More About Stochastic Modeling: Analysis and Simulation

Stochastic Modeling: Analysis And Simulation, Dover Publications, Inc. (1995), 336pp., by Barry L. Nelson, ISBN 0-486-42569-X. Also a solutions manual available from the publisher. The solutions manual includes detailed solutions to all exercises.

Stochastic Modeling: Analysis And Simulation is an introduction to techniques for modeling dynamic, stochastic systems, and to the mathematical, numerical and simulation tools used to analyze them. It is designed for engineering, computer science and mathematics undergraduates, but will be appropriate for some introductory graduate courses.

The unifying theme is that systems can be modeled in terms of how they would be simulated, whether or not simulation is actually employed for the analysis. Starting from this general formulation, the conditions that permit a mathematical-numerical analysis are revealed. Poisson and renewal processes, Markov chains in discrete and continuous time, semi-Markov processes and queueing processes are covered.

Each chapter begins with a miniature case that is carried throughout as an illustration. The presentation includes formulation of models, parameterizing models from data, analysis of models and interpretation of results. Programming-language independent algorithms are provided for all simulation and numerical procedures.

Table of Contents


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