| Description |
1 online resource (278 p.) |
| Contents |
Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Acknowledgments -- 1. Preliminaries -- 1.1. What Is a Stochastic Model? -- 1.1.1. Brief Description of the Stochastic Level Crossing Method (LC) -- 1.1.2. Examples of Input and Output Random Variables in a Stochastic Model -- 1.1.3. Diagram of General Stages in Analysis of a Stochastic Model -- 1.2. Sample Path of Key Random Variables of a Stochastic Model -- 1.2.1. Stationary and Transient (Time-Dependent) Probability Distributions Using LC |
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1.2.1.1. Quantities Based on Knowledge of Pdfs of Output Variables -- 1.2.2. The Stochastic Level Crossing Method (LC) -- 1.3. Sample Path and Level Crossings: Details -- 1.3.1. Sample Path -- 1.3.2. Focus on Level Crossings Made by Sample Paths -- 1.3.3. Focus on Sample-Path Crossing Rates of State-Space Levels -- 1.4. Some Basic Level Crossing Limit Theorems and Concepts -- 1.4.1. A Basic LC Limit Theorem for the Virtual Wait Process {W(t)}t≥0 in M/M/1 Queues -- 1.4.2. A Basic LC Limit Theorem for the Extended Age Process {V(t)}t≥0 in G/M/1 Queues |
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1.4.3. A Basic LC Limit Theorem for Dams, Inventories, and Related Models with Poisson Inputs -- 1.4.4. Dimension of r(x)f(x) -- 1.4.5. Geometric Sample-Path Level Crossingss -- 1.4.6. Rate Balance of a Sample-Path Across a State-space Level and Rate-Balance Equations Using Basic LC Limit Theorems -- 1.4.6.1. Rate Balance -- 1.4.7. Rate-Balance Equations for Pdfs Using Basic LC Limit Theorems -- 1.5. Exponential Distribution and Poisson Process -- 1.5.1. Memoryless Property of the Exponential Distribution -- 1.5.2. Bayes' Rule |
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1.5.3. Probability Distribution of the Minimum of Two or More Independent Exponential Random Variables -- 1.5.4. Poisson Process -- 1.5.4.1. Poisson Probability Distribution -- 1.5.4.2. Poisson Process Details -- 1.5.5. Focus on Connection between Exponential Distribution and Poisson Process -- 1.6. Birth and Death Process -- 1.7. Stability in Stochastic Models -- 1.8. Useful Related Concepts when Applying LC -- 1.8.1. Renewal Process -- 1.8.2. Regenerative Process -- 1.8.3. Elementary Renewal Theorem -- 1.8.4. Renewal Reward Theorem -- 1.8.5. Lindley Recursions -- 1.8.6. Dimensional Analysis |
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1.8.7. Review of Statistics -- 1.9. Exercises -- 2. Standard M/M/1 Queue and Variants -- 2.1. Standard M/M/1 Queue -- 2.1.1. Criterion for Existence of Stationary Pdf of Wait -- 2.1.2. PASTA Principle−""Poisson Arrivals See Time Averages -- 2.1.3. Rate Balance across State-Space Levels -- 2.1.4. Virtual Wait in M/M/1 Queue -- 2.1.5. Sample Path of Virtual Wait in M/M/1 Queue -- 2.1.6. Focus on Actual Wait in M/M/1 Queue -- 2.1.6.1. The Slope of the Sample Path of {W(t)}t≥0 Is −1 when W(t) > 0 -- 2.1.6.2. Customer-initiated Trapezoids and Triangles in Sample Path |
| Notes |
Description based upon print version of record |
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2.1.7. Basic LC Limit Theorems and Integral Equation for Stationary Pdf of Wait in M/M/1 Queue |
| Form |
Electronic book
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| ISBN |
9781000907377 |
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1000907376 |
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