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HF2000 Queuing Theory 7.5 credits

Course offerings are missing for current or upcoming semesters.
Headings with content from the Course syllabus HF2000 (Autumn 2007–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

  • Stochastic processes. Markov chains in discrete and continuous time. Chapman-Kolmogorov equations. Stationary probabilities. Poisson process. Birth-death processes.
  • Basic concepts in queuing theory. Little’s theorem.
  • Arrival processes and service time. Queuing disciplines. Stationary probabilities. Offered load (traffic). Blocked load. Effective load. Utilization. Blocking probability.
  • Markovian wait systems.
  • M/M/m: Queuing systems with m servers, infinite number of waiting positions, and infinite number of customers.
  • M/M/m/K: queuing system with m servers, limited number (=K) waiting positions, and infinite number of customers.
  • M/M/m/K/C: queuing system with m servers, limited number (=K) waiting positions, and limited number of customers (=C).
  • Markovian loss systems: Erlang’s loss system, Engset’s loss system, Binomial (Bernoulli’s) loss system.
  • Semi-markovian M/G/1 and G/M/l queuing systems. Pollacsek-Khinchin formula.
  • Survey on open and closed Jackson queuing networks.

Intended learning outcomes

After completion of the course the student should be able to:

  • Define and explain basic concepts in the theory Markov processes, M/M/m, M/M/m/K, and M/M/m/K/C queuing systems
  • Derive and apply main formulas for some properties (such as stationary probabilities, average waiting and system time, expected number of customers in the queue, etc.) of M/M/m, M/M/m/K, and M/M/m/K/C queuing systems
  • To calculate the traffic intensity, blocked traffic, and the utilization of some queuing systems
  • Solve some simple problems on queuing networks
  • Analyze and solve problems using computer aid (Maple, Matlab, or Mathematica)

Literature and preparations

Specific prerequisites

Basic knowledge in calculus, linear algebra and mathematical statistics.

Recommended prerequisites

No information inserted

Equipment

No information inserted

Literature

To be announced at course start. Last time the following book was used:
Hock, Ng Cheee, Queuing Modelling Fundamentals, John Wiley & Sons Ltd.

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

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

Examination

  • RED1 - Assignment, 3.0 credits, grading scale: P, F
  • TEN1 - Examination, 4.5 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

Passed exam (TEN1; 4.5 c.), grading A-F.
Passed lab work (RED1; 3 cr.), grading P/F.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

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.

Further information

Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

Main field of study

Mathematics

Education cycle

Second cycle

Add-on studies

No information inserted

Contact

Armin Halilovic, armin.halilovic@sth.kth.se