006, Monterey, California
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Kuhl, M. E., and J. R. Wilson. 2000. Least squares estimation of nonhomogeneous Poisson processes. Journal of Statistical Computation and Simulation 67:75--108. Available online via <ftp.ncsu.edu/pub/eos/pub/jwilson/kuh100jscs.pdf> {accessed July 13, 2007}.
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Kuhl, M. E., and J. R. Wilson. 2001. Modeling and simulating Poisson processes having trends or non-trigonometric cyclic effects. European Journal of Operational Research 133 (3): 566--582. Available online via <ftp.ncsu.edu/pub/eos/pub/jwilson/kuhl0lejor.pdf> {accessed July 13, 2007}.
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Kuhl, M. E., J. R. Wilson, and M. A. Johnson. 1997. Estimating and simulating Poisson processes having trends or multiple periodicities. IIE Transactions 29 (3): 201--211. Available online via <ftp.ncsu.edu/pub/eos/pub/jwilson/kuhl97iie.pdf> {accessed July 13, 2007}.
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Lee, S., J. R. Wilson, M. M. Crawford. 1991. Modeling and simulation of a nonhomogeneous Poisson process having cyclic behavior. Communications in Statistics---Simulation 20:777--809. Available online via <ftp.ncsu.edu/pub/eos/pub/jwilson/lee91.pdf> {accessed July 13, 2007}.
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Leemis, L. M. 2004. Nonparametric estimation and variate generation for a nonhomogeneous Poisson process from event count data. IIE Transactions 36 (12): 1155--1160.
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Matthews, J. L., E. K. Lada, L. M. Weiland, R. C. Smith, and D. J. Leo. 2006. Monte Carlo simulation of a solvated ionic polymer with cluster morphology. Smart Materials and Structures 15 (1): 187--199. Available online via <ftp.ncsu.edu/pub/eos/pub/jwilson/matthews06sms.pdf> {accessed July 13, 2007}.
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McBride, W. J., and C. W. McClelland. 1967. PERT and the beta distribution. IEEE Transactions on Engineering Management EM-14 (4): 166--169.
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Park, Y. 2005. A statistical process control approach for network intrusion detection. Ph.D. thesis, School of Industrial and Systems Engineering, Atlanta, Georgia. Available online via <hdl.handle.net/1853/6835> {accessed July 13, 2007}.
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Pearlswig, D. M. 1995. Simulation modeling applied to the single pot processing of effervescent tablets. Master's thesis, Integrated Manufacturing Systems Engineering Institute, North Carolina State University, Raleigh, North Carolina. Available online via <ftp.ncsu.edu/pub/eos/pub/jwilson/pearlswig95.pdf> {accessed July 14, 2007}.
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A. Alan B. Pritsker , David L. Martin , Janet S. Reust , Mary Ann Wagner , O. Patrick Daily , Ann M. Harper , Erick B. Edwards , Leah E. Bennett , James R. Wilson , Michael E. Kuhl , John P. Roberts , Margaret D. Allen , James F. Burdick, Organ transplantation policy evaluation, Proceedings of the 27th conference on Winter simulation, p.1314-1323, December 03-06, 1995, Arlington, Virginia, United States
[doi> 10.1145/224401.224813]
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Swain, J. J., S. Venkatraman, and J. R. Wilson. 1988. Least-squares estimation of distribution functions in Johnson's translation system. Journal of Statistical Computation and Simulation 29:271--297. Available online via <ftp.ncsu.edu/pub/eos/pub/jwilson/jnsn88jscs.pdf> {accessed July 13, 2007}.
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Wagner, M. A. F., and J. R. Wilson. 1996a. Using univariate Bézier distributions to model simulation input processes. IIE Transactions 28 (9): 699--711. Available online as <ftp.ncsu.edu/pub/eos/pub/jwilson/wagner96iie.pdf> {accessed July 13, 2007}.
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Weiland, L. M., E. K. Lada, R. C. Smith, and D. J. Leo. 2005. Application of rotational isomeric state theory to ionic polymer stiffness predictions. Journal of Materials Research 20 (9): 2443--2455. Available online via <ftp.ncsu.edu/pub/eos/pub/jwilson/weiland05jmr.pdf> {accessed July 13, 2007}.
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Zouaoui, F., and J. R. Wilson. 2003. Accounting for parameter uncertainty in simulation input modeling. IIE Transactions 35 (3): 781--792. Available online via <ftp.ncsu.edu/pub/eos/pub/jwilson/zouaoui03iie.pdf> {accessed July 13, 2007}.
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Zouaoui, F., and J. R. Wilson. 2004. Accounting for input-model and input-parameter uncertainties in simulation. IIE Transactions 36 (11): 1135--1151. Available online via <ftp.ncsu.edu/pub/eos/pub/jwilson/zouaoui04iie.pdf> {accessed July 13, 2007}.
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CITED BY
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Debra Elkins , A. Christine LaFleur , Earnest Foster , Jeffrey Tew , Bahar Biller , James R. Wilson, Clinic: correlated inputs in an automotive paint shop fire risk simulation, Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come, December 09-12, 2007, Washington D.C.
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