Well-defined generalized stochastic petri nets: a net-level method to specify priorities

Abstract

Generalized Stochastic Petri Nets (GSPN), with immediate transitions, are extensively used to model concurrent systems in a wide range of application domains, particularly including software and hardware aspects of computer systems, and their interactions. These models are typically used for system specification, logical and performance analysis, or automatic code generation. In order to keep modeling separate from the analysis and to gain in efficiency and robustness of the modeling process, the complete specification of the stochastic process underlying a model should be guaranteed at the net level, without requiring the generation and exploration of the state space. In this paper, we propose a net-level method that guides the modeler in the task of defining the priorities (and weights) of immediate transitions in a GSPN model, to deal with confusion and conflict problems. The application of this method ensures well-definition without reducing modeling flexibility or expressiveness.

Industrial applications of the PetriDotNet modelling and analysis tool

“…Generalised Stochastic Petri Nets (GSPNs) extend SPNs by allowing transitions with immediate firing behavior [6], which neccessitates using semi-Markov processes as the semantics of the net. PetriDotNet only implements analysis for CTMCs, thus all transitions must have exponentially timed behavior, i.e.…”

Getting the Priorities Right: Saturation for Prioritised Petri Nets

“…To ensure that probability distribution of GSPN markings evolve deterministically in time, conflicts must be resolved by assigning probability weights and priorities [1]. Conflict resolution may yield Prioritised Petri nets with many priority levels [12].…”

“…Assuming the priorities are given as integers (contrary to [8] but in accordance with [12]), the highest priority among enabled transitions π max is encoded into a separate data structure. This information is passed along with recursive calls in a modified saturation algorithm and used to decide whether a transition can be fired, similarly to the passing of constraints in constrained saturation [15].…”

“…To analyse the stochastic behaviour of a GSPN, the model must not express any nondeterminism. One way to guarantee this is to assign priorities to the transitions [12]. While explicit (graph-based) model checking algorithms naturally handle priorities, symbolic model checkers often have trouble representing the resulting complex transition relations compactly.…”

30 Years of GreatSPN

“…Drawing on these results, it became clear the danger of specifying "confused models", and thus the difficulty of constructing "correct models" including sequences of immediate transitions. To help analysts in specifying "well behaving nets", the concept of extended conflict set was formalized and methods were developed to find this structure at the net level [17,37]. In the analysis of GSPN models, immediate transitions are thus "pre-processed" to construct a reduced Embedded Markov chain defined on tangible markings only.…”