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An extended Petri Net model which considers modular partitioning along with timing restrictions and environment models is presented. Module constructs permit the specification of a complex system as a set of message passing modules with the timing semantics of Time Petri Nets. The state space of each individual module can be separately enumerated and assessed under the assumption of a partial specification of the intended module operation environment. State spaces of individual modules can be recursively integrated, to permit the assessment of module clusters and of the overall model, and to check the satisfaction of the assumptions made in the separate analysis of elementary component modules. In the intermediate stages between subsequent integration steps, the state spaces of module and module clusters can be projected onto reduced representations concealing local events that are not essential to the purposes of the analysis. The joint use of incremental enumeration and intermediate concealment of local events allows for a flexible management of state explosion, and permits a scalable approach to the validation of complex systems.

Oris is a tool for qualitative verification and quantitative evaluation of reactive timed systems, which supports modeling and analysis of various classes of timed extensions of Petri Nets. As most characterizing features, Oris implements symbolic state space analysis of preemptive Time Petri Nets, which enable schedulability analysis of real-time systems running under priority preemptive scheduling; and stochastic Time Petri Nets, which enable an integrated approach to qualitative verification and quantitative evaluation. In this paper, we present the current version of the tool and we illustrate its application to two different case studies in the areas of qualitative verification and quantitative evaluation, respectively.

Abstract-Time Petri Nets describe the state of a timed system through a marking and a set of clocks. If clocks take values in a dense domain, state space analysis must rely on equivalence classes. These support verification of logical sequencing and quantitative timing of events, but they are hard to be enriched with a stochastic characterization of nondeterminism necessary for performance and dependability evaluation. Casting clocks into a discrete domain overcomes the limitation, but raises a number of problems deriving from the intertwined effects of concurrency and timing. We present a discrete-time variant of Time Petri Nets, called stochastic preemptive Time Petri Nets, which provides a unified solution for the above problems through the adoption of a maximal step semantics in which the logical location evolves through the concurrent firing of transition sets. We propose an analysis technique, which integrates the enumeration of a succession relation among sets of timed states with the calculus of their probability distribution. This enables a joint approach to the evaluation of performance and dependability indexes as well as to the verification of sequencing and timeliness correctness. Expressive and analysis capabilities of the model are demonstrated with reference to a real-time digital control system.

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