# Before choosing course

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

## Content and learning outcomes

### Course contents

• 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

### 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)

### Course Disposition

No information inserted

## 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.

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

### Examination

• LAB1 - Laboratory Work, 1,5 hp, betygsskala: P, F
• TEN1 - Examination, 3,0 hp, betygsskala: A, B, C, D, E, FX, F
• TEN2 - Examination, 3,0 hp, betygsskala: 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

### 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 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 HF1001

### Offered by

CBH/Biomedical Engineering and Health Systems

### Main field of study

Information Technology, Technology

First cycle