Stochastic Modeling · Analysis and Simulation (Dover Books on Mathematics) by Nelson, Barry L. -- Read -- Imperial Library of Trantor

Index

Title Page Copyright Page Contents Preface 1. Why Are We Here 2. Sample Paths?

2.1 The Case of the Copy Enlargement 2.2 Notation and Review 2.3 Sample-Path Decomposition

2.3.1 Simulating the Self-Service System 2.3.2 Simulating the Full-Service System 2.3.3 Discussion

2.4 Exercises

3. Basics

3.1 Probability

3.1.1 Random Variables 3.1.2 Joint Distributions 3.1.3 Expected Value 3.1.4 Conditional Probability 3.1.5 Limit Distributions

3.2 Statistics 3.3 Random-Variate Generation 3.4 The Case of the Copy Enlargement, Revisited 3.5 Fine Points 3.6 Exercises

4. Simulation

4.1 The Case of the Leaky Bit Bucket 4.2 Notation and Review 4.3 Stochastic Processes 4.4 Simulating the Leaky Bit Bucket 4.5 A Generic Stochastic-Process Model 4.6 Simulating the Copy Enlargement 4.7 Simulation Programming 4.8 Fine Points 4.9 Exercises

5. Arrival-Counting Processes

5.1 The Case of the Reckless Beehunter 5.2 Notation and Review 5.3 A Generic Arrival-Counting-Process Model 5.4 Simulating the Reckless Beehunter 5.5 The Poisson Arrival Process

5.5.1 Probability Structure of the Sample Paths 5.5.2 Parameterizing Poisson Processes

5.6 More about Poisson Arrival Processes

5.6.1 Decomposition of a Poisson Process 5.6.2 Superposition of Poisson Processes 5.6.3 Nonstationary Poisson Processes

5.7 The Case of the Meandering Message 5.8 Derivations

5.8.1 Memoryless Property 5.8.2 Independent-Increments and Stationary-Increments Properties 5.8.3 Decomposition Property 5.8.4 Superposition Property 5.8.5 Nonstationary Poisson Process

5.9 Results for the Renewal Arrival-Counting Process

5.9.1 The Case of the Perpetual Payoff 5.9.2 Derivations 5.9.3 Other Arrival-Counting Processes

5.10 Fine Points 5.11 Exercises

6. Discrete-Time Processes

6.1 The Case of the Random Behavior 6.2 Notation and Review 6.3 Simulating the Random Behavior 6.4 Markov Chains

6.4.1 Probability Structure of the Sample Paths 6.4.2 Parameterizing Markov Chains 6.4.3 Transition Diagrams

6.5 The Case of the Defective Detective 6.6 Time-Dependent Performance Measures

6.6.1 Examples 6.6.2 Derivations

6.7 Time-Independent (Long-Run) Performance Measures

6.7.1 Classification of States 6.7.2 Performance Measures 6.7.3 Examples 6.7.4 Derivations

6.8 The Markov and Stationarity Properties Revisited 6.9 Fine Points 6.10 Exercises

7. Continuous-Time Processes

7.1 The Case of the Software Sellout 7.2 Notation and Review

7.2.1 Markov Chain Review 7.2.2 Properties of the Exponential and Geometric Distributions

7.3 Simulating the Software Sellout 7.4 Sample Paths of the Software Sellout 7.5 Markov Processes

7.5.1 Probability Structure of a Markov Process 7.5.2 Parameterizing Markov Processes

7.6 Analysis of Markov Process Sample Paths

7.6.1 Performance Measures 7.6.2 Time-Dependent Performance Measures 7.6.3 Time-Dependent Example 7.6.4 Time-Independent (Long-Run) Performance Measures 197 7.6.5 Time-Independent Example 7.6.6 Derivations

7.7 The Case of the Stressed-Out Student 7.8 The Markov and Stationarity Properties Revisited 7.9 Semi-Markov Processes 7.10 Fine Points 7.11 Exercises

8. Queueing Processes

8.1 The Case of the Last Parking Space on Earth 8.2 Notation and Review

8.2.1 Series and Recursions 8.2.2 Markov Process Review

8.3 A Queueing Model for the Last Parking Space on Earth 8.4 Markovian Queueing Processes

8.4.1 The Birth-Death Process 8.4.2 Performance Measures

8.5 Standard Formulations

8.5.1 Arrival Rates 8.5.2 Service Rates

8.6 Parameterizing Queueing Processes 8.7 Shorthand Notation and Examples

8.7.1 The M/M/s Queue 8.7.2 The M/M/s/n/k Queue with s = n

8.8 The Case of the Tardy Ticket 8.9 Networks of Markovian Queues

8.9.1 The Case of the Incredible Shrinking Leviathan 8.9.2 Markov Process Model of the Incredible Shrinking Leviathan 8.9.3 Open Jackson Networks

8.10 Non-Markovian Queues and Networks

8.10.1 A GI/G/s Approximation 8.10.2 A Queueing-Network Approximation

8.11 Exercises

9. Topics in Simulation of Stochastic Processes

9.1 Statistical Issues in Simulation

9.1.1 Initial-Condition Effects 9.1.2 Measures of Error 9.1.3 Random Number Assignment

9.2 Rough-Cut Modeling 9.3 Exercises

A Simulation Programming Examples

A.l Fortran A.2 SLAM II A.3 SIMAN IV A.4 GPSS/H

References Index

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