Introduction to Stochastic Processes and Simulation

Mastering chance has, for a long time, been a preoccupation of mathematical research. Today, we possess a predictive approach to the evolution of systems based on the theory of probabilities. Even so, uncovering this subject is sometimes complex, because it necessitates a good knowledge of the underlying mathematics. This book offers an introduction to the processes linked to the fluctuations in chance and the use of numerical methods to approach solutions that are difficult to obtain through an analytical approach. It takes classic examples of inventory and queueing management, and addresses more diverse subjects such as equipment reliability, genetics, population dynamics, physics and even market finance. It is addressed to those at Master's level, at university, engineering school or management school, but also to an audience of those in continuing education, in order that they may discover the vast field of decision support.

Preface ix

Part 1. Basic Mathematical Concepts 1

Chapter 1. Basic Reminders of Probability 3

Chapter 2. Probabilistic Models 25

Chapter 3. Inventory Management 45

Part 2. Stochastic Processes 69

Chapter 4. Markov Chains 71

Chapter 5. Markov Processes 95

Chapter 6. Queueing Systems 113

Chapter 7. Various Applications 131

Part 3. Simulation 181

Chapter 8. Generator Programs 183

Chapter 9. Principles of Simulation 203

Chapter 10. Simulation of Inventory Management 233

Chapter 11. Simulation of a Queueing Process 245

Chapter 12. Optimization and Simulation 257

References 285

Index 287

Gérard-Michel Cochard was made an Emeritus Professor at the University of Picardie Jules Verne, Amiens, France. In the past he held many responsibilities at National Conservatory of Arts and Crafts (CNAM) and the Ministry of National Education. At present, he researches within the Eco-Processes, Optimization and Decision Support (EPROAD) Laboratory at the University of Picardie Jules Verne.