Research Article
A symbolic approach to quantitative analysis of preemptive real-time systems with non-Markovian temporal parameters
@INPROCEEDINGS{10.4108/icst.valuetools.2011.245728, author={Laura Carnevali and Enrico Vicario and Johnny Giuntini}, title={A symbolic approach to quantitative analysis of preemptive real-time systems with non-Markovian temporal parameters}, proceedings={5th International ICST Conference on Performance Evaluation Methodologies and Tools}, publisher={ICST}, proceedings_a={VALUETOOLS}, year={2012}, month={6}, keywords={Quantitative evaluation non-Markovian Stochastic Petri Nets Generalized Semi-Markov Processes \% preemptive real-time systems approximate state space representation Difference Bounds Matrix Bernstein Polynomials}, doi={10.4108/icst.valuetools.2011.245728} }- Laura Carnevali
Enrico Vicario
Johnny Giuntini
Year: 2012
A symbolic approach to quantitative analysis of preemptive real-time systems with non-Markovian temporal parameters
VALUETOOLS
ICST
DOI: 10.4108/icst.valuetools.2011.245728
Abstract
The method of stochastic state classes provides a means for quantitative analysis of a rather wide class of non-Markovian models. As a major and structural limitation, the approach cannot be applied to models encompassing a preemptive policy, which in the practice rules out the mechanism of suspension and resume usually applied in many real-time systems.
We overcome here the limitation by proposing an approach that faces the complexity issues introduced by the suspension/resume mechanism in the structure of supports and distributions of remaining times. In particular, these are distributed over a polyhedral support according to a multivariate joint density function with analytic piecewise form over a partition into polyhedral subdomains. The approach resorts to an imprecise analysis that extends distributions over the tightest DBM zones enclosing polyhedral domains, and approximates them with Bernstein Polynomials to obtain a global (non-piecewise) analytic representation. Computational experience is reported to show the different impact of errors due to the approximation of supports and distributions.