Differentiable Programming & Network Calculus: Configuration Synthesis under Delay Constraints

TL;DR

This paper introduces Differential Network Calculus, enabling efficient optimization of network configurations under delay constraints by differentiating delay bounds with respect to network parameters, significantly improving synthesis speed.

Contribution

It extends Network Calculus to allow differentiation of delay bounds, facilitating the use of nonlinear optimization for network configuration synthesis under delay constraints.

Findings

Synthesizes flow paths and priorities in seconds

Outperforms existing methods by several orders of magnitude

Enables practical delay-constrained network design

Abstract

With the advent of standards for deterministic network behavior, synthesizing network designs under delay constraints becomes the natural next task to tackle. Network Calculus (NC) has become a key method for validating industrial networks, as it computes formally verified end-to-end delay bounds. However, analyses from the NC framework have been designed to bound the delay of one flow at a time. Attempts to use classical analyses to derive a network configuration have shown that this approach is poorly suited to practical use cases. Consider finding a delay-optimal routing configuration: one model had to be created for each routing alternative, then each flow delay had to be bounded, and then the bounds had to be compared to the given constraints. To overcome this three-step process, we introduce Differential Network Calculus. We extend NC to allow the differentiation of delay bounds w.r.t. to a wide range of network parameters - such as flow paths or priority. This opens up NC to a class of efficient nonlinear optimization techniques that exploit the gradient of the delay bound. Our numerical evaluation on the routing and priority assignment problem shows that our novel method can synthesize flow paths and priorities in a matter of seconds, outperforming existing methods by several orders of magnitude.