3,554 research outputs found
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
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
Combinatorial Continuous Maximal Flows
Maximum flow (and minimum cut) algorithms have had a strong impact on
computer vision. In particular, graph cuts algorithms provide a mechanism for
the discrete optimization of an energy functional which has been used in a
variety of applications such as image segmentation, stereo, image stitching and
texture synthesis. Algorithms based on the classical formulation of max-flow
defined on a graph are known to exhibit metrication artefacts in the solution.
Therefore, a recent trend has been to instead employ a spatially continuous
maximum flow (or the dual min-cut problem) in these same applications to
produce solutions with no metrication errors. However, known fast continuous
max-flow algorithms have no stopping criteria or have not been proved to
converge. In this work, we revisit the continuous max-flow problem and show
that the analogous discrete formulation is different from the classical
max-flow problem. We then apply an appropriate combinatorial optimization
technique to this combinatorial continuous max-flow CCMF problem to find a
null-divergence solution that exhibits no metrication artefacts and may be
solved exactly by a fast, efficient algorithm with provable convergence.
Finally, by exhibiting the dual problem of our CCMF formulation, we clarify the
fact, already proved by Nozawa in the continuous setting, that the max-flow and
the total variation problems are not always equivalent.Comment: 26 page
Tropical linear algebra with the Lukasiewicz T-norm
The max-Lukasiewicz semiring is defined as the unit interval [0,1] equipped
with the arithmetics "a+b"=max(a,b) and "ab"=max(0,a+b-1). Linear algebra over
this semiring can be developed in the usual way. We observe that any problem of
the max-Lukasiewicz linear algebra can be equivalently formulated as a problem
of the tropical (max-plus) linear algebra. Based on this equivalence, we
develop a theory of the matrix powers and the eigenproblem over the
max-Lukasiewicz semiring.Comment: 27 page
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