Efficient Performance Analysis of Modular Rewritable Petri Nets

TL;DR

This work defined rewritable PT nets (RwPT) using Maude, a declarative language that ensures consistent rewriting logic semantics, and proposed a modular approach that employs algebraic operators to build extensive RwPT models.

Abstract

Petri Nets (PN) are extensively used as a robust formalism to model concurrent and distributed systems; however, they encounter difficulties in accurately modeling adaptive systems. To address this issue, we defined rewritable PT nets (RwPT) using Maude, a declarative language that ensures consistent rewriting logic semantics. Recently, we proposed a modular approach that employs algebraic operators to build extensive RwPT models. This methodology uses composite node labeling to maintain hierarchical organization through net rewrites and has been shown to be effective. Once stochastic parameters are integrated into the formalism, we introduce an automated procedure to derive a lumped CTMC from the quotient graph generated by a modular RwPT model. To demonstrate the effectiveness of our method, we present a fault-tolerant manufacturing system as a case study.

Figures (3)

• Figure 1: Production Line (PL) and adaptation following a fault.
• Figure 2: One of the possible paths of the Gracefully Degrading Production System.
• Figure 3: System Throughput.

Theorems & Definitions (1)

• Definition 4.1: Symmetric Labeling