Network Synthesis under Delay Constraints: The Power of Network Calculus Differentiability

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 were thus far designed to bound one flow’s delay at a time. Attempts to use classical analyses for derivation of a network configuration revealed this approach to be poorly fitted for practical use cases. Take finding a delay-optimal routing configuration: One model for each routing alternative had to be created, then each flow delay had to be bounded, then the bounds were compared to the given constraints. To overcome this three-step procedure, we introduce Differential Network Calculus. We extend NC to allow for differentiation of delay bounds w.r.t. to a wide range of network parameters – such as flow routes. This opens up NC to a class of efficient nonlinear optimization techniques taking advantage of the delay bound computation’s gradient. Our numerical evaluation on the routing problem shows that our novel method can synthesize flow path in a matter of seconds, outperforming existing methods by multiple orders of magnitude.