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.

Lectures: to cover the theory part of the course

Recitations: for problem solving

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 recitation

Small project: to solve practical modelling problems and practice the use of mathematical tools.

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

All reading material is accessible throguh the course web in Canvas. There students can also find suggested books.

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

Funka - compensatory support for students with disabilities

Please inform the course coordinator if you need compensatory support during the course. Present a certificate from Funka.

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 to fit the present circumstances. On-line, open-book written exam for three hours, followed by oral examination for each student.

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

Assignments: 75% should be completed from each time of assignments.

Exam: 25 out of 50 points is needed for a pass grade. 

Students reaching 21 points receive FX and has to complement with a shorter written+oral exam.

It is allowed to try to raise approved grade.

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.

Compared to previous course rounds, the course is slightly changed to fit the circumstances of the distance education. The changes include:

- additional small home assignemnts from lecture to lecture

- shortened final written exam, which is now in open book format

- additional final oral exam, right after. the written exam