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