EIT046F

Temporary

Queuing Theory

7.5

Third-cycle course

7201 (Electrical and Information Technology)

 -11-08

FN1/Björn Regnell

English

Every other autumn semester

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.

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.

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

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.

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.

Lectures

Project

Self-study literature review

Oral exam

Written assignments

Seminars given by participants

Failed, pass

Kleinrock, L.: Queueing Systems. Wiley.

Course coordinator: Björn Landfeldt, bjorn.landfeldt@eit.lth.se

EIT046F

 -11-08

FN1/Björn Regnell