Some Specific Problems in the Applications of Discrete Event Systems

Ing. Zuzana Němcová

Doctoral thesis

Abstract:

The present thesis treats the solution of specific problems of discrete event systemsarising in the modeling of production systems, traffic or computer networks, andothers.The thesis is focused on two areas of such problems. The first one is the controlof the queues in a manufacturing system in order to optimize the total productioncost. The service times at particular servers naturally differ in such a system. Asa consequence, queues are created—the queues in front of the slower servers canincrease, whereas the queues in front of fast servers are decreasing and the servercan easily become idle. Both mentioned states are economically undesirable. Twomethods of finding the optimal setup of service capacities of the servers in each timeperiod during which the service times stay unchanged are suggested.The second area of issues covers the description of the steady states of systems performingin discrete time. This description is done using extremal algebras. Transitionmatrices with fuzzy values are applied to discrete time systems. Various triangularfuzzy t-norms are used, in dependence on the character of the system. The developmentof the system in time is then described by the power sequence of the transitionmatrix, computed in the so-called max-t fuzzy algebra. The steady states of the systemcorresponding to periodic behavior of the power sequence as well as the solutionof the eigenproblem are described.Both the knowledge of the development of the queues and the knowledge of the thesteady states in such systems is strategically important for the system manager, whocan then flexibly take actions and positively affect the performance of the system.

Keywords

extremal algebra, discrete event system, queuing systems, steady states

Language used: English

Date on which the thesis was submitted / produced: 30. 3. 2016

Thesis defence

• Date of defence: 15. 6. 2016
• Supervisor: prof. RNDr. Martin Gavalec, CSc.

University of Hradec Králové

Faculty of Informatics and Management

Doctoral programme / field:
Systémové inženýrství a informatika / Informační a znalostní management