Introduction to Stochastic Processes and Simulation

Table of contents

1. Cover
2. Preface
3. Part 1: Basic Mathematical Concepts
   1. 1 Basic Reminders of Probability
      1. 1.1. Chance
      2. 1.2. Counting and probability
      3. 1.3. Events and probability
      4. 1.4. Statistics and probability
      5. 1.5. Compound probability
      6. 1.6. Graphs, states, transitions
   2. 2 Probabilistic Models
      1. 2.1. Random variables
      2. 2.2. Mean, variance, standard deviation
      3. 2.3. Some common distributions
      4. 2.4. Stochastic processes
      5. 2.5. Appendix
   3. 3 Inventory Management
      1. 3.1. General
      2. 3.2. Introductory example
      3. 3.3. Wilson’s model: assumptions 3.1
      4. 3.4. Wilson’s model: assumptions 3.2
      5. 3.5. Probabilistic Wilson’s model: assumptions 3.3
      6. 3.6. Safety and quality
      7. 3.7. Appendix
4. Part 2: Stochastic Processes
   1. 4 Markov Chains
      1. 4.1. Markov chain concepts
      2. 4.2. Concepts in graphs
      3. 4.3. Ergodicity
      4. 4.4. Random paths
   2. 5 Markov Processes
      1. 5.1. The concept of Markov processes
      2. 5.2. Poisson process
      3. 5.3. Poisson distribution and exponential distribution
      4. 5.4. Birth process and death process
      5. 5.5. Combination of the two processes, birth and death
   3. 6 Queueing Systems
      1. 6.1. Introduction
      2. 6.2. M/M/1 queue with 1 station
      3. 6.3. M/M/S queue with S stations
      4. 6.4. Appendix: calculations for M/M/S
   4. 7 Various Applications
      1. 7.1. Reliability and availability of equipment
      2. 7.2. Applications in genetics
      3. 7.3. Population dynamics, predator–prey model
      4. 7.4. From physics to finance: Brownian motion
      5. 7.5. Appendix
5. Part 3: Simulation
   1. 8 Generator Programs
      1. 8.1. Random and pseudo-random numbers
      2. 8.2. Algorithms for the uniform distribution
      3. 8.3. Distribution function and random number generator
      4. 8.4. Generators for the normal distributions
      5. 8.5. Generators for any law
      6. 8.6. χ2 test
   2. 9 Principles of Simulation
      1. 9.1. General information on simulation
      2. 9.2. Simulation by example
      3. 9.3. Simulation according to a law of probability
      4. 9.4. Mathematical foundations
   3. 10 Simulation of Inventory Management
      1. 10.1. General provisions
      2. 10.2. Comparison of two inventory management policies
      3. 10.3. Comparison of various stock policies.
   4. 11 Simulation of a Queueing Process
      1. 11.1. General provisions
      2. 11.2. Simulation of an M/M/1 queue
      3. 11.3. Simulation of an M/M/S queue
   5. 12 Optimization and Simulation
      1. 12.1. Introduction
      2. 12.2. Local methods
      3. 12.3. Genetic algorithms
      4. 12.4. Ant colonies
6. References
7. Index
8. End User License Agreement