Dr. Kai Lampka

"Real-Time Calculus based System Analysis"

With the control function of a system being at least partially automated, one often assumes that the automated function is working correctly. Correctness includes on the one hand the calculation itself, i.e. is the correct result calculated. On the other hand, it also has to address the temporal behaviour, i.e. is the result provisioned before a pre-defined deadline. Confidence in the fulfilment of these fundamental properties must be formally substantiated by applying various methods. If the defectiveness of the system leads to the impairment of human life, the use of such methods to exclude systematic errors is even mandatory. This entails the application of corresponding industry standards like the ISO 26262. The massive progress in semiconductor technology and the associated computer-aided automation of systems means that control functions are now implemented purely electronically, which in turn leads to an explosion in the number of control functions as in their complexity. For this reason, the proof of correctness of today’s computer-controlled systems encompasses not only correctness of an isolated control algorithm and the hosting computing element, but requires the analysis of a complex, distributed system. Dedicated temporal behaviour of distributed systems can be investigated on the basis of stochastic queueing theory. Real-time calculus is based on a similar idea. In contrast to stochastic queueing theory, Real-time Calculus uses non-stochastic arrival and operation times. This has the advantage that the calculation of results is mathematically simpler and the obtained bounds on sojourn times and number of open jobs in the system can be understood as truly upper limits. The talk motivates the use of analysis methods in the area of embedded real-time systems, classifies the methods, gives an introduction to "Real-time Calculus" based system evaluation, presents two of the basic results and attempts to sensitise the audience to the tension between scalability of the method and its precision when calculating performance indicators.

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