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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 | |