Network performance analysis /
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 a...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
London : Hoboken, NJ :
ISTE ; John Wiley,
2011.
|
| Series: | ISTE.
|
| Subjects: | |
| Online Access: | CONNECT |
Table of Contents:
- 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
