Proxels Practically: The Meaning of the Lifetime Factor

Proxel-based simulation is a new and deterministic approach to analysing discrete stochastic models and studying their behaviour. Unfortunately, as it is the case with the deterministic approaches it suffers from the well-known state-space explosion problem, nevertheless having an advantage with respect to the other approaches. The proxelbased method benefits from the way it generates and stores the state-space, which is performed on-the-fly, meaning that only the truly reachable states are the ones that are stored. This in turn means that on-paper inspection of the model (i.e. its graphical representation in form of a Petri net or a reachability graph) does not determine how complex its behaviour will be in practice, and correspondingly its proxel-based analysis. Therefore, we needed a tactic to estimate the computational complexity of the proxel-based simulation for different models, thus allowing a better strategy for organisation of the data structures being used. We refer to the factor that determines the actual state-space of one model (the one that is stored and truly reachable) as lifetime of the discrete states and formalise its impact on the computational complexity of the proxel-based analysis of stochastic models.