運籌學應(yīng)用隨機模型

內(nèi)容概要

由Kulkarni編纂的((Modeling，Analysis，Design，and Control Of StochasticSystems>)一書較系統(tǒng)地講解了隨機模型的有關(guān)內(nèi)容，其特點是重點介紹各種原理和方法的基本概念及其應(yīng)用，對于較簡單的一般問題，以容易理解和接受的方式給出其詳細的證明過程，而對于較復雜的問題，則用直觀的說明來代替復雜而抽象的證明過程，同時每個章節(jié)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，易于學生消化和鞏固。
    《運籌學(應(yīng)用隨機模型)》即為該書的影印版，其主要內(nèi)容包括：基礎(chǔ)概率論、馬爾科夫過程、排隊系統(tǒng)、最優(yōu)設(shè)計、最優(yōu)控制等。本書可作為工科類及管理類本科生教材。

書籍目錄

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.  Problems2. 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. Problems3  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.  Problems4. 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.  Problems5. 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.  Problems6. 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. Problems7. 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.  Problems8. 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.  Problems10. 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 ProblemsBibliographyIndex

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