斯图尔特著的《概率论马尔科夫链排队和模拟》是一部讲述如何挖掘蕴藏在模型表现形式背后的数学过程的权威作品。详细的数学推导和大量图例使得更加易于研究生和高年级本科生作为学习随机过程的教材和参考资料。本书应用广泛，也适用于计算科学、工程、运筹学、统计和数学等学科。

Preface and Acknowledgments

Ⅰ PROBABILITY

1 Probability

1.1 Trials, Sample Spaces, and Events

1.2 Probability Axioms and Probability Space

1.3 Conditional Probability

1.4 Independent Events

1.5 Law of Total Probability

1.6 Bayes' Rule

1.7 Exercises

2 Combinatorics-The Art of Counting

2.1 Permutations

2.2 Permutations with Replacements

2.3 Permutations without Replacement

2.4 Combinations without Replacement

2.5 Combinations with Replacements

2.6 Bernoulli (Independent) Trials

2.7 Exercises

3 Random Variables and Distribution Functions

3.1 Discrete and Continuous Random Variables

3.2 The Probability Mass Function for a Discrete Random Variable

3.3 The Cumulative Distribution Function

3.4 The Probability Density Function for a Continuous Random Variable

3.5 Functions of a Random Variable

3.6 Conditioned Random Variables

3.7 Exercises

4 Joint and Conditional Distributions

4.1 Joint Distributions

4.2 Joint Cumulative Distribution Functions

4.3 Joint Probability Mass Functions

4.4 Joint Probability Density Functions

4.5 Conditional Distributions

4.6 Convolutions and the Sum of Two Random Variables

4.7 Exercises

5 Expectations and More

5.1 Definitions

5.2 Expectation of Functions and Joint Random Variables

5.3 Probability Generating Functions for Discrete Random Variables

5.4 Moment Generating Functions

5.5 Maxima and Minima of Independent Random Variables

5.6 Exercises

6 Discrete Distribution Functions

6.1 The Discrete Uniform Distribution

6.2 The Bernoulli Distribution

6.3 The Binomial Distribution

6.4 Geometric and Negative Binomial Distributions

6.5 The Poisson Distribution

6.6 The Hypergeometric Distribution

6.7 The Multinomial Distribution

6.8 Exercises

Continuous Distribution Functions

7.1 The Uniform Distribution

7.2 The Exponential Distribution

7.3 The Normal or Gaussian Distribution

7.4 The Gamma Distribution

7.5 Reliability Modeling and the Weibull Distribution

7.6 Phase-Type Distributions

7.6.1 The Erlang-2 Distribution

7.6.2 The Erlang-r Distribution

7.6.3 The Hypoexponential Distribution

7.6.4 The Hyperexponential Distribution

7.6.5 The Coxian Distribution

7.6.6 General Phase-Type Distributions

7.6.7 Fitting Phase-Type Distributions to Means and Variances

7.7 Exercises

8 Bounds and Limit Theorems

8.1 The Markov Inequality

8.2 The Chebychev Inequality

8.3 The Chernoff Bound

8.4 The Laws of Large Numbers

8.5 The Central Limit Theorem

8.6 Exercises

Ⅱ MARKOV CHAINS

Ⅲ QUEUEING MODELS

Ⅳ SIMULATION

Appendix A: The Greek Alphabet

Appendix B: Elements of Linear Algebra

Bibliography

Index