Author | Bratley, Paul. author |
---|---|

Title | A Guide to Simulation [electronic resource] / by Paul Bratley, Bennett L. Fox, Linus E. Schrage |

Imprint | New York, NY : Springer US, 1983 |

Connect to | http://dx.doi.org/10.1007/978-1-4684-0167-7 |

Descript | XIX, 383 p. online resource |

SUMMARY

Simulation means driving a model of a system with suitable inputs and observing the corresponding outputs. It is widely applied in engineering, in business, and in the physical and social sciences. Simulation methodยญ ology araws on computer. science, statistics, and operations research and is now sufficiently developed and coherent to be called a discipline in its own right. A course in simulation is an essential part of any operations reยญ search or computer science program. A large fraction of applied work in these fields involves simulation; the techniques of simulation, as tools, are as fundamental as those of linear programming or compiler construction, for example. Simulation sometimes appears deceptively easy, but perusal of this book will reveal unexpected depths. Many simulation studies are statistically defective and many simulation programs are inefficient. We hope that our book will help to remedy this situation. It is intended to teach how to simulate effectively. A simulation project has three crucial components, each of which must always be tackled: (1) data gathering, model building, and validation; (2) statistical design and estimation; (3) programming and implementation. Generation of random numbers (Chapters 5 and 6) pervades simulation, but unlike the three components above, random number generators need not be constructed from scratch for each project. Usually random number packages are available. That is one reason why the chapters on random numbers, which contain mainly reference material, follow the ch!lPters dealยญ ing with experimental design and output analysis

CONTENT

1 Introduction -- 1.1. Systems, Models, and Simulation -- 1.2. Verification, Approximation, and Validation -- 1.3. States, Events, and Clocks -- 1.4. Simulation โ{128}{148} Types and Examples -- 1.5. Introduction to Random Numbers -- 1.6. Perspective on Experimental Design and Estimation -- 1.7. Clock Mechanisms -- 1.8. Hints for Simulation Programming -- 1.9. Miscellaneous Problems -- 2 Variance Reduction -- 2.1. Common Random Numbers -- 2.2. Antithetic Variates -- 2.3. Control Variates -- 2.4. Stratification -- 2.5. Importance Sampling -- 2.6. Conditional Monte Carlo -- 2.7. Jackknifing -- 3 Output Analysis -- 3.1. Introduction -- 3.2. Analysis of Finite-Horizon Performance -- 3.3. Analysis of Steady-state Performance -- 3.4. Analysis of Transaction-Based Performance -- 3.5. Efficient Estimators and Indirect Estimators -- 3.6. Problems -- 3.7. Renewal Theory Primer -- 4 Rational Choice of Input Distributions -- 4.1. Addition and the Normal Distribution -- 4.2. Multiplication and the Lognormal -- 4.3. Memorylessness and the Exponential -- 4.4. Superposition, the Poisson, and the Exponential -- 4.5. Minimization and the Weibull Distribution -- 4.6. A Mixed Empirical and Exponential Distribution -- 4.7. Extreme Values and Spacings -- 4.8. When Not to Use a Theoretical Distribution -- 4.9. Nonstationary Poisson Processes -- 5 Nonuniform Random Numbers -- 5.1. Introduction -- 5.2. General Methods -- 5.3. Continuous Distributions -- 5.4. Discrete Distributions -- 5.5. Problems -- 5.6. Timings -- 6 Uniform Random Numbers -- 6.1. Random Introductory Remarks -- 6.2. What Constitutes Randomness -- 6.3. Classes of Generators -- 6.4. Choosing a Good Generator Based on Theoretical Considerations -- 6.5. Implementation of Uniform Random Number Generators -- 6.6. Empirical Testing of Uniform Random Number Generators -- 6.7. Proper Use of a Uniform Random Number Generator -- 6.8. Exploiting Special Features of Uniform Generators -- 7 Simulation Programming -- 7.1. Simulation with General-Purpose Languages -- 7.2. Simscript -- 7.3. GPSS -- 7.4. Simula -- 7.5. General Considerations in Simulation Programming -- 8 Programming to Reduce the Variance -- 8.1. Choosing an Input Distribution -- 8.2. Common Random Numbers -- 8.3. Antithetic Variates -- 8.4. Control Variates -- 8.5. Stratified Sampling -- 8.6. Importance Sampling -- 8.7. Conditional Monte Carlo -- 8.8. Summary -- Appendix A The Shapiro โ{128}{148} Wilk Test for Normality -- Appendix L Routines for Random Number Generation -- Appendix X Examples of Simulation Programming -- References -- Author Index

Mathematics
System theory
Calculus of variations
Mathematics
Systems Theory Control
Calculus of Variations and Optimal Control; Optimization