A symbolic approach to quantitative analysis of preemptive real-time systems with non-Markovian temporal parameters

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.