运筹学应用随机模型(影印版)

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
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