# 456-0354/01 – Stochastics Methods in Computer Science (SMI)

 Gurantor department Department of Computer Science Credits 5 Subject guarantor doc. RNDr. Jaroslav Markl Subject version guarantor doc. RNDr. Jaroslav Markl Study level undergraduate or graduate Requirement Optional Year 1 Semester summer Study language Czech Year of introduction 2006/2007 Year of cancellation 2009/2010 Intended for the faculties FEI Intended for study types Follow-up Master
Instruction secured by
MAR37 doc. RNDr. Jaroslav Markl
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined 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

Lectures
Tutorials

### Summary

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

### Prerequisities

Subject has no prerequisities.

### Co-requisities

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: 1960/1961 Summer semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 45 (45) 0
Written exam Written test 45  0
Examination Examination 55 (55) 0
Written examination Written examination 55  0
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2009/2010 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P Czech Ostrava 1 Optional study plan
2009/2010 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K Czech Ostrava 1 Optional study plan
2009/2010 (N2646) Information Technology (2612T025) Computer Science and Technology P Czech Ostrava 2 Optional study plan
2008/2009 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P Czech Ostrava 1 Optional study plan
2008/2009 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K Czech Ostrava 1 Optional study plan
2008/2009 (N2646) Information Technology (2612T025) Computer Science and Technology K Czech Ostrava 2 Optional study plan
2007/2008 (N2646) Information Technology (2612T025) Computer Science and Technology P Czech Ostrava 2 Optional study plan
2007/2008 (N2646) Information Technology (2612T025) Computer Science and Technology K Czech Ostrava 2 Optional study plan
2007/2008 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P Czech Ostrava 1 Optional study plan
2007/2008 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K Czech Ostrava 1 Optional study plan
2006/2007 (N2646) Information Technology (2612T025) Computer Science and Technology P Czech Ostrava 2 Optional study plan
2006/2007 (N2646) Information Technology (2612T025) Computer Science and Technology K Czech Ostrava 2 Optional study plan
2006/2007 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P Czech Ostrava 1 Optional study plan
2006/2007 (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