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xv | |
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xix | |
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xxvii | |
Foreword |
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xxix | |
Preface |
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xxxi | |
About the Author |
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xxxiii | |
Abbreviations |
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xxxv | |
Symbols |
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xxxvii | |
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3 | (10) |
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1.1 The Pillars Of Science And Engineering |
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3 | (1) |
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1.2 Studying The Queueing Phenomenon |
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4 | (1) |
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5 | (1) |
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1.4 Lifecycle Of A Simulation Study |
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6 | (3) |
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1.5 Advantages And Limitations Of Simulation |
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9 | (1) |
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10 | (1) |
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11 | (2) |
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Chapter 2 Building Conceptual Models |
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13 | (14) |
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2.1 What Is A Conceptual Model? |
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13 | (2) |
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2.2 Elements Of A Conceptual Model |
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15 | (3) |
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15 | (1) |
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15 | (1) |
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16 | (1) |
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17 | (1) |
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17 | (1) |
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2.3 The Single-Server Queueing System |
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18 | (4) |
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22 | (1) |
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2.5 Actual Time Versus Simulated Time |
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23 | (1) |
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24 | (1) |
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24 | (3) |
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Chapter 3 Simulating Probabilities |
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27 | (12) |
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3.1 Random Experiments And Events |
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27 | (1) |
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28 | (2) |
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3.3 Computing Probabilities |
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30 | (2) |
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3.4 Probability As A Sample Mean |
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32 | (4) |
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36 | (1) |
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36 | (3) |
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Chapter 4 Simulating Random Variables and Stochastic Processes |
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39 | (30) |
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4.1 What Are Random Variables? |
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39 | (7) |
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4.1.1 Probability Mass Functions |
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40 | (1) |
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4.1.2 Cumulative Distribution Functions |
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41 | (2) |
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4.1.3 Probability Density Functions |
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43 | (1) |
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44 | (2) |
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4.2 Some Useful Random Variables |
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46 | (10) |
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46 | (1) |
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47 | (1) |
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48 | (1) |
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49 | (1) |
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50 | (3) |
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53 | (1) |
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54 | (1) |
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54 | (1) |
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55 | (1) |
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56 | (2) |
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4.4 Dynamic System Evolution |
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58 | (2) |
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4.5 Simulating Queueing Processes |
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60 | (7) |
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4.5.1 Discrete-Time Markov Chains |
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62 | (2) |
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4.5.2 Continuous-Time Markov Chains |
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64 | (3) |
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67 | (1) |
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67 | (2) |
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Chapter 5 Simulating the Single-Server Queueing System |
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69 | (24) |
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69 | (6) |
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5.2 Collecting Simulated Data |
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75 | (1) |
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76 | (8) |
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76 | (1) |
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76 | (1) |
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77 | (2) |
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79 | (3) |
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82 | (2) |
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5.4 Independent Simulation Runs |
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84 | (2) |
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5.5 Transient And Steady Phases |
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86 | (5) |
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91 | (1) |
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91 | (2) |
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Chapter 6 Statistical Analysis of Simulated Data |
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93 | (16) |
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6.1 Populations And Samples |
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93 | (2) |
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6.2 Probability Distribution Of The Sample Mean |
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95 | (2) |
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97 | (7) |
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100 | (2) |
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6.3.2 Why Not Always Use a 99% Confidence Interval? |
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102 | (2) |
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6.4 Comparing Two System Designs |
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104 | (1) |
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105 | (1) |
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105 | (4) |
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Part II Managing Complexity |
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109 | (14) |
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7.1 What Is An Event Graph? |
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109 | (2) |
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111 | (6) |
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7.2.1 The Arrival Process |
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111 | (1) |
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7.2.2 Single-Server Queueing System |
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112 | (2) |
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7.2.3 Multiple-Server Queueing System |
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114 | (1) |
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7.2.4 Single-Server Queueing System with a Limited Queue Capacity |
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114 | (1) |
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7.2.5 Single-Server Queuing System with Failure |
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115 | (1) |
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7.2.6 Single-Server Queuing System with Reneging |
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116 | (1) |
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7.2.7 Single-Server Queuing System with Balking |
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116 | (1) |
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7.3 Translating Event Graphs Into Code |
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117 | (3) |
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120 | (1) |
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120 | (3) |
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Chapter 8 Building Simulation Programs |
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123 | (16) |
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8.1 Time-Driven Simulation |
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123 | (3) |
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8.2 Event-Driven Simulation |
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126 | (1) |
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8.3 Writing Event-Driven Simulation Programs |
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127 | (7) |
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134 | (1) |
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134 | (1) |
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8.4.2 Identifiers for Packets |
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134 | (1) |
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8.4.3 Stopping Conditions for the Simulation Loop |
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134 | (1) |
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135 | (1) |
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135 | (4) |
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Chapter 9 The Monte Carlo Method |
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139 | (26) |
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9.1 Estimating The Value Of π |
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139 | (3) |
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9.2 Numerical Integration |
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142 | (2) |
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9.3 Estimating A Probability |
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144 | (5) |
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9.3.1 Buffon's Needle Problem |
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144 | (2) |
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146 | (3) |
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9.4 Variance Reduction Techniques |
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149 | (12) |
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149 | (2) |
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9.4.2 Stratified Sampling |
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151 | (2) |
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9.4.3 Antithetic Sampling |
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153 | (3) |
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156 | (2) |
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9.4.5 Importance Sampling |
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158 | (3) |
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161 | (1) |
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161 | (4) |
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Part IV Sources of Randomness |
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Chapter 10 Random Variate Generation |
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165 | (22) |
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10.1 The Inversion Method |
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165 | (8) |
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10.1.1 Continuous Random Variables |
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167 | (2) |
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10.1.2 Discrete Random Variables |
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169 | (2) |
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10.1.2.1 Generating a Bernoulli Variate |
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171 | (1) |
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10.1.2.2 Generating a Binomial Variate |
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172 | (1) |
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10.1.2.3 Generating a Geometric Variate |
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173 | (1) |
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10.2 The Rejection Method |
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173 | (4) |
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10.3 The Composition Method |
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177 | (2) |
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10.4 The Convolution Method |
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179 | (3) |
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182 | (4) |
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10.5.1 The Poisson Distribution |
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182 | (2) |
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10.5.2 The Normal Distribution |
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184 | (2) |
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186 | (1) |
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186 | (1) |
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Chapter 11 Random Number Generation |
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187 | (22) |
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11.1 Pseudo-Random Numbers |
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187 | (2) |
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11.2 Characteristics Of A Good Generator |
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189 | (1) |
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11.3 Just Enough Number Theory |
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190 | (2) |
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190 | (1) |
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11.3.2 The Modulo Operation |
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190 | (1) |
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11.3.3 Primitive Roots for a Prime Number |
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191 | (1) |
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11.4 The Linear Congruential Method |
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192 | (1) |
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11.5 The Multiplicative Congruential Method |
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193 | (1) |
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193 | (1) |
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194 | (1) |
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11.6 Linear Feedback Shift Registers |
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194 | (5) |
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11.7 Statistical Testing Of RNGs |
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199 | (6) |
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11.7.1 The Chi-Squared Test |
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199 | (2) |
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201 | (1) |
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202 | (2) |
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204 | (1) |
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205 | (1) |
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205 | (4) |
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209 | (26) |
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209 | (9) |
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12.2 Packet Delivery Over A Wireless Channel |
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218 | (8) |
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226 | (7) |
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233 | (1) |
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233 | (2) |
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Appendix A Overview of Python |
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235 | (16) |
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235 | (2) |
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237 | (1) |
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238 | (1) |
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239 | (1) |
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240 | (1) |
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A.6 Generating Random Numbers And Random VARI-ATES |
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241 | (1) |
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A.7 Implementing The Event List |
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242 | (2) |
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242 | (1) |
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242 | (1) |
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243 | (1) |
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A.8 Passing A Function Name As An Argument |
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244 | (1) |
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245 | (1) |
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245 | (6) |
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Appendix B An Object-Oriented Simulation Framework |
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251 | (16) |
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Appendix C The Chi-Squared Table |
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267 | (2) |
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Appendix D The t-Distribution Table |
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269 | (2) |
Bibliography |
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271 | (2) |
Index |
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273 | |