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Informationen zum Autor Henk C. Tijms is a Dutch mathematician and Emeritus Professor of Operations Research at the VU University Amsterdam. He studied mathematics in Amsterdam where he graduated from the University of Amsterdam in 1972 under supervision of Gijsbert de Leve. Klappentext The field of applied probability has changed profoundly in the past twenty years. The development of computational methods has greatly contributed to a better understanding of the theory. A First Course in Stochastic Models provides a self-contained introduction to the theory and applications of stochastic models. Emphasis is placed on establishing the theoretical foundations of the subject, thereby providing a framework in which the applications can be understood. Without this solid basis in theory no applications can be solved.* Provides an introduction to the use of stochastic models through an integrated presentation of theory, algorithms and applications.* Incorporates recent developments in computational probability.* Includes a wide range of examples that illustrate the models and make the methods of solution clear.* Features an abundance of motivating exercises that help the student learn how to apply the theory.* Accessible to anyone with a basic knowledge of probability.A First Course in Stochastic Models is suitable for senior undergraduate and graduate students from computer science, engineering, statistics, operations resear ch, and any other discipline where stochastic modelling takes place. It stands out amongst other textbooks on the subject because of its integrated presentation of theory, algorithms and applications. Zusammenfassung An integrated presentation of theory, applications and algorithms that demonstrates how useful simple stochastic (random) models can be for gaining insight into the behaviour of complex stochastic systems. The methods described can be used to obtain solutions to problems in statistics, operations research, finance, economics and engineering. Inhaltsverzeichnis Preface ix 1 The Poisson Process and Related Processes 1 1.0 Introduction 1 1.1 The Poisson Process 1 1.1.1 The Memoryless Property 2 1.1.2 Merging and Splitting of Poisson Processes 6 1.1.3 The M/G/¿ Queue 9 1.1.4 The Poisson Process and the Uniform Distribution 15 1.2 Compound Poisson Processes 18 1.3 Non-Stationary Poisson Processes 22 1.4 Markov Modulated Batch Poisson Processes 24 Exercises 28 Bibliographic Notes 32 References 32 2 Renewal-Reward Processes 33 2.0 Introduction 33 2.1 Renewal Theory 34 2.1.1 The Renewal Function 35 2.1.2 The Excess Variable 37 2.2 Renewal-Reward Processes 39 2.3 The Formula of Little 50 2.4 Poisson Arrivals See Time Averages 53 2.5 The Pollaczek-Khintchine Formula 58 2.6 A Controlled Queue with Removable Server 66 2.7 An Up- And Downcrossing Technique 69 Exercises 71 Bibliographic Notes 78 References 78 3 Discrete-Time Markov Chains 81 3.0 Introduction 81 3.1 The Model 82 3.2 Transient Analysis 87 3.2.1 Absorbing States 89 3.2.2 Mean First-Passage Times 92 3.2.3 Transient and Recurrent States 93 3.3 The Equilibrium Probabilities 96 3.3.1 Preliminaries 96 3.3.2 The Equilibrium Equations 98 3.3.3 The Long-run Average Reward per Time Unit 103 3.4 Computation of the Equilibrium Probabilities 106 3.4.1 Methods for a Finite-State Markov Chain 107 3.4.2 Geometric Tail Approach for an Infinite State Space 111 3.4.3 Metropolis-Hastings Algorithm 116 3.5 Theoretical Considerations 119 3.5.1 State Classification 119 3.5.2 Ergodic Theorems 126 Exercises 134 Bibliographic Notes 139 References 139
