Network performance analysis [[electronic resource] /] / Thomas Bonald, Mathieu Feuillet

• Record Nr.: UNINA9910138863003321
• Autore: Bonald Thomas
• Pubbl/distr/stampa: London, : ISTE; Hoboken, N.J., : John Wiley, 2011
• ISBN: 1-118-60291-9; 1-118-60285-4; 1-118-60283-8; 1-299-18780-3
• Descrizione fisica: 1 online resource (267 p.)
• Collana: ISTE
• Altri autori (Persone): FeuilletMathieu
• Disciplina: 621.382
• Soggetti: Computer networks - Evaluation; Network performance (Telecommunication); Queuing theory
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover; Title Page; Copyright Page; Table of Contents; Preface; Chapter 1. Introduction; 1.1. Motivation; 1.2. Networks; 1.3. Traffic; 1.4. Queues; 1.5. Structure of the book; 1.6. Bibliography; Chapter 2. Exponential Distribution; 2.1. Definition; 2.2. Discrete analog; 2.3. An amnesic distribution; 2.4. Minimum of exponential variables; 2.5. Sum of exponential variables; 2.6. Random sum of exponential variables; 2.7. A limiting distribution; 2.8. A ""very"" random variable; 2.9. Exercises; 2.10. Solution to the exercises; Chapter 3. Poisson Processes; 3.1. Definition; 3.2. Discrete analog; 3.3. An amnesic process3.4. Distribution of the points of a Poisson process; 3.5. Superposition of Poisson processes; 3.6. Subdivision of a Poisson process; 3.7. A limiting process; 3.8. A ""very"" random process; 3.9. Exercises; 3.10. Solution to the exercises; Chapter 4. Markov Chains; 4.1. Definition; 4.2. Transition probabilities; 4.3. Periodicity; 4.4. Balance equations; 4.5. Stationary measure; 4.6. Stability and ergodicity; 4.7. Finite state space; 4.8. Recurrence and transience; 4.9. Frequency of transition; 4.10. Formula of conditional ; transitions; 4.11. Chain in reverse time; 4.12. Reversibility4.13. Kolmogorov's criterion; 4.14. Truncation of a Markov chain; 4.15. Random walk; 4.16. Exercises; 4.17. Solution to the exercises; Chapter 5. Markov Processes; 5.1. Definition; 5.2. Transition rates; 5.3. Discrete analog; 5.4. Balance equations; 5.5. Stationary measure; 5.6. Stability and ergodicity; 5.7. Recurrence and transience; 5.8. Frequency of transition; 5.9. Virtual transitions; 5.10. Embedded chain; 5.11. Formula of conditional transitions; 5.12. Process in reverse time; 5.13. Reversibility; 5.14. Kolmogorov's criterion; 5.15. Truncation of a reversible process; 5.16. Product of independent Markov processes5.17. Birth-death processes; 5.18. Exercises; 5.19. Solution to the exercises; Chapter 6. Queues; 6.1. Kendall's notation; 6.2. Traffic and load; 6.3. Service discipline; 6.4. Basic queues; 6.5. A general queue; 6.6. Little's formula; 6.7. PASTA property; 6.8. Insensitivity; 6.9. Pollaczek-Khinchin's formula; 6.10. The observer paradox; 6.11. Exercises; 6.12. Solution to the exercises; Chapter 7. Queuing Networks; 7.1. Jackson networks; 7.2. Traffic equations; 7.3. Stationary distribution; 7.4. MUSTA property; 7.5. Closed networks; 7.6. Whittle networks7.7. Kelly networks; 7.8. Exercises; 7.9. Solution to the exercises; Chapter 8. Circuit Traffic; 8.1. Erlang's model; 8.2. Erlang's formula; 8.3. Engset's formula; 8.3.1. Model without blocking; 8.3.2. Model with blocking; 8.4. Erlang's waiting formula; 8.4.1. Waiting probability; 8.4.2. Mean waiting time; 8.5. The multiclass Erlang model; 8.6. Kaufman-Roberts formula; 8.7. Network models; 8.8. Decoupling approximation; 8.9. Exercises; 8.10. Solutions to the exercises; Chapter 9. Real-time Traffic; 9.1. Flows and packets; 9.2. Packet-level model; 9.3. Flow-level model; 9.4. Congestion rate
• Sommario/riassunto: The book presents some key mathematical tools for the performance analysis of communication networks and computer systems.Communication networks and computer systems have become extremely complex. The statistical resource sharing induced by the random behavior of users and the underlying protocols and algorithms may affect Quality of Service.This book introduces the main results of queuing theory that are useful for analyzing the performance of these systems. These mathematical tools are key to the development of robust dimensioning rules and engineering methods. A number of examples i