### Queueing Theory

#### Queueing Theory - BE2M32THOA

 Credits 6 Semesters Winter Completion Assessment + Examination Language of teaching English Extent of teaching 3P + 1L
Annotation
The aim of the course is to present an overview of dimensioning of telecommunication networks on the basis of results of the queuing theory (QT) and to introduce possibilities of simulation and modelling of networks, both from the point of view of grade of service (GoS) and quality of service (QoS). Results of the QT are applied on different service systems and telecommunication networks being currently operated and developed. Theoretical knowledge about models of service systems can be applied on dimensioning of different service systems in real life - not only on the telecommunications one.
Study targets
The aim of the course is to get acquainted with dimensioning of telecommunications networks on the basis of results of the queuing theory (QT). The acquired knowledge will be applied in an individual project focused on dimensioning of a data network.
Course outlines
1. Queueing theory in telecommunications. Types of service systems (SeSy), description and structure.
2. Mathematical model of SeSy, the assumptions of solution, derivation of probability state space. Kendall's notation of SeSy.
3. Flow of demands, characteristics, mathematical description. Poisson's flow, nature and character.
4. Parameters of SeSy. Traffic - lost and carried, blocking probability. Estimation of offered traffic.
5. Models M/G/N/0 specification. Generalized Erlang's model, application to packet networks.
6. Telecommunication network (TN) dimensioning. Overflow traffic - characteristics - SeSy dimensioning.
7. Models M/M/N/oo/FIFO (RANDOM, LIFO), parameters GoS.
8. Models M/M/N/R, specification, parameters GoS. Dimensioning.
9. Models G/M/N/, M/G/N/ and G/G/N/. Application.
10. Quality of service (QoS, GoS, NP). Dependability, availability and reliability of item / network.
11. Modeling of SeSy and TN. Matlab, SimEvents, OMNeT++.
12. Priority SeSy. Application in practice, models of queueing discipline and memory organisation (packet networks, PQ, CQ, LLQ, FQ, WFQ).
13. Service systems - models and methods of overload protections.
14. Traffic forecast methods, regression functions. Summary of the theory of loss and waiting SeSy for practical applications.
Exercises outlines
1. Introduction to seminars. Input information on the project.
2. Lab.: Loss SeSy - dimensioning - models M/G/N/0.
3. Lab.: Application of G/M/N, M/G/N and G/G/N models in telecommunication networks.
4. Lab.: Dimensioning of no-priority SeSy with waiting, application of M/M/N/R model.
5. Lab.: Introduction to SimEvents simulator, simulation of M/M/N/R SeSy.
6. Lab.: Influence of queueing discipline (FIFO, WFQ, CQ, PQ) on QoS in a packet network.
7. Applications of generalized Erlang's model in dimensioning. Assignment of credits.
Literature
[1] Gross, D., Harris, C., M. Fundamentals of queuing theory. Third Edition. New York, London: J. Wiley and Sons, 1998. 439 p. ISBN 0-471-17083-6.
[2] Villy B. Iversen. Teletraffic Engineering and Network Planning. Geneva: ITC in cooperation with ITU-D SG2, May 2010. ftp://ftp.dei.polimi.it/users/Flaminio.Borgonovo/Teoria/teletraffic_Iversen.pdf, 623 p.
[3] Cooper R.B. Introduction to queueing theory. North Holland, 2nd edition,1981. 347 p. ISBN-13: 978-0444003799 http://www.cse.fau.edu/~bob/publications/IntroToQueueingTheory_Cooper.pdf
[4] Amir Ranjbar. CCNP ONT Official Exam Certification Guide. Cisco Press; Har/Cdr edition, 2007. 408 p. ISBN-10: 1587201763, ISBN-13: 978-1587201769.
[5] http://www.itu.int/rec/T-REC/e
Requirements
The student should be familiar with the basics of the theory of stochastic processes and probability methods used for their description in the scope of course "Probability and Statistics".