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Preface |
6 |
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Contents |
9 |
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Basic Probability Review |
14 |
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Basic Definitions |
14 |
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Random Variables and Distribution Functions |
17 |
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Mean and Variance |
23 |
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Important Distributions |
26 |
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Multivariate Distributions |
36 |
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Combinations of Random Variables |
44 |
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Fixed Sum of Random Variables |
45 |
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Random Sum of Random Variables |
45 |
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Mixtures of Random Variables |
47 |
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Appendix |
48 |
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Problems |
50 |
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References |
56 |
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Basics of Monte Carlo Simulation |
57 |
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Simulation by Hand |
58 |
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Generation of Random Numbers |
61 |
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Multiplicative Linear Congruential Generators |
62 |
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A Multiple Recursive Generator |
64 |
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Composite Generators |
65 |
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Generation of Random Variates |
67 |
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Discrete Random Variates |
67 |
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Continuous Random Variates |
73 |
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Bivariate Continuous Random Variates |
76 |
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Random Variates from Empirical Distributions |
78 |
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Appendix |
79 |
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Problems |
81 |
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References |
84 |
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Basic Statistical Review |
85 |
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Collection of Data |
85 |
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Preliminary Definitions |
86 |
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Graphical Representations |
87 |
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Parameter Estimation |
90 |
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Method of Moments |
92 |
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Maximum Likelihood Estimation |
93 |
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Confidence Intervals |
94 |
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Means |
95 |
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Proportions |
99 |
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Variances |
99 |
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Correlation Coefficient |
101 |
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Fitting Distributions |
102 |
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The Chi-Square Test |
103 |
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The Kolmogorov-Smirnov Test |
107 |
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Fitting Models |
111 |
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Ordinary Least Squares Regression |
112 |
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Maximum Likelihood Estimates for Linear Models |
117 |
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Appendix |
117 |
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Problems |
121 |
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References |
125 |
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Poisson Processes |
126 |
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Basic Definitions |
126 |
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Properties and Computations |
129 |
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Extensions of a Poisson Process |
132 |
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Compound Poisson Processes |
132 |
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Non-stationary Poisson Process |
134 |
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Poisson Regression |
135 |
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Poisson Regression with One Independent Variable |
135 |
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Poisson Regression with Several Independent Variables |
139 |
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Appendix |
144 |
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Problems |
147 |
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References |
150 |
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Markov Chains |
151 |
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Basic Definitions |
152 |
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Multistep Transitions |
155 |
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Classification of States |
159 |
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Steady-State Behavior |
167 |
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Computations |
172 |
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Appendix |
179 |
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Problems |
181 |
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References |
188 |
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Markov Processes |
190 |
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Basic Definitions |
190 |
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Steady-State Properties |
193 |
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Revenues and Costs |
197 |
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Time-Dependent Probabilities |
200 |
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Appendix |
204 |
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Problems |
205 |
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Queueing Processes |
209 |
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Basic Definitions and Notation |
209 |
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Single Server Systems |
211 |
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Infinite Capacity Single-Server Systems |
211 |
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Finite Capacity Single Server Systems |
218 |
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Multiple Server Queues |
221 |
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Approximations |
225 |
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Appendix |
227 |
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Problems |
228 |
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References |
233 |
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Queueing Networks |
234 |
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Jackson Networks |
234 |
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Open Jackson Networks |
235 |
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Closed Jackson Networks |
239 |
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Network Approximations |
242 |
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Deterministic Routing with Poisson Input |
243 |
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Deterministic Routing with non-Poisson Input |
249 |
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Appendix |
252 |
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Problems |
253 |
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References |
256 |
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Event-Driven Simulation and Output Analyses |
257 |
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Event-Driven Simulations |
257 |
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Statistical Analysis of Output |
268 |
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Terminating Simulations |
269 |
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Steady-State Simulations |
272 |
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Comparing Systems |
281 |
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Problems |
285 |
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References |
290 |
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Inventory Theory |
291 |
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The News-Vendor Problem |
292 |
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Single-Period Inventory |
295 |
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No Setup Costs |
295 |
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Setup Costs |
298 |
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Multi-Period Inventory |
301 |
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Problems |
305 |
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References |
309 |
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Replacement Theory |
310 |
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Age Replacement |
310 |
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Discrete Life Times |
311 |
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Continuous Life Times |
314 |
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Minimal Repair |
317 |
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Minimal Repairs without Early Replacements |
318 |
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Minimal Repairs with Early Replacements |
319 |
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Block Replacement |
321 |
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Problems |
324 |
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Markov Decision Processes |
327 |
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Basic Definitions |
328 |
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Expected Total Discounted Cost Criterion |
330 |
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Average Long-Run Cost Criterion |
331 |
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Stationary Policies |
331 |
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Discounted Cost Algorithms |
333 |
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Value Improvement for Discounted Costs |
335 |
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Policy Improvement for Discounted Costs |
336 |
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Linear Programming for Discounted Costs |
340 |
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Average Cost Algorithms |
341 |
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Policy Improvement for Average Costs |
344 |
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Linear Programming for Average Costs |
348 |
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The Optimal Stopping Problem |
350 |
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Problems |
353 |
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Advanced Queues |
359 |
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Difference Equations |
360 |
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Batch Arrivals |
362 |
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Quasi-Birth-Death Processes |
364 |
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Batch Arrivals (continued) |
366 |
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Phase-Type Distributions |
368 |
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Systems with Phase-Type Service |
372 |
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The M/Ph/1 Queueing System |
372 |
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The M/Ph/c Queueing System |
376 |
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Systems with Phase-Type Arrivals |
378 |
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Problems |
379 |
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References |
383 |
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Matrix Review |
384 |
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Matrix Addition and Subtraction |
385 |
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Matrix Multiplication |
385 |
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Determinants |
386 |
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Determinants by Cofactor Expansion |
388 |
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Nonsingular Matrices |
389 |
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Inversion-in-Place |
390 |
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Derivatives |
393 |
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References |
395 |
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Index |
396 |
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