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 process -- 3.4. 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. Reversibility -- 4.13. 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 processes -- 5.17. 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 networks -- 7.7. 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 -- 9.5. Mean throughput -- 9.6. Loss rate -- 9.7. Multirate model -- 9.8. Recursive formula -- 9.9. Network models -- 9.10. Gaussian approximation -- 9.11. Exercises -- 9.12. Solution to the exercises -- Chapter 10. Elastic Traffic -- 10.1. Bandwidth sharing -- 10.2. Congestion rate -- 10.3. Mean throughput -- 10.4. Loss rate -- 10.5. Multirate model -- 10.6. Recursive formula -- 10.7. Network model -- 10.8. Exercises -- 10.9. Solution to the exercises -- Chapter 11. Network Performance.

11.1. IP access networks -- 11.1.1. Poisson arrivals -- 11.1.2. Finite population -- 11.1.3. Approximation -- 11.2. 2G mobile networks -- 11.2.1. Voice traffic -- 11.2.2. Data traffic -- 11.3. 3G mobile networks -- 11.3.1. Uplink -- 11.3.2. Downlink -- 11.4. 3G+ mobile networks -- 11.4.1. Homogeneous case -- 11.4.2. Heterogeneous case -- 11.5. WiFi access networks -- 11.5.1. UDP traffic -- 11.5.2. TCP traffic -- 11.5.3. Random traffic -- 11.6. Data centers -- 11.6.1. Static routing -- 11.6.2. Greedy routing -- 11.6.3. Adaptive routing -- 11.7. Cloud computing -- 11.8. Exercises -- 11.9. Solution to the exercises -- Index.