Courses Currently Offered in English

Course Version

Course Code:EDRP
Version Number:1
Course Name:Discrete Random Processes
Credit Units:4
Cost Units:30
Examination type (E-with exam):E
Grading threshold:5
Initiation semester:01Z
Person responsible:prof. nzw. dr hab. Paweł Szabłowski
Description:ICT programme taught in English

Hours per week

Class typeHours

Class types: W - lecture, C - tutorial, L - laboratory, P - project


Prerequisite TypePrerequisite NumberCourse CodeName
W1EPRSTProbability and Statistics

Prerequitise types: W - required, Z - recommended

Similar Courses


Last Course Instances

Semester codeInstance codeLecturerInstituteMax. number of students
18ZAprof. nzw. dr hab. Paweł SzabłowskiMA30

Thematic Classification

Class CodeClass name (in Polish)
ANGLAll Courses in English (A)


Summary (in Polish)

Celem kursu jest zapoznanie studentów z prostymi procesami dyskretnymi, nauczenie ich symulowania tych procesów na komputerze a przez to zapoznaie się z podstawowymi ich własnościami a wreszcie wskazanie na ważne zastosowania tych procesów w technice.

Lecture contents
  1. Review of important notions of probability theory (4h).

  2. A few remarks on stochastic processes : Definition of a Stochastic process, Notion of the state and realization of the process, Classification of Stochastic processes.Probability and Moment generating functions and their properties (2h).

  3. Branching processes Galton process :Probability of extinction , Applications in demography and nuclear physics (4h).

  4. Poisson processes and its applications. Exponentioal distribution and its properties, . Poisson Process and their properties : Distribution of periods between successive calls , Summing independent Poisson processes, Conditional distributions of inter-arrival times , Generalizations of Poisson processes , nonuniform distribution , Composed Poisson process (6h).

  5. Simple queuing systems: M/M/c systems without and with queue.: Probability of blocking, probability of the delay and average waiting time (4h).

  6. Renewal Processes (6h).

  7. Review (4h).

Tutorial contents

The aim of exercises is to solve problems concerning each of the discussed processes i.e. Poissson, Branching, queuing systems and renewal processes

Laboratory contents

The aim of exercises is to solve problems concerning each of the discussed processes i.e. Poissson, Branching, queuing systems and renewal processes. The aim of laboratory is to teach students to simulate selected processes and observe their properties.

  1. Sheldon Ross. Introduction to Probability Models. Harcourt Acad. Press, N.Y. 2000
  2. L. Kosten, Stochastic Theory of Service Systems, Pergamon Press, N.Y. 1973
  3. Geoffrey Grimmett and David Stirzaker, One Thousand Exercises in Probability, Oxford University Press, N.Y. 2001.

The main purpose of the course is to expose students to simple stochastic processes, teach them how to simulate these processes and hence observe their properties and finaly indicate real life applications of those processes.