# 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

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

No information inserted

### 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

Second cycle