342-0963/01 – Stochastic Computational Methods (SVM)

Gurantor departmentInstitute of TransportCredits10
Subject guarantordoc. Ing. Michal Dorda, Ph.D.Subject version guarantordoc. Ing. Michal Dorda, Ph.D.
Study levelpostgraduateRequirementChoice-compulsory type B
YearSemesterwinter + summer
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFSIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
DOR028 doc. Ing. Michal Dorda, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 25+0
Part-time Examination 25+0

Subject aims expressed by acquired skills and competences

The student is able to characterize the individual types of queueing systems and can define what input data he / she needs to obtain for modeling the solved queueing system. These data can be processed by appropriate statistical methods. He has an overview of the mathematical models of queueing systems and can use these models to solve practical problems. It controls the modeling methods of queueing systems and is able to create mathematical models of queueing systems. Can use colorful Petri nets for modeling and simulation of queueing systems.

Teaching methods

Individual consultations
Project work


The course is devoted to methods of modeling and simulation of queueing systems. The student is acquainted with the methods used for modeling of mass control systems in time (so called transition analysis) and in steady state. Within the subject are discussed the models of individual mass control systems differing in assumptions, from the elementary Markov models to models requiring a more demanding mathematical apparatus. For simulation of mass control systems, the Petri color network is used.

Compulsory literature:

BOLCH, Gunter. Queueing networks and Markov chains: modeling and performance evaluation with computer science applications. 2nd ed. Hoboken: Wiley, c2006. ISBN 0-471-56525-3. ORTUZAR, Juan de Dios; WILLUMSEN, Luis G. Modelling transport. 2002.

Recommended literature:

HENSHER, David A.; BUTTON, Kenneth J. (ed.). Handbook of transport modelling. Emerald Group Publishing Limited, 2007. HILLIER, Frederick S. a LIEBERMAN, Gerald J. Introduction to operations research [CD-ROM]. 8th ed. Burr Ridge: McGraw-Hill Higher Education, c2005. ISBN 0-07-321114-1. Introduction to logistics systems planning and control [online]. Hoboken: Wiley, 2005 [cit. 2018-01-10]. ISBN 0-470-01404-0. ZEIGLER, Bernard P., PRAEHOFER, Herbert a KIM, Tag Gon. Theory of modeling and simulation: integrating discrete event and continuous complex dynamic systems. 2nd ed. San Diego: Academic Press, c2000. ISBN 0-12-778455-1. SOKOLOWSKI, John A. a BANKS, Catherine M., ed. Principles of modeling and simulation: a multidisciplinary approach [online]. Hoboken: John Wiley & Sons, 2008 [cit. 2018-01-10]. ISBN 978-0-470-40356-3.

Way of continuous check of knowledge in the course of semester

Oral examination.


Other requirements

Solution and defense of the project on the given topic.


Subject has no prerequisities.


Subject has no co-requisities.

Subject syllabus:

1) Selected pieces of knowledge of probability theory - generating functions, random variables used in the queueing theory, convolution. 2) Baysian statistical principles. 3) Stochastic programming. 4) Theory of random processes with continuous and discrete time. 5) Advanced knowledge of the queueing theory - methods of input flow modeling, methods of modeling of the operating time, methods of calculation of performance measures. 6) Markov queueing systems and methods of their modeling in time (transition analysis). 7) Markov queueing systems and their modeling methods in steady state. 8) Modeling of queueing systems with Erlang input flow and / or Erlang service time. 9) Modeling of M/D/1, M/G/1 and G/M/1 queueing systems. 10) Multi-operator systems with service lines that do not work continuously (due to malfunctions, maintenance, etc.). 11) Queueing networks and their modeling. 12) Possibilities of computer modeling of queueing systems (Witness, colored Petri nets).

Conditions for subject completion

Part-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2022/2023 (P1041D040006) Transport Systems K Czech Ostrava Choice-compulsory type B study plan
2022/2023 (P1041D040006) Transport Systems P Czech Ostrava Choice-compulsory type B study plan
2021/2022 (P1041D040006) Transport Systems P Czech Ostrava Choice-compulsory type B study plan
2021/2022 (P1041D040006) Transport Systems K Czech Ostrava Choice-compulsory type B study plan
2020/2021 (P1041D040006) Transport Systems P Czech Ostrava Choice-compulsory type B study plan
2020/2021 (P1041D040006) Transport Systems K Czech Ostrava Choice-compulsory type B study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner