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Simulation-based response surface computation in the presence of monotonicity

Published: 03 December 2006 Publication History

Abstract

In many stochastic models, it is known that the response surface corresponding to a particular performance measure is monotone in the underlying parameter. For example, the steady-state mean waiting time for customers in a single server queue is known to be monotone in the service rate. In other contexts, the simulator may believe, on the basis of intuition, that the response surface is monotone. This paper describes an appropriate methodology for incorporating such monotonicity constraints into one's response surface estimator.

References

[1]
Asmussen, S., and P. W. Glynn. 2007. Stochastic Simulation: Algorithms and Analysis. Springer-Verlag, to appear.
[2]
Ayer, M., H. D. Brunk, G. M. Ewing, W. T. Reid, and E. Silverman. 1955. An empirical distribution function for sampling with incomplete information. Annals of Mathematical Statistics 26:641--647.
[3]
Barlow, R. E., D. J. Bartholomew, J. M. Bremmer, and H. D. Brunk. 1972. Statistical inference under order restrictions. New York:Wiley.
[4]
Bauerle, N. 1997. Monotonicity results for MR/GI/1 queues. Journal of Applied Probability 34(2):514--524.
[5]
Bauerle, N., and T. Rolski. 1998. A monotonicity result for the workload in Markov-modulated queues. Journal of Applied Probability 35:741--747.
[6]
Berger, A. W., and W. Whitt. 1992. Comparison of multiserver queues with finite waiting rooms. Stochastic Models 8(4):719--732.
[7]
Bondi, A. B., and W. Whitt. 1986. The influence of service-time variability in a closed network of queues. Performance Evaluation 6:219--234.
[8]
Bratley, P., B. L. Fox, and L. E. Schrage. 1983. A guide to simulation. New York: Springer Verlag.
[9]
Brunk, H. D. 1958. On the estimation of parameters restricted by inequalities. Annals of Mathematical Statistics. 29:437--454.
[10]
Brunk, H. D. 1970. Estimation of isotonic regression. Nonparametric techniques in statistical inference. Cambridge, 177--195.
[11]
Budka, K. C., and D. D. Yao. 1990. Monotonicity and convexity properties of rate control throttles. In Proceedings of 29th IEEE conference on Decision and Control, 883--884.
[12]
Chang, C. S., X. Chao, and M. Pinedo. 1990. Monotonicity results for queues with doubly stochastic Poisson arrivals: Ross' conjecture. Advances in Applied Probability 23:210--228.
[13]
Chang, C., X. Chao, M. Pinedo, and J. Shanthikumar. 1991. Stochastic convexity for multidimensional processes and its applications. IEEE Transactions on Automatic Control 36(12):1347--1355.
[14]
Frank, M., and P. Wolfe. 1956. An algorithm for quadratic programming. Naval Research Logistics Quarterly 3:95--110.
[15]
Gill, P. E., W. Murray, and M. A. Saunders. 2006. User's guide for SQOPT version 7: software for large-scale linear and quadratic programming. Available online via <http://www.cam.ucsd.edu/~peg/sqdoc7.pdf> {accessed August 7, 2006}.
[16]
Jean-Marie, A., and L. Gun. 1993. Parallel queues with resequencing. Journal of the ACM 40(6):1188--1208.
[17]
Law, A. M., and W. D. Kelton. 2000. Simulation modelling and analysis. McGraw-Hill, Inc.
[18]
Lee, C. C. 1981. The Quadratic loss of isotonic regression under normality. Annals of Statistics 9(3):686--688.
[19]
Shaked, M., and J. G. Shanthikumar. 1988. Stochastic convexity and its applications. Advances in Applied Probability 20:427--446.
[20]
Shen, A., and N. K. Vereshchagin. 2002. Basic set theory. American Mathematical Society. Student mathematical library, Vol. 17.
[21]
Van Oyen, M. 1997. Monotonicity of optimal performance measures for polling systems. Probability in Engineering and Information Science 11(2):219--228.
[22]
Weber, R. R. 1983. A note on waiting times in single server queues. Operations Research 31:950--951.
[23]
Whitt, W. 1983. Comparison conjectures about the M/G/s queue. Operations Research Letters 2(5): 203--208.
[24]
Whitt, W. 1989. Planning queueing simulations. Management Science 35(11):1341--1366.
[25]
Ziya, S., H. Ayhan, and R. D. Foley. 2004. A monotonicity result for the blocking probability in a G/GI/c/m queueing system. Available online via <http://www2.isye.gatech.edu/people/faculty/Hayriye_Ayhan/block-note.pdf> {accessed August 7, 2006}.

Cited By

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  • (2015)Monotonic response surface estimation by constrained coefficientsProceedings of the 2015 Winter Simulation Conference10.5555/2888619.2888697(689-700)Online publication date: 6-Dec-2015
  • (2013)Density estimation of simulation output using exponential EPI-splinesProceedings of the 2013 Winter Simulation Conference: Simulation: Making Decisions in a Complex World10.5555/2675983.2676081(755-765)Online publication date: 8-Dec-2013
  • (2012)Consistency of Multidimensional Convex RegressionOperations Research10.1287/opre.1110.100760:1(196-208)Online publication date: 1-Jan-2012
  • Show More Cited By

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Published In

cover image ACM Conferences
WSC '06: Proceedings of the 38th conference on Winter simulation
December 2006
2429 pages
ISBN:1424405017

Sponsors

  • IIE: Institute of Industrial Engineers
  • ASA: American Statistical Association
  • IEICE ESS: Institute of Electronics, Information and Communication Engineers, Engineering Sciences Society
  • IEEE-CS\DATC: The IEEE Computer Society
  • SIGSIM: ACM Special Interest Group on Simulation and Modeling
  • NIST: National Institute of Standards and Technology
  • (SCS): The Society for Modeling and Simulation International
  • INFORMS-CS: Institute for Operations Research and the Management Sciences-College on Simulation

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Winter Simulation Conference

Publication History

Published: 03 December 2006

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WSC06
Sponsor:
  • IIE
  • ASA
  • IEICE ESS
  • IEEE-CS\DATC
  • SIGSIM
  • NIST
  • (SCS)
  • INFORMS-CS
WSC06: Winter Simulation Conference 2006
December 3 - 6, 2006
California, Monterey

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WSC '06 Paper Acceptance Rate 177 of 252 submissions, 70%;
Overall Acceptance Rate 3,413 of 5,075 submissions, 67%

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Cited By

View all
  • (2015)Monotonic response surface estimation by constrained coefficientsProceedings of the 2015 Winter Simulation Conference10.5555/2888619.2888697(689-700)Online publication date: 6-Dec-2015
  • (2013)Density estimation of simulation output using exponential EPI-splinesProceedings of the 2013 Winter Simulation Conference: Simulation: Making Decisions in a Complex World10.5555/2675983.2676081(755-765)Online publication date: 8-Dec-2013
  • (2012)Consistency of Multidimensional Convex RegressionOperations Research10.1287/opre.1110.100760:1(196-208)Online publication date: 1-Jan-2012
  • (2010)Response surface computation via simulation in the presence of convexityProceedings of the Winter Simulation Conference10.5555/2433508.2433660(1246-1254)Online publication date: 5-Dec-2010

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