Queues Applied to Telecoms: Courses and Exercises

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Cover Title Page Copyright Page Contents Notations Preface Part 1. Typical Processes in Queues Chapter 1. The Poisson Process 1.1. Review of the exponential distribution 1.1.1. Definitions 1.1.2. The properties of an exponential distribution 1.2. Poisson process 1.2.1. Definitions 1.2.2. Properties of the Poisson process 1.3. Exercises Chapter 2. Markov Chains 2.1. Markov chains in discrete time 2.1.1. Definitions 2.1.2. Evolution of a stochastic vector over time 2.1.3. Asymptotic behavior 2.1.4. Holding time in a state 2.1.5. Time-reversible chain 2.1.6. Reversible Markov chains 2.1.7. Kolmogorov’s criterion 2.2. Markov chains in continuous time 2.2.1. Definitions 2.2.2. Evolution over time 2.2.3. Resolving the state equation 2.2.4. Asymptotic behavior 2.3. Birth and death process 2.3.1. Definition 2.3.2. Infinitesimal stochastic generator 2.3.3. Stationary distribution 2.4. Exercises Part 2. Queues Chapter 3. Common Queues 3.1. Arrival process of customers in a queue 3.1.1. The Poisson process 3.1.2. Using the Poisson distribution 3.1.3. Exponential distribution of delay times 3.2. Queueing systems 3.2.1. Notation for queueing systems 3.2.2. Little distributions 3.2.3. Offered traffic 3.3. M/M/1 queue 3.3.1. Stationary distribution 3.3.2. Characteristics of the M/M/1 queue 3.3.3. Introducing a factor of impatience 3.4. M/M/‡ queue 3.5. M/M/n/n queue 3.5.1. Stationary distribution 3.5.2. Erlang-B formula 3.5.3. Characteristics of the M/M/n/n queue 3.6. M/M/n queue 3.6.1. Stationary distribution 3.6.2. Erlang-C formula 3.6.3. Characteristics of the M/M/n queue 3.7. M/GI/1 queue 3.7.1. Stationary distribution 3.7.2. Characteristics of the M/GI/1 queue 3.8. Exercises Chapter 4. Product-Form Queueing Networks 4.1. Jackson networks 4.1.1. Definition of a Jackson network 4.1.2. Stationary distribution 4.1.3. The particular case of the Jackson theorem for open networks 4.1.4. Generalization of Jackson networks: BCMP networks 4.2. Whittle networks 4.2.1. Definition of a Whittle network 4.2.2. Stationary distribution 4.2.3. Properties of a Whittle network 4.3. Exercise Part 3. Teletraffic Chapter 5. Notion of Teletraffic 5.1. Teletraffic and its objectives 5.2. Definitions 5.2.1. Measures in teletraffic 5.2.2. Sources and resources 5.2.3. Requests and holding time 5.2.4. Traffic 5.3. Measuring and foreseeing traffic 5.3.1. Traffic and service quality 5.3.2. Measuring traffic 5.3.3. Markovian model of traffic 5.3.4. Economy and traffic forecasting 5.4. Exercises Chapter 6. Resource Requests and Activity 6.1. Infinite number of sources 6.1.1. Distribution of requests in continuous time 6.1.2. Distribution of requests in discrete time 6.1.3. Duration of activity distributions 6.1.4. Distribution of busy sources 6.2. Finite number of sources 6.2.1. Modeling with birth and death processes 6.2.2. Distribution of requests 6.3. Traffic peaks and randomness 6.3.1. Traffic peaks 6.3.2. Pure chance traffic 6.4. Recapitulation 6.5. Exercises Chapter 7. The Teletraffic of Loss Systems 7.1. Loss systems 7.1.1. Definitions 7.1.2. Blocking and loss 7.2. The Erlang model 7.2.1. Infinite number of resources 7.2.2. Finite number of resources 7.2.3. Erlang-B formula 7.2.4. Dimensioning principles 7.3. Engset model 7.3.1. Sufficient number of resources 7.3.2. Insufficient number of resources 7.3.3. On the Engset loss formula 7.4. Imperfect loss systems 7.4.1. Loss probability in an imperfect system with limited and constant accessibility 7.4.2. Losses in a system with limited and variable accessibility 7.5. Exercises Chapter 8. Teletraffic in Delay Systems 8.1. Delay system 8.1.1. Description 8.1.2. Characteristics of delay 8.2. Erlang model 8.2.1. Infinitely long queue 8.2.2. Erlang-C formula 8.2.3. Distribution of delays 8.3. Finite waiting capacity model 8.3.1. Queues of finite length 8.3.2. Limitations affecting the delay 8.4. Palm model 8.4.1. M/M/n/N/N queue 8.4.2. Characteristics of traffic 8.5. General distribution model for activity 8.5.1. The Pollaczek–Khinchine formula 8.5.2. Activity with a constant duration 8.6. Exercises Part 4. Answers to Exercises Chapter 9. Chapter 1 Exercises Chapter 10. Chapter 2 Exercises Chapter 11. Chapter 3 Exercises Chapter 12. Chapter 4 Exercise Chapter 13. Chapter 5 Exercises Chapter 14. Chapter 6 Exercises Chapter 15. Chapter 7 Exercises Chapter 16. Chapter 8 Exercises Part 5. Appendices Appendix 1 Appendix 2 References Index EULA