EP2930 Queuing Theory 7.5 credits

Köteori

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 queueing systems
  • derive and apply main formulas for some properties (such as stationary probabilities, average waiting and system time, expected number of customers in the que, etc. ) of M/M/m, M/M/m/K and M/M/m/K/C queueing systems.
  • to calculate the traffic intensity, blocked traffic and the utilization of some queueing systems
  • solve some simple problems on queueing networks
  • analyze and solve problems using computer aid (Maple, Matlab or Mathematica).

Offering and execution

Course offering missing for current semester as well as for previous and coming semesters

Course information

Content and learning outcomes

Course contents *

No information inserted

Intended learning outcomes *

  • 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: Queueing system with m servers, infinite number of waiting positions and infinite number of customers.
  • M/M/m/K: Queueing system with m servers, limited number (=K) waiting positions and infinite number of customers.
  • M/M/m/K/C: Queueing 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/1 queueing systems. Pollaczek-Khinchin formula .
  • Survey on open and closed Jackson queuing networks

Course Disposition

No information inserted

Literature and preparations

Specific prerequisites *

No information inserted

Recommended prerequisites

Basic knowledge in calculus, linear algebra and mathematical statistics.

Equipment

No information inserted

Literature

To be announced at course start. Last time the following books were used:
Ng Cheee Hock: QUEUEING MODELLING FUNDAMENTALS,
John Wiley & Sons LTD

Examination and completion

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 exams:
TEN1, (4.5 ECTS Cr.), grading: A/B/C/D/E/Fx/F
Passed lab work
RED1, (3 ECTS Cr.), grading: failed, passed

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

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Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web EP2930

Offered by

EECS/Communication

Main field of study *

Electrical Engineering

Education cycle *

Second cycle

Add-on studies

No information inserted

Contact

Armin Halilovic

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.