• Real-Time Analysis
• Real-Time Scheduling Theory
• Real-Time Theory
• Distribution Theory
• Linear Algebra

• Winter 22/23
  • Exercise Design Methodology of Embedded Real-Time Systems
  • Seminar Real-Time Theory
• Summer 2023
  • Exercise Architecture of Embedded Systems
  • Seminar Real-Time Theory
• Summer 2024
  • Exercise Architecture of Embedded Systems
  • Seminar Real-Time Theory
• Winter 24/25
  • Exercise Design Methodology of Embedded Real-Time Systems
  • MATLAB/Mathematica Programming Lab
  • Seminar Real-Time Theory

Publications listed on Google Scholar

Publications at Wolfram Mathematica

A special property of a real-time system compared to a conventional computer is that it has to react to changes in its physical environment within a certain time frame. This time frame is called the deadline. In order to check whether the real-time system meets its deadlines, we develop models for the analysis of the timing behavior at our institute. Bachelor's and Master's theses as well as project work are possible within the framework of this topic. These can range from the development of models and analyses, which are more theoretically oriented, to the implementation of such analyses, which is more practically oriented. Depending on the level of difficulty and effort required, this results in a Bachelor's or Master's thesis. Here are possible subject areas:

Development of model and analysis for real-time systems

The methods we have developed are to be further developed. There are some open problems in real-time analysis that have not yet been solved. This means that there are certain hardware or software architectures and scheduling algorithms for which no real-time analysis exists yet. The task here would be to model an architecture specified by us and a certain scheduling algorithm using our methods and then to develop an analysis. There is preliminary work from our research that needs to be studied and implemented to solve the problem. Such work requires an interest in theoretical tasks and mathematics. The lectures Architecture of Embedded Systems and Design Methodology of Embedded Systems are recommended. Such work is recommended more as a master's thesis.

Comparison of existing methods of real-time analysis from the literature

The methods we have developed should be compared with the methods from the literature. This can be a comparison of the models or a comparison by means of the implementation of the methods. When comparing models, we examine on a mathematical level which model is, for example, more powerful, provides a more precise analysis or which model leads to algorithms with a lower runtime complexity. When comparing implementations, the methods from the literature and ours should be implemented. The algorithms should then be examined experimentally. In addition to our investigations on a mathematical level, the experiments help us to understand the average runtime behavior of the algorithms and their precision. From the observations of the experiments we may draw conclusions that we can then formally examine in the model. This closes the circle between the mathematical and the experimental approach. Depending on your interests, you can concentrate on comparing the models or the implementations (or both) in a student project.

Monte Carlo simulation of the time behavior of real-time systems

Conventional real-time analysis examines the time behavior of the real-time system in extreme cases. The question is what the maximum response time of a real-time system is to a new impulse from the physical environment. You have to know this in order to check whether the deadlines of a real-time system are met. Apart from this one value, the maximum response time, we do not receive any further information from the real-time analysis. This means that, apart from the extreme case, we do not know the timing behavior of the real-time system. For example, we do not know how often this extreme case can occur. In order to find this out, among other things, we would like to examine the average time behavior of the real-time system using the Monte Carlo simulation method. The model for real-time systems developed at our institute not only allows the analysis of extreme cases, but also the analysis of the timing behavior using random experiments in the sense of a Monte Carlo simulation. Since both the real-time analysis and the Monte Carlo simulation take place in the same model, a comparison of extreme cases with random cases is possible, which provides new insights into the timing behavior. As part of student work, the existing Monte Carlo simulation in our model would be expanded to include additional system architectures or scheduling algorithms or compared with other simulation tools from the literature.