Stochastic modeling and analysis of telecom networks /
Laurent Decreusefond, Pascal Moyal ; series editor Nikolaos Limnios.
- Hoboken, NJ : London : J. Wiley & Sons ; ISTE, 2012.
- 1 online resource (1 volume) : illustrations.
- ISTE .
- ISTE. .
Includes bibliographical references and index.
Cover; Stochastic Modeling and Analysis of Telecom Networks; Title Page; Copyright Page; Table of Contents; Preface; Chapter 1. Introduction; 1.1. Traffic, load, Erlang, etc.; 1.2. Notations and nomenclature; 1.3. Lindley and Beneš; 1.4. Notes and comments; PART 1: DISCRETE-TIME MODELING; Chapter 2. Stochastic Recursive Sequences; 2.1. Canonical space; 2.2. Loynes's scheme; 2.3. Coupling; 2.4. Comparison of stochastic recursive sequences; 2.5. Notes and comments; Chapter 3. Markov Chains; 3.1. Definition and examples; 3.2. Strong Markov property; 3.3. Classification of states. 3.4. Invariant measures and invariant probability3.5. Effective calculation of the invariant probability; 3.6. Problems; 3.7. Notes and comments; Chapter 4. Stationary Queues; 4.1. Single server queues; 4.2. Processor sharing queue; 4.3. Parallel queues; 4.4. The queue with S servers; 4.5. Infinite servers queue; 4.6. Queues with impatient customers; 4.7. Notes and comments; Chapter 5. The M/GI/1 Queue; 5.1. The number of customers in the queue; 5.2. Pollacek-Khinchin formulas; 5.3. Sojourn time; 5.4. Tail distribution of the waiting time; 5.5. Busy periods; PART 2: CONTINUOUS-TIME MODELING. Chapter 6. Poisson Process6.1. Definitions; 6.2. Properties; 6.3. Discrete analog: the Bernoulli process; 6.4. Simulation of the Poisson process; 6.5. Non-homogeneous Poisson process; 6.6. Cox processes; 6.7. Problems; Chapter 7. Markov Process; 7.1. Preliminaries; 7.2. Pathwise construction; 7.3. Markovian semi-group and infinitesimal generator; 7.4. Martingale problem; 7.5. Reversibility and applications; 7.6. Markov Modulated Poisson Processes; 7.7. Problems; 7.8. Notes and comments; Chapter 8. Systems with Delay; 8.1. Little's Formula; 8.2. Single server queue; 8.3. Multiple server queue. 8.4. Processor sharing queue8.5. The M / M / "queue; 8.6. The departure process; 8.7. Queuing networks; 8.8. Problems; 8.9. Notes and comments; Chapter 9. Loss Systems; 9.1. General; 9.2. Erlang model; 9.3. The M/M/1/1 + C queue; 9.4. The "trunk" effect; 9.5. Engset model; 9.6. IPP/M/S/S queue; 9.7. Generalized Erlang models; 9.8. Hierarchical networks; 9.9. A model with balking; 9.10. A call center with impatient customers; 9.11. Problems; 9.12. Notes and comments; PART 3: SPATIAL MODELING; Chapter 10. Spatial Point Processes; 10.1. Preliminary; 10.2. Stochastic geometry. 10.3. Poisson process; 10.4. Stochastic analysis; 10.5. Problems; 10.6. Notes and comments; Appendix A. Mathematical Toolbox; A.1. Probability spaces and processes; A.2. Conditional expectation; A.3. Vector spaces and orders; A.4. Bounded variation processes; A.5. Martingales; A.6. Laplace transform; A.7. Notes and comments; Bibliography; Index.
This book addresses the stochastic modeling of telecommunication networks, introducing the main mathematical tools for that purpose, such as Markov processes, real and spatial point processes and stochastic recursions, and presenting a wide list of results on stability, performances and comparison of systems. The authors propose a comprehensive mathematical construction of the foundations of stochastic network theory: Markov chains, continuous time Markov chains are extensively studied using an original martingale-based approach. A complete presentation of stochastic recursions from an.
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