# EP2200 Queuing Theory and Teletraffic Systems 7.5 credits

#### Köteori och teletrafiksystem

Queuing theory is the basis for performance evaluation and dimensioning of telecommunication and computer communication networks, road traffic systems, and transport systems in general. This course treats queuing systems with an emphasis on the classical models. The theory is illustrated by problems drawn from telecommunication and computer communication.

### Offering and execution

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## Course information

### Content and learning outcomes

#### Course contents *

The classical theory of queueing systems:

• Discrete and continuous time Markov chains, birth-death processes, and the Poisson process.
• Basic terminology of queuing systems, Kendall’s notation and Little’s theorem.
• Markovian waiting systems with one or more servers, and systems with infinite as well as finite buffers and finite user populations (M/M/).
• Systems with general service distributions (M/G/1):  the method of stages, Pollaczek-Khinchin mean-value formula and and systems with priority and interrupted service.
• Loss systems according to Erlang, Engset and Bernoulli.
• Open and closed queuing networks, Jacksonian networks.

The theory is illustrated by examples from telecommunication and computer communication such as blocking in circuit switched networks, preventive and reactive congestion control, and traffic control for guaranteeing quality of service.

Furthermore, students develop their skills to perform performance analysis of queuing systems and to present the results, using mathematical software and suitable text editors.

#### Intended learning outcomes *

After passing the course, the student should be able to

• explain the basic theory of Markov-processes and apply the theory to model queuing systems,
• derive and use analytic models of of Markovian queuing systems, queuing networks and also some simpler non-Markovian systems,
• explain and use results derived for complex non-Markovian systems,
• define queuing models of communication or computer systems, and derive the performance of these systems,
• use adequate tools to present scientific work,

in order to be able to carry out mathematical modeling based performance evaluation of communication, computing, or other resource sharing systems.

#### Course Disposition

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### Literature and preparations

#### Specific prerequisites *

For non-program students: 120 credits and English B or the equivalent

#### Recommended prerequisites

SF1901 Probability Theory and Statistics, or similar. Basic knowledge in networking is helpful, but not mandatory.

#### Equipment

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#### Literature

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### Examination and completion

A, B, C, D, E, FX, F

#### Examination *

• INL1 - Assignment, 1.5 credits, Grading scale: P, F
• TEN1 - Examination, 6.0 credits, Grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

#### Other requirements for final grade *

Written examination (TEN1;  5 credits)
Written assignment (INL1;  1.5 credits)

#### Opportunity to complete the requirements via supplementary examination

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#### Opportunity to raise an approved grade via renewed examination

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### Further information

#### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web EP2200

#### Offered by

EECS/Computer Science

#### Main field of study *

Computer Science and Engineering, Information and Communication Technology

#### Education cycle *

Second cycle

EP2300 Management of Networks and Networked Systems
EP2210 Performance analysis of communication networks

Viktoria Fodor

#### Ethical approach *

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

#### Supplementary information

In this course, the EECS code of honor applies, see: http://www.kth.se/en/eecs/utbildning/hederskodex.