Skip to main content
SpringerLink
Log in
Book cover

Foundations and Methods of Stochastic Simulation pp 1–6Cite as

Why Do We Simulate?

  • Chapter
  • First Online:

  • 5432 Accesses

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 187))

Abstract

Stochastic simulation is a method for analyzing the performance of systems whose behavior depends on the interaction of random processes, processes that can be fully characterized by probability models. Stochastic simulation is a companion to mathematical and numerical analysis of stochastic models (e.g., Nelson 1995), and is often employed when the desired performance measures are mathematically intractable or there is no numerical approximation whose error can be bounded. Computers make stochastic simulation practical, but the method can be described independently of any computer implementation, which is what we do here.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Albright, S. C. (2007). VBA for modelers: Developing decision support systems using Microsoft Excel (2nd ed.). Belmont: Thompson Higher Eduction.

    Google Scholar 

  • Alexopoulos, C. (2006). Statistical estimation in computer simulation. In S. G. Henderson & B. L. Nelson (Eds.), Handbooks in operations research and management science: Simulation. New York: North-Holland.

    Google Scholar 

  • Andradóttir, S. (1999). Accelerating the convergence of random search methods for discrete stochastic optimization. ACM Transactions on Modeling and Computer Simulation, 9, 349–380.

    Article  Google Scholar 

  • Andradóttir, S. (2006a). An overview of simulation optimization via random search. In S. G. Henderson & B. L. Nelson (Eds.), Handbooks in operations research and management science: Simulation. New York: North-Holland.

    Google Scholar 

  • Andradóttir, S. (2006b). Simulation optimization with countably infinite feasible regions: Efficiency and convergence. ACM Transactions on Modeling and Computer Simulation, 16, 357–374.

    Article  Google Scholar 

  • Andradóttir, S., & Kim, S. (2010). Fully sequential procedures for comparing constrained systems via simulation. Naval Research Logistics, 57, 403–421.

    Article  Google Scholar 

  • Ankenman, B. E., & Nelson, B. L. (2012, in press). A quick assessment of input uncertainty. Proceedings of the 2012 Winter Simulation Conference, Berlin.

    Google Scholar 

  • Asmussen, S. & Glynn, P. W., (2007). Stochastic simulation: Algorithms and analysis. New York: Springer.

    Google Scholar 

  • Batur, D., & Kim, S. (2010). Finding feasible systems in the presence of constraints on multiple performance measures. ACM Transactions on Modeling and Computer Simulation, 20, 13:1–13:26.

    Google Scholar 

  • Bechhofer, R. E., Santner, T. J., & Goldsman, D. (1995). Design and analysis of experiments for statistical selection, screening and multiple comparisons. New York: Wiley.

    Google Scholar 

  • Biller, B., & Corlu, C. G. (2012). Copula-based multivariate input modeling. Surveys in Operations Research and Management Science, 17, 69–84.

    Article  Google Scholar 

  • Biller, B., & Ghosh, S. (2006). Multivariate input processes. In S. G. Henderson & B. L. Nelson (Eds.), Handbooks in operations research and management science: Simulation. New York: North-Holland.

    Google Scholar 

  • Biller, B., & Nelson, B. L. (2003). Modeling and generating multivariate time-series input processes using a vector autoregressive technique. ACM Transactions on Modeling and Computer Simulation, 13, 211–237.

    Article  Google Scholar 

  • Biller, B., & Nelson, B. L. (2005). Fitting time series input processes for simulation. Operations Research, 53, 549–559.

    Article  Google Scholar 

  • Billingsley, P. (1995). Probability and measure (3rd ed.). New York: Wiley.

    Google Scholar 

  • Boesel, J., Nelson, B. L., & Kim, S. (2003). Using ranking and selection to “clean up” after simulation optimization. Operations Research, 51, 814–825.

    Article  Google Scholar 

  • Bratley, P., Fox, B. L., & Schrage, L. E. (1987). A guide to simulation (2nd ed.). New York: Springer.

    Book  Google Scholar 

  • Burt, J. M., & Garman, M. B. (1971). Conditional Monte Carlo: A simulation technique for stochastic network analysis. Management Science, 19, 207–217.

    Article  Google Scholar 

  • Cario, M. C. & Nelson, B. L. (1998). Numerical methods for fitting and simulating autoregressive-to-anything processes. INFORMS Journal on Computing, 10, 72–81.

    Article  Google Scholar 

  • Cash, C., Nelson, B. L., Long, J., Dippold, D., & Pollard, W. (1992). Evaluation of tests for initial-condition bias. Proceedings of the 1992 Winter Simulation Conference (pp. 577–585). Piscataway, New Jersey: IEEE.

    Google Scholar 

  • Chatfield, C. (2004). The analysis of time series: An introduction (6th ed.). Boca Raton: Chapman & Hall/CRC.

    Google Scholar 

  • Chen, H. (2001). Initialization for NORTA: Generation of random vectors with specified marginals and correlations. INFORMS Journal on Computing, 13, 312–331.

    Article  Google Scholar 

  • Chow, Y. S., & Robbins, H. (1965). On the asymptotic theory of fixed-width sequential confidence intervals for the mean. The Annals of Mathematical Statistics, 36, 457–462.

    Article  Google Scholar 

  • Devroye, L. (1986). Non-uniform random variate generation. New York: Springer.

    Google Scholar 

  • Devroye, L. (2006). Nonuniform random variate generation. In S. G. Henderson & B. L. Nelson (Eds.), Handbooks in operations research and management science: Simulation. New York: North-Holland.

    Google Scholar 

  • Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. Boca Raton: Chapman & Hall/CRC.

    Google Scholar 

  • Elizandro, D., & Taha, H. (2008). Simulation of industrial systems: Discrete event simulation using Excel/VBA. New York: Auerbach Publications.

    Google Scholar 

  • Frazier, P. I. (2010). Decision-theoretic foundations of simulation optimization. In J. J. Cochran (Ed.), Wiley encyclopedia of operations research and management sciences. New York: Wiley.

    Google Scholar 

  • Fu, M. C. (2006). Gradient estimation. In S. G. Henderson & B. L. Nelson (Eds.), Handbooks in operations research and management science: Simulation. New York: North-Holland.

    Google Scholar 

  • Gerhardt, I., & Nelson, B. L. (2009). Transforming renewal processes for simulation of nonstationary arrival processes. INFORMS Journal on Computing, 21, 630–640.

    Article  Google Scholar 

  • Ghosh, S., & Henderson, S. G. (2002). Chessboard distributions and random vectors with specified marginals and covariance matrix. Operations Research, 50, 820–834.

    Article  Google Scholar 

  • Glasserman, P. (2004). Monte Carlo methods in financial engineering. New York: Springer.

    Google Scholar 

  • Glasserman, P., & Yao, D. D. (1992). Some guidelines and guarantees for common random numbers. Management Science, 38, 884–908.

    Article  Google Scholar 

  • Glynn, P. W. (2006). Simulation algorithms for regenerative processes. In S. G. Henderson & B. L. Nelson (Eds.), Handbooks in operations research and management science: Simulation. New York: North-Holland.

    Google Scholar 

  • Glynn, P. W., & Whitt, W. (1992). The asymptotic validity of sequential stopping rules for stochastic simulations. The Annals of Applied Probability, 2, 180–198.

    Article  Google Scholar 

  • Goldsman, D., Kim, S., Marshall, S. W., & Nelson, B. L. (2002). Ranking and selection for steady-state simulation: Procedures and perspectives. INFORMS Journal on Computing, 14, 2–19.

    Article  Google Scholar 

  • Goldsman, D., & Nelson, B. L. (1998). Comparing systems via simulation. In J. Banks (Ed.), Handbook of simulation (pp. 273–306). New York: Wiley.

    Chapter  Google Scholar 

  • Goldsman, D., & Nelson, B. L. (2006). Correlation-based methods for output analysis. In S. G. Henderson & B. L. Nelson (Eds.), Handbooks in operations research and management science: Simulation. New York: North-Holland.

    Google Scholar 

  • Gross, D., Shortle, J. F., Thompson, J. M., & Harris, C. M. (2008). Fundamentals of queueing theory (4th ed.). New York: Wiley.

    Google Scholar 

  • Haas, P. J. (2002). Stochastic petri nets: Modeling, stability, simulation. New York: Springer.

    Google Scholar 

  • Henderson, S. G. (2003). Estimation of nonhomogeneous Poisson processes from aggregated data. Operations Research Letters, 31, 375–382.

    Article  Google Scholar 

  • Henderson, S. G. (2006). Mathematics for simulation. In S. G. Henderson & B. L. Nelson (Eds.), Handbooks in operations research and management science: Simulation. New York: North-Holland.

    Google Scholar 

  • Henderson, S. G., & Nelson, B. L. (2006). Stochastic computer simulation. In S. G. Henderson & B. L. Nelson (Eds.), Handbooks in operations research and management science: Simulation. New York: North-Holland.

    Google Scholar 

  • Hill, R. R., & Reilly, C. H. (2000). The effects of coefficient correlation structure in two-dimensional knapsack problems on solution procedure performance. Management Science, 46, 302–317.

    Article  Google Scholar 

  • Hong, L. J., & Nelson, B. L. (2007a). Selecting the best system when systems are revealed sequentially. IIE Transactions, 39, 723–734.

    Article  Google Scholar 

  • Hong, L. J., & Nelson, B. L. (2007b). A framework for locally convergent random-search algorithms for discrete optimization via simulation. ACM Transactions on Modeling and Computer Simulation, 17, 19/1-19/22.

    Google Scholar 

  • Hörmann, W. (1993). The transformed rejection method for generating Poisson random variables. Insurance: Mathematics and Economics, 12, 39–45.

    Article  Google Scholar 

  • Iravani, S. M. R., & Krishnamurthy, V. (2007). Workforce agility in repair and maintenance environments. Manufacturing and Service Operations Management, 9, 168–184.

    Article  Google Scholar 

  • Iravani, S. M., Van Oyen, M. P., & Sims, K. T. (2005). Structural flexibility: A new perspective on the design of manufacturing and service operations. Management Science, 51, 151–166.

    Article  Google Scholar 

  • Johnson, M. E. (1987). Multivariate statistical simulation. New York: Wiley.

    Google Scholar 

  • Johnson, N. L., Kemp, A. W., & Kotz, S. (2005). Univariate discrete distributions (3rd ed.). New York: Wiley.

    Book  Google Scholar 

  • Johnson, N. L., Kotz, S., & Balakrishnan, N. (1994). Continuous univariate distributions (2nd ed., Vol. 1). New York: Wiley.

    Google Scholar 

  • Johnson, N. L., Kotz, S., & Balakrishnan, N. (1995). Continuous univariate distributions (2nd ed., Vol. 2). New York: Wiley.

    Google Scholar 

  • Johnson, N. L., Kotz, S., & Balakrishnan, N. (1997). Discrete multivariate distributions. New York: Wiley.

    Google Scholar 

  • Kachitvichyanukul, V., & Schmeiser, B. (1990). Noninverse correlation induction: Guidelines for algorithm development. Journal of Computational and Applied Mathematics, 31, 173–180.

    Article  Google Scholar 

  • Karian, A. Z., & Dudewicz, E. J. (2000). Fitting statistical distributions: The generalized lambda distribution and generalized bootstrap methods. New York: CRC.

    Book  Google Scholar 

  • Karlin, S., & Taylor, H. M. (1975). A first course in stochastic processes (2nd ed.). New York: Academic.

    Google Scholar 

  • Kelton, W. D. (2006). Implementing representations of uncertainty. In S. G. Henderson & B. L. Nelson (Eds.), Handbooks in operations research and management science: Simulation. New York: North-Holland.

    Google Scholar 

  • Kelton, W. D., Smith, J. S., & Sturrock, D. T. (2011). Simio and simulation: Modeling, analysis and applications (2nd ed.). New York: McGraw-Hill.

    Google Scholar 

  • Kim, S., & Nelson, B. L. (2001). A fully sequential procedure for indifference-zone selection in simulation. ACM Transactions on Modeling and Computer Simulation, 11, 251–273.

    Article  Google Scholar 

  • Kim, S., & Nelson, B. L. (2006). Selecting the best system. In S. G. Henderson & B. L. Nelson (Eds.), Handbooks in operations research and management science: Simulation. New York: North-Holland.

    Google Scholar 

  • Knuth, D. E. (1998). The art of computer programming, Vol. 2: Seminumerical algorithms (3rd ed.). Boston: Addison-Wesley.

    Google Scholar 

  • Kotz, S., Balakrishnan, N., & Johnson, N. L. (2000). Continuous multivariate distributions, Vol. 1, models and applications (2nd ed.). New York: Wiley.

    Book  Google Scholar 

  • Kulkarni, V. G. (1995). Modeling and analysis of stochastic systems. London: Chapman & Hall.

    Google Scholar 

  • Lakhany, A., & Mausser, H. (2000). Estimating the parameters of the generalized lambda distribution. ALGO Research Quarterly, 3, 47–58.

    Google Scholar 

  • Law, A. M. (2007). Simulation modeling and analysis (4th ed.). New York: McGraw-Hill.

    Google Scholar 

  • Law, A. M., & Kelton, W. D. (2000). Simulation modeling and analysis (3rd ed.). New York: McGraw-Hill.

    Google Scholar 

  • L’Ecuyer, P. (1988). Efficient and portable combined random number generators. Communications of the ACM, 31, 742–749.

    Article  Google Scholar 

  • L’Ecuyer, P. (1990). A unified view of IPA, SF, and LR gradient estimation techniques. Management Science, 36, 1364–1383.

    Article  Google Scholar 

  • L’Ecuyer, P. (1999). Good parameters and implementations for combined multiple recursive random number generators. Operations Research, 47, 159–164.

    Article  Google Scholar 

  • L’Ecuyer, P. (2006). Uniform random number generation. In S. G. Henderson & B. L. Nelson (Eds.), Handbooks in operations research and management science: Simulation. New York: North-Holland.

    Google Scholar 

  • L’Ecuyer, P., & Simard, R. (2001). On the performance of birthday spacings tests for certain families of random number generators. Mathematics and Computers in Simulation, 55, 131–137.

    Article  Google Scholar 

  • L’Ecuyer, P., Simard, R., Chen, E. J., & Kelton, W. D. (2002). An object-oriented random-number package with many long streams and substreams. Operations Research, 50, 1073-1075.

    Article  Google Scholar 

  • Lee, S., Wilson, J. R., & Crawford, M. M. (1991). Modeling and simulation of a nonhomogeneous Poisson process having cyclic behavior. Communications in Statistics-Simulation and Computation, 20, 777–809.

    Article  Google Scholar 

  • Leemis, L. M. (1991). Nonparameteric estimation of the cumulative intensity function for a nonhomogeneous Poisson process. Management Science, 37, 886–900.

    Article  Google Scholar 

  • Leemis, L. M. (2006). Arrival processes, random lifetimes and random objects. In S. G. Henderson & B. L. Nelson (Eds.), Handbooks in operations research and management science: Simulation. New York: North-Holland.

    Google Scholar 

  • Leemis, L. M., & McQueston, J. T. (2008). Univariate distribution relationships. The American Statistician, 62, 45–53.

    Article  Google Scholar 

  • Lehmann, E. L. (2010). Elements of large-sample theory. New York: Springer.

    Google Scholar 

  • Lewis, T. A. (1981). Confidence intervals for a binomial parameter after observing no successes. The American Statistician, 35, 154.

    Google Scholar 

  • Marse, K., & Roberts, S. D. (1983). Implementing a portable FORTRAN uniform (0,1) generator. Simulation, 41, 135–139.

    Article  Google Scholar 

  • Montgomery, D. C. (2009). Design and analysis of experiments (7th ed.). New York: Wiley.

    Google Scholar 

  • Nádas, A. (1969). An extension of a theorem of Chow and Robbins on sequential confidence intervals for the mean. The Annals of Mathematical Statistics, 40, 667–671.

    Article  Google Scholar 

  • Nelson, B. L. (1990). Control-variate remedies. Operations Research, 38, 974–992.

    Article  Google Scholar 

  • Nelson, B. L. (1995). Stochastic modeling: Analysis and simulation. Mineola: Dover Publications, Inc.

    Google Scholar 

  • Nelson, B. L. (2008). The MORE plot: Displaying measures of risk and error from simulation output. Proceedings of the 2008 Winter Simulation Conference (pp. 413–416). Piscataway, New Jersey: IEEE.

    Google Scholar 

  • Nelson, B. L., & Taaffe, M. R. (2004). The Ph t  ∕ Ph t  ∕ ∞ queueing system: Part I: The single node. INFORMS Journal on Computing, 16, 266–274.

    Article  Google Scholar 

  • Nelson, B. L., Swann, J., Goldsman, D., & Song, W. (2001). Simple procedures for selecting the best simulated system when the number of alternatives is large. Operations Research, 49, 950–963.

    Article  Google Scholar 

  • Pasupathy, R., & Schmeiser, B. (2010). The initial transient in steady-state point estimation: Contexts, a bibliography, the MSE criterion, and the MSER statistic. Proceedings of the 2010 Winter Simulation Conference (pp. 184–197). Piscataway, New Jersey: IEEE.

    Google Scholar 

  • Sargent, R. G. (2011). Verification and validation of simulation models. Proceedings of the 2011 Winter Simulation Conference (pp. 183–198). Piscataway, New Jersey: IEEE.

    Google Scholar 

  • Schmeiser, B. (1982). Batch size effects in the analysis of simulation output. Operations Research, 30, 556–568.

    Article  Google Scholar 

  • Schruben, L. (1982). Detecting initialization bias in simulation output. Operations Research, 30, 569–590.

    Article  Google Scholar 

  • Schruben, L., Singh, H., & Tierney, L. (1983). Optimal tests for initialization bias in simulation output. Operations Research, 31, 1167–1178.

    Article  Google Scholar 

  • Shapiro, A., Dentcheva, D., & Ruszczyński, A. (2009). Lectures on stochastic programming: Modeling and theory. Philadelphia: Society for Industrial and Applied Mathematics.

    Book  Google Scholar 

  • Shechter, S. M., Schaefer, A. J., Braithwaite, R. S., & Roberts, M. S. (2006). Increasing the efficiency of Monte Carlo cohort simulations with variance reduction techniques. Medical Decision Making, 26, 550–553.

    Article  Google Scholar 

  • Snell, M., & Schruben, L. (1985). Weighting simulation data to reduce initialization effects. IIE Transactions, 17, 354–363.

    Article  Google Scholar 

  • Steiger, N. M., & Wilson, J. R. (2001). Convergence properties of the batch means method for simulation output analysis. INFORMS Journal on Computing, 13, 277–293.

    Article  Google Scholar 

  • Stigler, S. M. (1986). The history of statistics: The measurement of uncertainty before 1900. Cambridge, MA: Belknap.

    Google Scholar 

  • Swain, J. J., Venkatraman, S., & Wilson, J. R. (1988). Least-squares estimation of distribution functions in Johnson’s translation system. Journal of Statistical Computation and Simulation, 29, 271–297.

    Article  Google Scholar 

  • Tafazzoli, A., & Wilson, J. R. (2011). Skart: A skewness-and-autoregression-adjusted batch-means procedure for simulation analysis. IIE Transactions, 43, 110-128.

    Article  Google Scholar 

  • Walkenbach, J. (2010). Excel 2010 power programming with VBA. New York: Wiley.

    Book  Google Scholar 

  • White, K. P. (1997). An effective truncation heuristic for bias reduction in simulation output. Simulation, 69, 323–334.

    Article  Google Scholar 

  • Whitt, W. (1981). Approximating a point process by a renewal process: The view through a queue, an indirect approach. Management Science, 27, 619–636.

    Article  Google Scholar 

  • Whitt, W. (1989). Planning queueing simulations. Management Science, 35, 1341–1366.

    Article  Google Scholar 

  • Whitt, W. (2006). Analysis for design. In S. G. Henderson & B. L. Nelson (Eds.), Handbooks in operations research and management science: Simulation. New York: North-Holland.

    Google Scholar 

  • Whitt, W. (2007). What you should know about queueing models to set staffing requirements in service systems. Naval Research Logistics, 54, 476–484.

    Article  Google Scholar 

  • Xu, J., Hong, L. J., & Nelson, B. L. (2010). Industrial strength COMPASS: A comprehensive algorithm and software for optimization via simulation. ACM Transactions on Modeling and Computer Simulation, 20, 1–29.

    Article  Google Scholar 

  • Xu, J., Nelson, B. L., & Hong, L. J. (2012, in press). An adaptive hyperbox algorithm for high-dimensional discrete optimization via simulation problems. INFORMS Journal on Computing.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, USA

    Barry L. Nelson

Authors
  1. Barry L. Nelson
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Nelson, B.L. (2013). Why Do We Simulate?. In: Foundations and Methods of Stochastic Simulation. International Series in Operations Research & Management Science, vol 187. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-6160-9_1

Download citation

Publish with us

Policies and ethics

Search

Navigation