Improved Delay Bound for a Service Curve Element with Known Transmission Rate

Network calculus is often used to prove delay bounds in deterministic networks, using arrival and service curves. We consider a FIFO system that offers a rate-latency service curve and where packet transmission occurs at line rate without pre-emption. The existing network calculus delay bounds take advantage of the service curve guarantee but not of the fact that transmission occurs at full line rate. In this letter, we provide a novel, improved delay bound which takes advantage of these two features. Contrary to existing bounds, ours is per-packet and depends on the packet length. We prove that it is tight.Comment: 4 pages, 2 figure

A Basic Result on the Superposition of Arrival Processes in Deterministic Networks

Time-Sensitive Networking (TSN) and Deterministic Networking (DetNet) are emerging standards to enable deterministic, delay-critical communication in such networks. This naturally (re-)calls attention to the network calculus theory (NC), since a rich set of results for delay guarantee analysis have already been developed there. One could anticipate an immediate adoption of those existing network calculus results to TSN and DetNet. However, the fundamental difference between the traffic specification adopted in TSN and DetNet and those traffic models in NC makes this difficult, let alone that there is a long-standing open challenge in NC. To address them, this paper considers an arrival time function based max-plus NC traffic model. In particular, for the former, the mapping between the TSN / DetNet and the NC traffic model is proved. For the latter, the superposition property of the arrival time function based NC traffic model is found and proved. Appealingly, the proved superposition property shows a clear analogy with that of a well-known counterpart traffic model in NC. These results help make an important step towards the development of a system theory for delay guarantee analysis of TSN / DetNet networks

Differentiable Programming & Network Calculus: Configuration Synthesis under Delay Constraints

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

Isospeed: Improving (min,+) Convolution by Exploiting (min,+)/(max,+) Isomorphism

(min,+) convolution is the key operation in (min,+) algebra, a theory often used to compute performance bounds in real-time systems. As already observed in many works, its algorithm can be computationally expensive, due to the fact that: i) its complexity is superquadratic with respect to the size of the operands; ii) operands must be extended before starting its computation, and iii) said extension is tied to the least common multiple of the operand periods. In this paper, we leverage the isomorphism between (min,+) and (max,+) algebras to devise a new algorithm for (min,+) convolution, in which the need for operand extension is minimized. This algorithm is considerably faster than the ones known so far, and it allows us to reduce the computation times of (min,+) convolution by orders of magnitude

Duality of the max-plus and min-plus network calculus

Duality of the Max-Plus and Min-Plus Network Calculus gives an accessible and concise review of the research conducted in Network Calculus to date