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.

翻译：随着确定性网络行为标准的出现，在时延约束下综合网络设计成为自然而然的下一项任务。网络演算（NC）已成为验证工业网络的关键方法，因为它可以计算经过形式验证的端到端时延上界。然而，NC框架中的分析方法被设计为一次仅能约束一个流的时延。尝试使用经典分析方法推导网络配置表明，这种方法在实际应用场景中适应性较差。考虑寻找时延最优的路由配置：需要为每种路由选择创建一个模型，然后约束每个流的时延，最后将约束结果与给定约束进行比较。为克服这一三步过程，我们引入了微分网络演算。我们扩展了NC，允许对时延上界关于广泛网络参数（例如流路径或优先级）进行微分。这为NC开辟了一类利用时延上界梯度的高效非线性优化技术。我们在路由与优先级分配问题上的数值评估表明，我们的新方法能在数秒内综合出流路径和优先级，性能超越现有方法数个数量级。