460-4032/01 – Stochastics Methods in Computer Science (SMI)

Gurantor departmentDepartment of Computer ScienceCredits5
Subject guarantorIng. Martin Kot, Ph.D.Subject version guarantorIng. Martin Kot, Ph.D.
Study levelundergraduate or graduateRequirementOptional
Study languageCzech
Year of introduction2010/2011Year of cancellation2011/2012
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
KOT06 Ing. Martin Kot, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 10+0

Subject aims expressed by acquired skills and competences

To understand the basic concepts and methods of mathematical information and communication theory To gain basic experience with solving simple queueing systems and/or reliability systems by means of markovian models and methods

Teaching methods



The course deals with stochastic models and methods often used in computer science, namely with information and communication theory, queue theory and reliability theory. The accent is put on simple markovian models that can be completly solved by standard mathematical methods.

Compulsory literature:

http://en.wikipedia.org/wiki/Information_theory Trivedi K.S.:Probability and Statistics with Reliability, Queueing and Computer Science Applications. New York, John Wiley, 2002.

Recommended literature:

Stochastické metody v informatice

Way of continuous check of knowledge in the course of semester

Requirements during a semester: - A written test during a semester (for 35 points) Requirements for a credit: - To get a credit, a student must obtain from the written test at least 15 points. The exam: - The exam is of a written form. It is possible to get 65 points for the exam. To pass out the exam it is necessary to get at least 20 points.


Other requirements


Subject has no prerequisities.


Subject has no co-requisities.

Subject syllabus:

Lectures: Probability theory recapitulation: random event, basic rules for probability, random variables and their distributions. Information theory 1.: entropy, conditional entropy, information measures, mutual information. Information theory 2.: language and its information characteristics, measures of redundancy, basic notions of coding theory. Information theory 3.: communication and memory channels and their information characteristics, noisy channels, error correcting codes, Hamming codes. Random process theory 1.: types of stochastic processes, markovian and semi-markovian processes, Poisson flow of events. Random process theory 2.: homogenous and stable markovian processes, transient and steady state, computation of steady-state probabilities. Queueing theory 1.: basic notions (arrival, service, server, queue, service discipline,...), Kendall clasification of queueing systems. Queueing theory 2.: selected models of opened systems, with or without losses, with or without finite buffers, with or without limitations on waiting time. Queueing theory 3.: selected models of closed systems, general queueing systems, stochastic nets nets. Dependability (reliability) theory 1.: fundamentals, markovian dependability models. Dependability theory 2.: selected models of non- recovered systems. Dependability theory 3.: selected models of recovered systems. Stochastic Petri nets (SPN) and generalized stochastic Petri nets (GSPN). Using SPN and GSPN for systems performace analysis. Exercises: The content of exercises is determined by the content of lectures. The main goals are: Recapitulation of some necessary prerequisities from probability theory and theory of stochastic processes Confirm understanding of theoretical knowledge by means of solving simple examples Master the technique of markovian approximation of more complex stochastic processes Gain some experience with standard queueing and reliability models solving

Conditions for subject completion

Full-time form (validity from: 2010/2011 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 35 (35) 15
                Test Written test 35  15
        Examination Examination 65 (65) 20
                Written exam Written examination 65  20
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2011/2012 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P Czech Ostrava 1 Optional study plan
2011/2012 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K Czech Ostrava 1 Optional study plan
2010/2011 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P Czech Ostrava 1 Optional study plan
2010/2011 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K Czech Ostrava 1 Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner