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Stochastic Models in Operations Research Stochastic Processes and Operating Characteristics

ISBN-10: 0486432599

ISBN-13: 9780486432595

Edition: 2004 (Unabridged)

Authors: Matthew J. Sobel, Daniel P. Heyman

List price: $29.95
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Description:

This two-volume set of texts explores the central facts and ideas of stochastic processes, illustrating their use in models based on applied and theoretical investigations. They demonstrate the interdependence of three areas of study that usually receive separate treatments: stochastic processes, operating characteristics of stochastic systems, and stochastic optimization. Comprehensive in its scope, they emphasize the practical importance, intellectual stimulation, and mathematical elegance of stochastic models and are intended primarily as a graduate-level texts.
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Book details

List price: $29.95
Copyright year: 2004
Publisher: Dover Publications, Incorporated
Publication date: 12/10/2003
Binding: Paperback
Pages: 560
Size: 6.00" wide x 9.00" long x 1.00" tall
Weight: 1.496
Language: English

Preface
Introduction
Overview of the Book
Using the Book
Notation
Stochastic Processes and Models
Posterity Analysis
Introduction
Maintenance of a Computer
Congestion at a Bank
Cash Management
Reservoir Regulation
Inventory Replenishment
Fishery Harvests
Prologue to Stochastic Processes
Definitions and Basic Concepts
Special Classes of Stochastic Processes
Notation for Models of Queues
Bibliographic Guide
Birth-and-Death Processes
Introduction
The Definition of a Birth-and-Death Process
Examples
Transition Function
Steady-State Probabilities
Start-up and Shut-down in Queues
Sample-Path Properties
Relationships among Averages
First-Passage Times
Transient Analysis of the M/M/1 Queue
Exploding Birth-and-Death Processes
Bibliographic Guide
Renewal Theory
Examples and a Nonintuitive Result
Elementary Properties of a Renewal Process
Asymptotic Results for N(t)
Renewal Function
Recurrence Times
Delayed, Equilibrium, and Alternating Renewal Processes
More about the Poisson Process
Superposition of Renewal Processes
A Probabilistic Proof of Black well's Renewal Theorem
Bibliographic Guide
Renewal-Reward and Regenerative Processes
Definition of the Renewal-Reward Process and Examples
Sums of a Random Number of Random Variables
Limit Theorems for Renewal-Reward Processes
Regenerative Processes
Branching Processes
Bibliographic Guide
Markov Chains
Definition and Examples
Algebraic Solution of Finite Markov Chains
First-Passage Times
Embedded Renewal Processes in Markov Chains
Classification of Markov Chains
Limiting and Stationary Probabilities
Further Results about Limiting Distributions
Simple-Random-Walk and Gambler's Ruin Processes
Analysis of Generating Functions
Bibliographic Guide
Continuous-Time Markov Chains
Definitions and Examples
Sample-Path Properties
Transition Function
More Examples
Algebraic Solution of Finite Continuous-Time Markov Chains
Limiting and Stationary Probabilities
Another Construction of the Continuous-Time Markov Chain
Reversible Markov Chains
Bibliographic Guide
Markov Processes
Semi-Markov Processes
Markov Renewal Processes
Random Walks on the Line
Diffusion Processes
Bibliographic Guide
Stationary Processes and Ergodic Theory
Definition and Examples
Ergodic Theorems for Stationary Processes
Stationary Regenerative Processes
Bibliographic Guide
Operating Characteristics of Stochastic Systems
System Properties
Work-in-System (Virtual-Delay) Process
Poisson Arrivals "See" Time Averages
The Queueing Formula L = [lambda]W: Applications and Generalizations
Effects of Order of Service on Waiting Times
Effects of Priorities on Waiting Times
Start-up and Shut-down Queueing Models
Insensitivity in Queueing Models
Bibliographic Guide
Networks of Queues
Jackson Networks
Waiting Times in Tandem Queues
Bibliographic Guide
Bounds and Approximations
Bounds for Queueing Models
Diffusion Process Approximations
System Approximations
Bibliographic Guide
Background Material
Rudiments of Probability Theory
Exponential Family of Distributions
Laplace Transforms and Generating Functions
A Short List of Laplace Transforms and Generating-Function Pairs
Facts from Mathematical Analysis
Bibliographic Guide
Indexes
Name Index
Subject Index