# Queueing Theory

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 (Main course) B2M32THOA
 Credits 6 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
Annotation
Cílem předmětu je podat přehled dimenzování telekomunikačních sítí na základě poznatků z teorie hromadné obsluhy
THO. Seznamit s možnostmi simulace a modelování sítí z hlediska posouzení kvality obsluhy GOS i jakosti služby QoS.
Závěry THO jsou aplikovány na typy obsluhových systémů a telekomunikačních sítí, které se v současné době provozují
a rozvíjejí. Teoretické poznatky o modelech obsluhových systémů umožňují aplikace i na jiné obsluhové systémy než
ryze telekomunikační
Course outlines
1. Aplikace THO v telekomunikacích. Klasifikace obsluhových systémů (OS), jejich popis a uspořádání.
2. Matematický model OS, předpoklady řešení, odvození pravděpodobností stavů. Kendallovo značení OS.
3. Tok požadavků, matematický popis. Poissonovský tok, vlastnosti.
4. Parametry OS. Ztráta, blokování, výkon. Odhad nabídky.
5. Modely OS typu M/G/N/0. Zobecněný Erlangův model, aplikace na sítě s přepojováním paketů.
6. Dimenzování TS. Přeliv toků - charakter - dimenzování OS.
7. Modely OS typu M/M/N/inf./FIFO (RANDOM, LIFO), parametry GoS.
8. Modely OS typu M/M/N/R, popis, parametry GoS. Dimenzování.
9. Modely OS typu G/M/N, M/G/N a G/G/N. Aplikace.
10. Hodnocení jakosti služeb (QoS, GoS, NP). Spolehlivost, bezporuchovost, pohotovost prvku a sítě.
11. Principy simulace OS a TS, aplikační možnosti, omezení nástrojů MATLAB, SimEvents, OMNeT++.
12. OS s prioritami. Aplikace v praxi, metody režimů fronty a organizace pamětí (paketové sítě, PQ, CQ, LLQ, FQ, WFQ).
13. Přetížení sítě, modely omezení toků před a při přetížení sítě.
14. Metody předpovědi vývoje, regresní funkce. Závěry z teorie OS se ztrátou a smíšených pro aplikace v praxi.
Exercises outlines
1. Úvod do cvičení, seznámení se zadáním projektu.
2. Lab.: Dimenzování OS se ztrátou - modely typu M/G/N/0.
3. Lab.: Aplikace modelů G/M/N, M/G/N a G/G/N.
4. Lab.: Dimenzování OS s čekáním bez priorit, aplikace modelu M/M/N/R.
5. Lab.: Úvod do prostředí SimEvents, simulace systému M/M/N/R.
6. Lab.: Vliv režimů fronty (FIFO, WFQ, CQ, PQ) na QoS v paketové síti.
7. Aplikace zobecněného Erlangova modelu na dimenzování. Zápočet.
Literature
[1] Křížovský, F., Kříž, P. Šťastný, M, Vaněk, N. Provozní zatížení v telekomunikacích - nepublikováno. Kapitoly 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
##### Sizing of communications networks XP32DKS
 Credits 4 Semesters Summer Completion Exam Language of teaching Czech Extent of teaching 2P + 2C+ 2D
Annotation
No data.
Course outlines
1. Network topology, network types, queueing theory
2. Using graph theory, algorithms over graphs
3. Flows in networks, sizing of edges and nodes
4. Reliability of communication networks, methods of increasing reliability
5. Classification of service systems, mathematical description
6. Waiting and lost serving systems
7. Models of G / G / N / X service systems
8. Service quality parameters, consequences for sizing
9. Conclusions from the theory of service systems, matrix description
10. Application of queueing theory, queueing mechanisms
11. Using simulation environments for network modelling
12. Input flow description and simulation runtime control
13. Output flow analysis, statistical processing
14. Search for behaviour patterns and sorting of network responses
Exercises outlines
1. Introduction to network modelling
2. Working with topological data, import from GIS
3. Operations over graphs, optimization tasks
4. Using graph theory
5. Application of the queueing theory
6. Simulation environment OMNET / OMNEST
7. Description of input flows
8. Simulation runtime control
9. Display of simulation outputs
10. Output flow analysis
11. Statistical processing of simulation results
12. Project in the OMNET / OMNEST environment
13. Project in the OMNET / OMNEST environment
14. Evaluation of Project in the OMNET / OMNEST environment
Literature
Gross, D., Harris, C., M. Fundamentals of queuing theory. Third Edition. New York: J. Wiley and Sons,INC. 1998.
Medhi, J. Stochastics Models in Queueing Theory. Second Edition. Amsterdam: Academic Press 2003.
Nader F. Mir. Computer and Communication Networks. Prentice Hall, 2014. ISBN 0133814831
Martin Charles Golumbic, Irith Ben-Arroyo Hartman. Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications. Springer, 2011. ISBN 1441937234
Responsible for the data validity: Study Information System (KOS)