TAPAAL SMC: Statistical Model Checking of Stochastic Timed-Arc Petri Nets

2026-06-01

AI Summary

This work addresses the challenge of effectively verifying stochastic real-time systems with classical timed Petri nets by introducing, for the first time, a stochastic semantics for Timed-Arc Petri Nets (TAPNs), formally characterizing their behavior and establishing key theoretical properties. Building on this foundation, the authors integrate statistical model checking (SMC) techniques to develop an efficient verification algorithm within the TAPAAL platform, supporting both quantitative and qualitative analysis. The approach accommodates complex modeling features such as age invariants, time intervals, invariants, inhibitor arcs, and transport arcs. Case studies demonstrate that the proposed method overcomes the traditional trade-off between expressiveness and decidability, substantially enhancing the modeling and verification capabilities for complex stochastic real-time systems.

Abstract

Timed-Arc Petri net (TAPN) is a timed extension of the classical Petri net model where tokens have their age and input arcs are associated with time intervals restricting the ages of tokens available for transition firing. Additionally, a TAPN can also contain place invariants constraining the ages of tokens in places, inhibitor arcs preventing a transition from firing and transport arcs that preserve token ages upon firing. This set of features, as much as it allows us to model complex systems, also often makes verification problems computationally hard or even undecidable. Moreover, in order to model real-life examples, additional stochastic aspects are often necessary to capture the desired behaviour. We suggest the first stochastic semantics for TAPNs and design and implement the quantitative and qualitative Statistical Model Checking (SMC) algorithms in the model checker TAPAAL. We argue for the semantic choices we made in the stochastic semantics and prove that the semantics is well-behaving. On a number of case studies we demonstrate the practical applicability of our modelling formalism and its SMC implementation.

Problem

• Stochastic Timed-Arc Petri Nets
• Statistical Model Checking
• Stochastic Semantics
• Timed Systems
• Quantitative Verification

Innovation

• Stochastic Timed-Arc Petri Nets
• Statistical Model Checking
• Stochastic Semantics
• TAPAAL
• Quantitative Verification