Network Calculus with Flow Prolongation -- A Feedforward FIFO Analysis enabled by ML

TL;DR

This work tackles the challenge of computing tight worst-case delay bounds in feedforward FIFO networks by augmenting the Flow Prolongation (FP) technique with a Graph Neural Network (GNN)–based predictor, DeepFP. By predicting a small, high-quality subset of FP prolongations, DeepFP enables scalable use of FP within the Network Calculus FIFO analysis, achieving average delay bound reductions of about $12.1\%$ with minimal computational overhead and scaling to networks with up to roughly $500$ flows. The authors compare RL- and SL-based training, finding that RL-based DeepFP often outperforms expert heuristics and SL, especially on larger networks, and demonstrate that DeepFP can outperform prior ML-guided counterparts like DeepTMA in the FIFO setting. Overall, the work shows that FP can meaningfully tighten NC FIFO bounds when guided by ML, enabling practical analysis of larger networks while preserving correctness of the bounds. The approach offers a path toward more accurate and scalable real-time network performance guarantees in systems such as automotive, avionics, and industrial automation.

Abstract

The derivation of upper bounds on data flows' worst-case traversal times is an important task in many application areas. For accurate bounds, model simplifications should be avoided even in large networks. Network Calculus (NC) provides a modeling framework and different analyses for delay bounding. We investigate the analysis of feedforward networks where all queues implement First-In First-Out (FIFO) service. Correctly considering the effect of data flows onto each other under FIFO is already a challenging task. Yet, the fastest available NC FIFO analysis suffers from limitations resulting in unnecessarily loose bounds. A feature called Flow Prolongation (FP) has been shown to improve delay bound accuracy significantly. Unfortunately, FP needs to be executed within the NC FIFO analysis very often and each time it creates an exponentially growing set of alternative networks with prolongations. FP therefore does not scale and has been out of reach for the exhaustive analysis of large networks. We introduce DeepFP, an approach to make FP scale by predicting prolongations using machine learning. In our evaluation, we show that DeepFP can improve results in FIFO networks considerably. Compared to the standard NC FIFO analysis, DeepFP reduces delay bounds by 12.1% on average at negligible additional computational cost.

Figures (11)

• Figure 1: Comparison between the (a) exhaustive FP with $O(n^m)$NC analyses and (b) DeepFP with one prediction.
• Figure 2: Sample network with prolongations and a specific FP alternative we will evalaute as an example
• Figure 3: Sample network in \ref{['fig:example_network:nc']} analyzed with FIFO requires find the best among two possible cut locations
• Figure 4: Improvements of the foi's delay bound and output bound burstiness by applying FP alternative \ref{['fig:example_network:nc:single_fp']} in the NC FIFO analysis of the network in \ref{['fig:example_network:nc']}
• Figure 5: Flows successfully analyzed with a 1h deadline and at most 5GB memory usage

Theorems & Definitions (9)

• Definition 1: Arrival Curve
• Definition 2: Service Curve
• Definition 3: NC Operations
• Theorem 1: Performance Bounds
• Theorem 2: Residual Service Curves for FIFO Multiplexing
• Corollary 1: Delay Increase due to FP
• Proof 1
• Corollary 2: FP Delay Bound Validity
• Proof 2