Probabilistic Nets-within-Nets

TL;DR

This paper introduces a probabilistic extension to Hornets, a Nets-within-Nets formalism, enabling the quantitative analysis of self-modifying, self-adaptive systems with independent firing rates for nested Petri nets.

Contribution

It extends Hornets with firing probabilities and operators that can modify net-tokens' firing rates, facilitating modeling of self-adaptive systems performing MAPE-like loops.

Findings

Enables quantitative analysis of self-modifying systems.

Supports modeling of self-adaptive systems with probabilistic behaviors.

Provides algebraic operations for dynamic modification of net-tokens.

Abstract

In this paper we study Hornets extended with firing probabilities. Hornets are a Nets-within-Nets formalism, i.e., a Petri net formalism where the tokens are Petri nets again. Each of these net-tokens has its own firing rate, independent from the rates of other net-tokens. Hornets provide algebraic operations to modify net-tokens during the firing. For our stochastic extension these operators could also modify the net-token's firing rate. We use our model to analyse self-modifying systems quantitatively. Hornets are very well suited to model self-adaptive systems performing a MAPE-like loop (monitoring-analyse-plan-execute). Here, the system net describes the loop, and the net-tokens describe the adapted model elements.