Course Syllabus for

# Queuing Theory Köteori

## EIT046F, 7.5 credits

Valid from: Autumn 2013
Decided by: FN1/Björn Regnell
Date of establishment: 2013-11-08

## General Information

Division: Electrical and Information Technology
Course type: Third-cycle course
Teaching language: English

## Aim

Modern multi-service communication systems are designed to support a large variety of flows. This is in contrast with traditional telecommunication systems where the dominant service was telephony. However, distributed server systems exhibit many similarities with traditional telecommunication systems from a stochastic performance point of view. It is necessary to understand the similarities and differences between these systems and their performance models in order to effectively conduct research in the areas of communication networks and distributed systems. Specifically, it is of utmost importance to be able to evaluate algorithm and component design when placed in their operational systems context in order to be able to compare design solutions and to be able to derive theoretical performance bounds. This course extends the material coverage from foundational queuing theory courses and studies in-depth, the effects of individual and combinations of different traffic regimes. The course also covers modeling of highly complex systems which enables the researcher to draw generalised conclusions about queuing modeling results. Students who successfully complete the course will be equipped with a deep understanding of the use of queuing theory to investigate and design distributed stochastic systems.

## Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• understand the methodologies and ways of attacking the theoretical properties and models of queuing systems.
• demonstrate understanding of the process of formulating models based on the z- and Laplace transforms, systems in equilibrium and Markov models.
• demonstrate understanding of the PASTA principle, the effect of large variances and non-standard probability distributions on the queuing models, i.e. M/G/1, G/M/1 and G/G/1 systems

Competences and Skills

For a passing grade the doctoral student must

• be able to independently construect models for queuing systems and be able to study their properties analytically.
• be able to study the system using busy periods and waiting time analysis.
• be able to develop their own worked examples in accordance with specific educational outcomes to undergraduate students.

Judgement and Approach

For a passing grade the doctoral student must

• be able to critically evaluate the correctness of obtained results
• be able to evaluate trustworthiness of obtained theoretical results from analysis with non-standard probability distributions.
• be well versed in the limitations of existing theory with general distributions and demonstrate sober judgement of the validity and accuracy of obtained results.

## Course Contents

The course covers queuing theory with applications in general distributed systems. The material focusses on the fundamental principles for the derivation of queuing models and their application in performance modeling. Strong emphasis is placed on modeling using Markov chains and the development of complex systems models from scratch. The course further covers different system models from distributed systems and networks and compares and contrasts them. Finally, the course covers the effects of heavy tailed distributions in both arrival rates and service rates.

## Course Literature

Kleinrock, L.: Queueing Systems. Wiley.

## Instruction Details

Types of instruction: Lectures, project, self-study literature review

## Examination Details

Examination formats: Oral exam, written assignments, seminars given by participants