- Basic concepts of probability theory. Combinatorics. Sample space. The axioms of probability. Conditional probability. Independence of events.
- Discrete and continues random variables
- 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
HF1001 Queuing Theory and Mathematical Statistics 7.5 credits
Course offerings are missing for current or upcoming semesters.
Headings with content from the Course syllabus HF1001 (Autumn 2007–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
Intended learning outcomes
After completion of the course the student should be able to
- define and explain basic concepts in descriptive statistics and probability theory
- solve some standard problems that include random variables
- construct a confidence interval to estimate a population mean
- 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
- analyze and solve problems using computer aid (Maple, Matlab or Mathematica)
Literature and preparations
Specific prerequisites
No information inserted
Recommended prerequisites
No information inserted
Equipment
No information inserted
Literature
Will be decided before each start of the course.
Last time Vännman, Kerstin: Matematisk statistik
Körner, Ulf: Köteori was used.
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
- LAB1 - Laboratory Work, 1.5 credits, grading scale: P, F
- TEN1 - Examination, 3.0 credits, grading scale: A, B, C, D, E, FX, F
- TEN2 - Examination, 3.0 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.
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
Information Technology, Technology
Education cycle
First cycle
Add-on studies
No information inserted
Contact
Armin Halilovic, armin.halilovic@sth.kth.se