Modeling a New AQM Model for Internet Chaotic Behavior Using Petri Nets

Formal modeling is considered one of the fundamental phases in the design of network algorithms, including Active Queue Management (AQM) schemes. This article focuses on modeling with Petri nets (PNs) a new scheme of AQM. This innovative AQM is based on a discrete dynamical model of random early detection (RED) for controlling bifurcations and chaos in Internet congestion control. It incorporates new parameters (alpha, beta) that make possible better stability control over oscillations of an average queue length (AQL) at the router. The PN is validated through the matrix equation approach, reachability tree, and invariant analysis. The correctness is validated through the key properties of reachability, boundedness, reversibility, deadlock, and liveness.

Automated summary

This article focuses on modeling a new AQM scheme using Petri nets, incorporating a discrete dynamical model and new parameters for better stability control over router queue length oscillations. The study validates the model through matrix equation approach, reachability tree, and invariant analysis, confirming key properties such as reachability, boundedness, reversibility, deadlock, and liveness.