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.

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.

Self-study based on video and other on-line material. The self study is a significant part of the course. The students should reserve at least 10 hours per week for self-study.

Lectures in class: to cover and discuss the challening parts of the theory content

Problem solving in class: to discuss numerical examples and previous exam problems

Home assignments:

- two large home assignments to practice probability theory, and basic queuing theory

- several small home assignments to check the understanding of the theory before attending the in class activities

Project: to solve practical modelling problems, to practice the use of mathematical software tools, and to practice scientific writing.

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

During the course you will have to use Latex (e.g., on Overleaf) and mathmatical software, like Matlab or Mathematica. You should make sure that these run smoothly on your computer.

All reading material is accessible throguh the course web in Canvas. If you want to use a more advanced book, you can find suggestions in Canvas.

Students will have to use Latex as text editor.

Some math software (e.g., Matlab or Matematica) is needed for the project.

Students at KTH with a permanent disability can get support during studies from Funka:

Funka - compensatory support for students with disabilities

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

• 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.

Assignment ( INL1 )

Includes two large home assignments, several small home assignments and a small project. Each of these has to be completed to 75% to pass this examination moment.

Examination ( TEN1 )

The format of the final exam is changed in 2022. There is a short written part, followed by an oral part. 

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

Assignments: 75% should be completed in each home assignment, in the project, and across all the small assignments.

Exam: E,D can be achieved with correct and well preseneted written problems. The grade can be increased to C,B,A in the oral part. The written part is compulsory. The oral part is not compulsory.

As oral examination is included in the final exam, no students will get FX. Supplementary examination is not possible.

It is allowed to try to raise approved grade in the re-examination period.

Students who did not pass the Assignment moment, but were active throughout the course can receive additional problems to complement.

The results of the Assignments moment are registered within a week after the last deadline.

The results of the final exam, and the final results of the course are registered within three weeks after the final exam.

• 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.

The learning activities are changed in this course round. The examination was changed in 2022.

Learning activities: Video recordings are available for all theory and problem solving topics, together with written material. Therefore, a flipped classroom model is followed with significant part of self study and weekly in-class meetings to discuss the challenging parts of the theory and to look at non-trivial numerical problems together. 

Examination:

- To ensure continuous learning,  there are small home assignments for each topic. 

- The final exam consists of a written and an oral part.