運籌學:套用隨機模型

運籌學:套用隨機模型

《運籌學:套用隨機模型》是2007年出版的一本圖書,作者是V. G. Kulkarni 。

基本介紹

  • 書名:運籌學:套用隨機模型
  • 作者:V. G. Kulkarni 
  • ISBN:9787302088622
  • 定價::38元
  • 裝幀::平裝
  • 印刷日期::2007-9-7
圖書信息,圖書簡介,圖書前言,圖書目錄,

圖書信息

作者:V. G. Kulkarni
圖書詳細信息:
ISBN:9787302088622
定價:38元
印次:1-2
裝幀:平裝
印刷日期:2007-9-7

圖書簡介

由Kulkarni編纂的《Modeling, Analysis, Design, and Control of Stochastic Systems》一書較系統地講解了隨機模型的有關內容,其特點是重點介紹各種原理和方法的基本概念及其套用,對於較簡單的一般問題,以容易理解和接受的方式給出其詳細的證明過程,而對於較複雜的問題,則用直觀的說明來代替複雜而抽象的證明過程,同時每個章節都有豐富的例子和大量的練習題,習題按照概念題和計算題分類,易於學生消化和鞏固。
《運籌學(套用隨機模型)》即為該書的影印版,其主要內容包括:基礎機率論、馬爾科夫過程、排隊系統、最優設計、最優控制等。本書可作為工科類及經管類本科生教材。

圖書前言

本教材系列的出版正值中國學術界工業工程學科經歷巨大發展、實際工作中對工業工程的概念、方法和工具的使用興趣日漸濃厚之時。在實際工作中有效地套用工業工程的手段將無疑會提高生產率、工作質量、合作的滿意度和效果。
該系列中的書籍對工業工程的本科生、研究生和工業界中需要解決工程系統設計、運作和管理諸方面問題的人士最為適用。
加弗瑞爾·沙爾文迪
清華大學工業工程系
普渡大學工業工程學院(美國)
2002年4月

圖書目錄

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

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