Measuring performance of continuous-time stochastic processes using timed automata

Authors:
Tomás Brázdil;Jan Krcál;Jan Kretínský;Antonín Kucera;Vojtech Řehák
Affiliations:
Faculty of Informatics, Masaryk University, Brno, Czech Rep;Faculty of Informatics, Masaryk University, Brno, Czech Rep;Faculty of Informatics, Masaryk University, Brno, Czech Rep;Faculty of Informatics, Masaryk University, Brno, Czech Rep;Faculty of Informatics, Masaryk University, Brno, Czech Rep
Venue:
Proceedings of the 14th international conference on Hybrid systems: computation and control
Year:
2011

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Abstract

We propose deterministic timed automata (DTA) as a model-independent language for specifying performance and dependability measures over continuous-time stochastic processes. Technically, these measures are defined as limit frequencies of locations (control states) of a DTA that observes computations of a given stochastic process. Then, we study the properties of DTA measures over semi-Markov processes in greater detail. We show that DTA measures over semi-Markov processes are well-defined with probability one, and there are only finitely many values that can be assumed by these measures with positive probability. We also give an algorithm which approximates these values and the associated probabilities up to an arbitrarily small given precision. Thus, we obtain a general and effective framework for analysing DTA measures over semi-Markov processes.