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 | 2 | 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 |
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
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
Way of continuous check of knowledge in the course of semester
E-learning
Other requirements
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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