Modeling and Analysis of Stochastic Systems, Third Edition

✍ Scribed by Vidyadhar G. Kulkarni

• Publisher: CRC Press;Chapman and Hall/CRC
• Year: 2017
• Tongue: English
• Leaves: 606
• Series: Chapman & Hall/CRC Texts in Statistical Science
• Edition: 3
• Category: Library

✦ Synopsis

Building on the author’s more than 35 years of teaching experience, Modeling and Analysis of Stochastic Systems, Third Edition, covers the most important classes of stochastic processes used in the modeling of diverse systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models.

The third edition has been updated with several new applications, including the Google search algorithm in discrete time Markov chains, several examples from health care and finance in continuous time Markov chains, and square root staffing rule in Queuing models. More than 50 new exercises have been added to enhance its use as a course text or for self-study. The sequence of chapters and exercises has been maintained between editions, to enable those now teaching from the second edition to use the third edition.

Rather than offer special tricks that work in specific problems, this book provides thorough coverage of general tools that enable the solution and analysis of stochastic models. After mastering the material in the text, readers will be well-equipped to build and analyze useful stochastic models for real-life situations.

✦ Table of Contents

Content: Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
1: Introduction
1.1 What in the World Is a Stochastic Process?
1.2 How to Characterize a Stochastic Process
1.3 What Do We Do with a Stochastic Process?
1.3.1 Characterization
1.3.2 Transient Behavior
1.3.3 First Passage Times
1.3.4 Limiting Distribution
1.3.5 Costs and Rewards
2: Discrete-TimeMarkov Chains: Transient Behavior
2.1 Definition and Characterization
2.2 Examples
2.3 DTMCs in Other Fields
2.3.1 Genomics
2.3.2 Genetics
2.3.3 Genealogy
2.3.4 Finance
2.3.5 Manpower Planning. 2.3.6 Telecommunications2.3.7 Google Search
2.4 Marginal Distributions
2.5 Occupancy Times
2.6 Computation of Matrix Powers
2.6.1 Method of Diagonalization
2.6.2 Method of Generating Functions
2.7 Modeling Exercises
2.8 Computational Exercises
2.9 Conceptual Exercises
3: Discrete-TimeMarkov Chains: First Passage Times
3.1 Definitions
3.2 Cumulative Distribution Function of T
3.3 Absorption Probabilities
3.4 Expectation of T
3.5 Generating Function and Higher Moments of T
3.6 Computational Exercises
3.7 Conceptual Exercises
4: Discrete-TimeMarkov Chains: Limiting Behavior. 4.1 Exploring the Limiting Behavior by Examples4.2 Classification of States
4.2.1 Irreducibility
4.2.2 Recurrence and Transience
4.2.3 Periodicity
4.3 Determining Recurrence and Transience: Finite DTMCs
4.4 Determining Recurrence and Transience: Infinite DTMCs
4.4.1 Foster's Criterion
4.5 Limiting Behavior of Irreducible DTMCs
4.5.1 The Transient Case
4.5.2 The Discrete Renewal Theorem
4.5.3 The Recurrent Case
4.5.4 The Null Recurrent Case
4.5.5 The Positive Recurrent Aperiodic Case
4.5.6 The Positive Recurrent Periodic Case. 4.5.7 Necessary and Sufficient Condition for Positive Recurrence4.5.8 Examples
4.6 Examples: Limiting Behavior of Infinite State-Space Irreducible DTMCs
4.7 Limiting Behavior of Reducible DTMCs
4.8 DTMCs with Costs and Rewards
4.8.1 Discounted Costs
4.8.2 Average Costs
4.9 Reversibility
4.10 Computational Exercises
4.11 Conceptual Exercises
5: Poisson Processes
5.1 Exponential Distributions
5.1.1 Memoryless Property
5.1.2 Hazard Rate
5.1.3 Probability of First Failure
5.1.4 Minimum of Exponentials
5.1.5 Strong Memoryless Property
5.1.6 Sum of iid Exponentials. 5.1.7 Sum of Distinct Exponentials5.1.8 Random Sums of iid Exponentials
5.2 Poisson Process: Definitions
5.3 Event Times in a Poisson Process
5.4 Superposition and Splitting of Poisson Processes
5.4.1 Superposition
5.4.2 Splitting
5.5 Non-Homogeneous Poisson Process
5.5.1 Event Times in an NPP
5.6 Compound Poisson Process
5.7 Computational Exercises
5.8 Conceptual Exercises
6: Continuous-Time Markov Chains
6.1 Definitions and Sample Path Properties
6.2 Examples
6.3 CTMCs in Other Fields
6.3.1 Organ Transplants
6.3.2 Disease Progression
6.3.3 Epidemics
6.3.4 Order Books.

✦ Subjects

Stochastic processes;Stochastic systems