### Teletraffic Theory

#### Course Description

#### General Competencies

Students gain knowledge in the fundamental models of information traffic flows and elementary methods for the traffic analysis, including voice and video traffic. Specifically, students develop a good understanding of the discrete and continuous time Markov chain and its application to different traffic scenarios in packet networks. Students gain a deep understanding of the loss network model applied to the heterogeneous guaranteed services in packet networks and techniques for the capacity sizing.

#### Learning Outcomes

- identify characteristic of queueing system
- explain models and methods for analyze queueing systems in communication networks
- apply simple methods from Traffic theory to communication networks analyzis
- analyze performance of information and communication systems
- explain phenomens in different application of queueing theory
- estimate and evaluate performances of different information and communication systems

#### Forms of Teaching

**Lectures**First cycle (seven weeks): lectures then Midterm exam, and Second cycle (six veeks): lectures and Final exam. Lecture duration: 3 hours per week

**Exams**Midterm exam: 8th week; Final exam: 15th week.

**Consultations**Every week in terms defined by lecturer.

**Other Forms of Group and Self Study**Homeworks

#### Grading Method

Continuous Assessment | Exam | |||||
---|---|---|---|---|---|---|

Type | Threshold | Percent of Grade | Threshold | Percent of Grade | ||

Mid Term Exam: Written | 0 % | 50 % | 0 % | |||

Final Exam: Written | 0 % | 40 % | ||||

Final Exam: Oral | 10 % | |||||

Exam: Written | 0 % | 90 % | ||||

Exam: Oral | 10 % |

##### Comment:

Although homeworks have 0% in a total share in this course, students are obliged to complete them successfully because it is a precondition for passing the exams.

#### Week by Week Schedule

- Markov processes: elementary models of telecommunication traffic. Discrete-time Markov chains. Continuous-time Markov chains. Birth-death processes. Numerical methods, evaluation of steady-state probabilities, global and local balance equations.
- Elementary Markov models. Reversibility and Burkes theorem. Evaluation of queuing models M/M/1, M/M/m, M/M/1/k, M/M/m/k, M/M/m/m. Application of Littles theorem.
- Loss networks. Erlangs model, Engsets model, multiservice loss networks, Kaufman-Roberts recursion.
- Numerical methods for analysis of loss networks. Jagermans approximation, Labourdette-Hart uniform asymptotic approximation (UAA), reduced load approximation, Kelly and Pascal reduced load approximation.
- Computer based modeling of telecommunication traffic. The use of Markov chains for modeling traffic, modeling telephone traffic according to Erlang and Engset models, modeling long-range dependent traffic. Tools for traffic analysis of telecommunication networks. NS2 simulator, OPNET simulator and others.
- Networks of queues. Open and closed queuing networks, product form solution and Jacksons theorem, local and global balance equations, BCMP networks.
- Numerical methods for evaluation of networks of Markovian queues. Convolution algorithms for closed networks, MVA, approximation and simulation procedures.
- Midterm examination.
- Analysis of M/GI/1 and GI/M/1 queuing system. Embedded Markov chain and its application to M/GI/1 and GI/M/1 queuing systems.
- M/GI/1 queuing systems with priorities. Analysis of the queuing system with the preemptive LCFS queuing discipline, queuing system with HOL service discipline, static priority queuing systems.
- Network traffic modeling (1). Continuous time and discrete time models: Poisson process, deterministic and Bernoulli process, modulated processes, general interrupted and switched stochastic processes, regressive models, fluid models, ARMA models.
- Network traffic modeling (2). Self-similarity in real packet networks, self-similar stochastic process, Hurst parameter, physical origins of the self-similarity, sub-exponential distributions, central limit theorem for distributions with infinite variances, a-stable distribution.
- Network traffic modeling (3). Analysis of real traffic traces and estimation of self-similarity level, Whittle’s estimator, fractal teletraffic models: fractional Brownian noise, fractional ARIMA process.
- Modeling of voice and video traffic. Voice traffic models based on continuous and discrete time Markov models; autoregressive, Markov, TES (Transform-Expand-Sample) and self-similar models of video traffic.
- Final examination.

#### Study Programmes

##### University graduate

#### Prerequisites

#### Literature

*Queuing Systems, Volume 1: Theory*, Wiley, New York

*Fundamentals of Queueing Theory, 4th ed.*, Wiley, New York

*Queuing Theory with Applications to Packet Telecommunication*, Springer

*System Modeling and Analysis: Foundations of System Performance Evaluation*, Pearson-Prentice Hall

*Computer Nertworks and Systems: Queueing Theory and Performance Evaluation?, 3rd ed.*, Springer

*Foundations of Queueig Theory N.U. Prabhu Kluwer 1997*,

#### Lecturers

#### General

**ID**34460

**5**ECTS

**L0**English Level

**L1**e-Learning

**45**Lectures

**0**Exercises

**0**Laboratory exercises

**0**Project laboratory

#### Grading System

**85**Excellent

**70**Very Good

**55**Good

**40**Acceptable