### Queueing Theory

##### B232 - Summer 23/24
This is a grouped Moodle course. It consists of several separate courses that share learning materials, assignments, tests etc. Below you can see information about the individual courses that make up this Moodle course.

#### Queueing Theory - B2M32THO

##### Main course
 Credits 5 Semesters Winter Completion Assessment + Examination Language of teaching Czech 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. Application of queuing theory in telecommunications. Classification of service systems (SeSy), description and structure.
2. Flow of demands, characteristics, mathematical specification. Poisson flow, its nature and character.
3. Mathematical model of SeSy, assumptions of solution, probabilities of states derivation. Kendall's notation.
4. Parameters of SeSy. Traffic - lost and carried, blocking probability. Estimation of offered traffic. Traffic forecast methods, regression functions.
5. Models M/G/N/0 - specification, GoS parameters.
6. Telecommunication network (TN) dimensioning, traffic overflow, Wilkinson's equivalent method.
7. Models M/M/N/R - specification, GoS parameters. Dimensioning.
8. Models G/M/N, M/G/N and G/G/N. Application in UMTS networks.
9. Quality of service (QoS, GoS, NP). Dependability, availability and reliability of an item / network.
10. Modelling of SeSy and TN, application possibilities, limits of tools: MATLAB, SimEvents, OMNeT++.
11. SeSy with priorities. Application in data networks, realisations of queueing discipline (PQ, CQ, LLQ, FQ, WFQ).
12. Service systems - models and methods of overload protection.
13. Generalized Erlang's model, application in networks with packet switching, dimensioning.
14. Summary of the theory of loss SeSy and queuing 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] Křížovský, F., Kříž, P. Šťastný, M, Vaněk, N. Provozní zatížení v telekomunikacích - unpublished. Chapters 1 - 5. http://moodle.fel.cvut.cz
[2] 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.
[3] 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.
[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".

#### Applied Queueing Theory - A8M32AQT

 Credits 6 Semesters Winter Completion Assessment + Examination Language of teaching Czech Extent of teaching 3P + 1C