是一部講述如何挖掘蘊藏在模型表現形式背后的數學過程的權威作品。詳細的數學推導和大量圖例使得更加易於研究生和高年級本科生作為學習隨機過程的教材和參考資料。《概率論、馬爾科夫鏈、排隊和模擬》應用廣泛，也適用於計算科學、工程、運籌學、統計和數學等學科。

Preface and AcknowledgmentsⅠ PROBABILITY1 Probability1.1 Trials, Sample Spaces, and Events1.2 Probability Axioms and Probability Space1.3 Conditional Probability1.4 Independent Events1.5 Law of Total Probability1.6 Bayes’’ Rule1.7 Exercises2 Combinatorics-The Art of Counting2.1 Permutations2.2 Permutations with Replacements2.3 Permutations without Replacement2.4 Combinations without Replacement2.5 Combinations with Replacements2.6 Bernoulli (Independent) Trials2.7 Exercises3 Random Variables and Distribution Functions3.1 Discrete and Continuous Random Variables3.2 The Probability Mass Function for a Discrete Random Variable3.3 The Cumulative Distribution Function3.4 The Probability Density Function for a Continuous Random Variable3.5 Functions of a Random Variable3.6 Conditioned Random Variables3.7 Exercises4 Joint and Conditional Distributions4.1 Joint Distributions4.2 Joint Cumulative Distribution Functions4.3 Joint Probability Mass Functions4.4 Joint Probability Density Functions4.5 Conditional Distributions4.6 Convolutions and the Sum of Two Random Variables4.7 Exercises5 Expectations and More5.1 Definitions5.2 Expectation of Functions and Joint Random Variables5.3 Probability Generating Functions for Discrete Random Variables5.4 Moment Generating Functions5.5 Maxima and Minima of Independent Random Variables5.6 Exercises6 Discrete Distribution Functions6.1 The Discrete Uniform Distribution6.2 The Bernoulli Distribution6.3 The Binomial Distribution6.4 Geometric and Negative Binomial Distributions6.5 The Poisson Distribution6.6 The Hypergeometric Distribution6.7 The Multinomial Distribution6.8 ExercisesContinuous Distribution Functions7.1 The Uniform Distribution7.2 The Exponential Distribution7.3 The Normal or Gaussian Distribution7.4 The Gamma Distribution7.5 Reliability Modeling and the Weibull Distribution7.6 Phase-Type Distributions7.6.1 The Erlang-2 Distribution7.6.2 The Erlang-r Distribution7.6.3 The Hypoexponential Distribution7.6.4 The Hyperexponential Distribution7.6.5 The Coxian Distribution7.6.6 General Phase-Type Distributions7.6.7 Fitting Phase-Type Distributions to Means and Variances7.7 Exercises8 Bounds and Limit Theorems8.1 The Markov Inequality8.2 The Chebychev Inequality8.3 The Chernoff Bound8.4 The Laws of Large Numbers8.5 The Central Limit Theorem8.6 ExercisesⅡ MARKOV CHAINS9 Discrete- and Continuous-Time Markov Chains9.1 Stochastic Processes and Markov Chains9.2 Discrete-Time Markov Chains: Definitions9.3 The Chapman-Kolmogorov Equations9.4 Classification of States9.5 Irreducibility9.6 The Potential, Fundamental, and Reachability Matrices9.6.1 Potential and Fundamental Matrices and Mean Time to Absorption9.6.2 The Reachability Matrix and Absorption Probabilities9.7 Random Walk Problems9.8 Probability Distributions9.9 Reversibility9.10 Continuous-Time Markov Chains9.10.1 Transition Probabilities and Transition Rates9.10.2 The Chapman-Kolmogorov Equations9.10.3 The Embedded Markov Chain and State Properties9.10.4 Probability Distributions9.10.5 Reversibility9.11 Semi-Markov Processes9.12 Renewal Processes9.13 Exercises10 Numerical Solution of Markov Chains10.1 Introduction10.1.1 Setting the Stage10.1.2 Stochastic Matrices10.1.3 The Effect of Discretization10.2 Direct Methods for Stationary Distributions10.2.1 Iterative versus Direct Solution Methods10.2.2 Gaussian Elimination and LU Factorizattons10.3 Basic Iterative Methods for Stationary Distributions10.3.1 The Power Method10.3.2 The Iterative Methods of Jacobi and Gauss-Seidel10.3.3 The Method of Successive Overrelaxation10.3.4 Data Structures for Large Sparse Matrices10.3.5 Initial Approximations, Normalization, and Convergence10.4 Block Iterative Methods10.5 Decomposition and Aggregation Methods10.6 The Matrix Geometric/Analytic Methods for Structured Markov Chains10.6.1 The Quasi-Birth-Death Case10.6.2 Block Lower Hessenberg Markov Chains10.6.3 Block Upper Hessenberg Markov Chains10.7 Transient Distributions10.7.1 Matrix Scaling and Powering Methods for Small State Spaces10.7.2 The Uniformization Method for Large State Spaces10.7.3 Ordinary Differential Equation Solvers10.8 ExercisesⅢ QUEUEING MODELS11 Elementary Queueing Theory11.1 Introduction and Basic Definitions11.1.1 Arrivals and Service11.1.2 Scheduling Disciplines11.1.3 Kendall’’s Notation11.1.4 Graphical Representations of Queues11.1.5 Performance Measures--Measures of Effectiveness11.1.6 Little’’s Law11.2 Birth-Death Processes: The M/M/I Queue11.2.1 Description and Steady-State Solution11.2.2 Performance Measures11,2.3 Transient Behavior11.3 General Birth-Death Processes11,3. I Derivation of the State Equations11.3.2 Steady-State Solution11.4 Multiserver Systems11.4.1 The M/M/c Queue11.4.2 The M/M/∞ Queue11.5 Finite-Capacity Systems--The M/M/1/K Queue11.6 Multiserver, Finite-Capacity Systems--The M/M/c/K Queue11.7 Finite-Source Systems-The M/M/c//M Queue11.8 State-Dependent Service11.9 Exercises12 Queues with Phase-Type Laws: Neuts’’ Matrix-Geometric Method12.1 The Erlang-r Service Model--The M/Er/l Queue12.2 The Erlang-r Arrival Model-The Er/M/] Queue12.3 The M/H2/1 and H2/M/1 Queues12.4 Automating the Analysis of Single-Server Phase-Type Queues12.5 The H2/E3/1 Queue and General Ph/Ph/1 Queues12.6 Stability Results for Ph/Ph/l Queues12.7 Performance Measures for Ph/Ph/1 Queues12.8 Matlab code for Ph/Ph/1 Queues12.9 Exercises13 The z-Transform Approach to Solving Markovian Queues13.1 The z-Transform13.2 The Inversion Process13.3 Solving Markovian Queues using z-Transforms13.3.1 The z-Transform Procedure13.3.2 The M/M/1 Queue Solved using z-Transforms13.3.3 The M/M/1 Queue with Arrivals in Pairs13.3.4 The M/Er/1 Queue Solved using z-Transforms13.3.5 The Er/M/1 Queue Solved using z-Transforms13.3.6 Bulk Queueing Systems13.4 Exercises14 The M/G/1 and G/M/1 Queues14.1 Introduction to the M/G/1 Queue14.2 Solution via an Embedded Markov Chain14.3 Performance Measures for the M/G/1 Queue14.3.1 The Pollaczek-Khintchine Mean Value Formula14.3.2 The Pollaczek-Khintchine Transform Equations14.4 The M/G/1 Residual Time: Remaining Service Time14.5 The M/G/1 Busy Period14.6 Priority Scheduling14.6.1 M/M/1: Priority Queue with Two Customer Classes14.6.2 M/G/1: Nonpreemptive Priority Scheduling……Ⅳ SIMULATIONAppendix A: The Greek AlphabetAppendix B: Elements of Linear AlgebraBibliographyIndex