运筹学

1. Probability

1.1. Probability Model

1.2. Sample Space

1.3. Events

1.4. Probability of Events

1.5. Conditional Probability

1.6. Law of Total Probability

1.7. Bayes' Rule

1.8. Independence

1.9. Problems

2. Univariate Random Variables

2.1. Random Variables

2.2. Cumulative Distribution Function

2.3. Discrete Random Variables

2.4. Common Discrete Random Variables

1. Probability

1.1. Probability Model

1.2. Sample Space

1.3. Events

1.4. Probability of Events

1.5. Conditional Probability

1.6. Law of Total Probability

1.7. Bayes' Rule

1.8. Independence

1.9. Problems

2. Univariate Random Variables

2.1. Random Variables

2.2. Cumulative Distribution Function

2.3. Discrete Random Variables

2.4. Common Discrete Random Variables

2.5. Continuous Random Variables

2.6. Common Continuous Random Variables

2.7. Functions of Random Variables

2.8. Expectation of a Discrete Random Variable

2.9. Expectation of a Continuous Random Variable

2.10. Expectation of a Function of a Random Variable

2.11. Reference Tables

2.12. Problems

3.Multivariate Random Variables

3.1. Multivariate Random Variables

3.2. Multivariate Discrete Random Variables

3.3. Multivariate Continuous Random Variables

3.4. Marginal Distributions

3.5. Independence

3.6. Sums of Random Variables

3.7. Expectations

3.8. Problems

4. Conditional Probability and Expectations

4.1. Introduction.

4.2. Conditional Probability Mass Function.

4.3. Conditional Probability Density Function

4.4. Computing Probabilities by Conditioning

4.5. Conditional Expectations

4.6. Computing Expectations by Conditioning

4.7. Problems

5. Discrete-Time Markov Models

5.1. What Is a Stochastic Process?

5.2. Discrete-Time Markov Chains

5.3. Examples of Markov Models

5.4. Transient Distributions

5.5. Occupancy Times

5.6. Limiting Behavior

5.7. Cost Models.

5.7.1. Expected Total Cost Over a Finite Horizon

5.7.2. Long-Run Expected Cost Per Unit Time

5.8. First Passage Times

5.9. Problems

6. Continuous-Time Markov Models

6.1. Continuous-Time Stochastic Processes

6.2. Continuous-Time Markov Chains

6.3. Exponential Random Variables

6.4. Examples of CTMCs: I

6.5. Poisson Processes

6.6. Examples of CTMCs: II

6.7. Transient Analysis: Uniformization

6.8. Occupancy Times

6.9. Limiting Behavior

6.10. Cost Models.

6.10.1. Expected Total Cost

6.10.2. Long-Run Cost Rates

6.11. First Passage Times.

Appendix A: Proof Of Theorem 6.4

Appendix B: Uniformization Algorithm to Compute P(t)

Appendix C: Uniformization Algorithm to Compute M(T)

6.12. Problems

7. Generalized Markov Models

7.1. Introduction.

7.2. Renewal Processes.

7.3. Cumulative Processes

7.4. Semi-Markov Processes: Examples

7.5. Semi-Markov Processes: Long-Term Analysis

7.5.1. Mean Inter-Visit Times

7.5.2. Occupancy Distributions

7.5.3. Long-Run Cost Rates

7.6. Problems

8. Queueing Models

8.1. Queueing Systems

8.2. Single-Station Queues: General Results

8.3. Birth and Death Queues with Finite Capacity

8.3.1. M/M/1/K Queue

8.3.2. M/M/s/K Queue

8.3.3. M/M/K/K Queue

8.4. Birth and Death Queues with Infinite Capacity

8.4.1. M/M/1 Queue

8.4.2. M/M/s Queue

8.4.3. M/M/oo Queue

8.5. M/G/1 Queue

8.6. G/M/1 Queue

8.7. Networks of Queues.

8.7.1. Jackson Networks

8.7.2. Stability

8.7.3. Limiting Behavior

8.8. Problems

9.Optimal Design

9.1. Introduction.

9.2. Optimal Order Quantity

9.3. Optimal Leasing of Phone Lines

9.4. Optimal Number of Tellers

9.5. Optimal Replacement

9.6. Optimal Server Allocation

9.7. Problems

10. Optimal Control

10.1. Introduction

10.2. Discrete-Time Markov Decision Processes: DTMDPs

10.3. Optimal Policies for DTMDPs

10.4. Optimal Inventory Control

10.5. Semi-Markov Decision Processes: SMDPs

10.6. Optimal Policies for SMDPs

10.7. Optimal Machine Operation

10.8. Problems.

Answers to Selected Problems

Bibliography

Index

由Kulkarni编纂的((Modeling，Analysis，Design，and Control Of
StochasticSystems>)一书较系统地讲解了随机模型的有关内容，其特点是重点介绍各种原理和方法的基本概念及其应用，对于较简单的一般问题，以容易理解和接受的方式给出其详细的证明过程，而对于较复杂的问题，则用直观的说明来代替复杂而抽象的证明过程，同时每个章节都有丰富的例子和大量的练习题，习题按照概念题和计算题分类，易于学生消化和巩固。

　　《运筹学(应用随机模型)》即为该书的影印版，其主要内容包括：基础概率论、马尔科夫过程、排队系统、最优设计、最优控制等。本书可作为工科类及管理类本科生教材。