arXiv subjects

Steffen Bondorf

Publications and source records attributed to Steffen Bondorf.

6 recordsLinked to original sources

arXiv2023

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.

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arXiv2022

Network Calculus with Flow Prolongation -- A Feedforward FIFO Analysis enabled by ML

The derivation of upper bounds on data flows' worst-case traversal times is an important task in many application areas. For accurate bounds, model simplifications should be avoided even in large networks. Network Calculus (NC) provides a modeling framework and different analyses for delay bounding. We investigate the analysis of feedforward networks where all queues implement First-In First-Out (FIFO) service. Correctly considering the effect of data flows onto each other under FIFO is already a challenging task. Yet, the fastest available NC FIFO analysis suffers from limitations resulting in unnecessarily loose bounds. A feature called Flow Prolongation (FP) has been shown to improve delay bound accuracy significantly. Unfortunately, FP needs to be executed within the NC FIFO analysis very often and each time it creates an exponentially growing set of alternative networks with prolongations. FP therefore does not scale and has been out of reach for the exhaustive analysis of large networks. We introduce DeepFP, an approach to make FP scale by predicting prolongations using machine learning. In our evaluation, we show that DeepFP can improve results in FIFO networks considerably. Compared to the standard NC FIFO analysis, DeepFP reduces delay bounds by 12.1% on average at negligible additional computational cost.

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arXiv2020

On the Robustness of Deep Learning-predicted Contention Models for Network Calculus

The network calculus (NC) analysis takes a simple model consisting of a network of schedulers and data flows crossing them. A number of analysis "building blocks" can then be applied to capture the model without imposing pessimistic assumptions like self-contention on tandems of servers. Yet, adding pessimism cannot always be avoided. To compute the best bound on a single flow's end-to-end delay thus boils down to finding the least pessimistic contention models for all tandems of schedulers in the network - and an exhaustive search can easily become a very resource intensive task. The literature proposes a promising solution to this dilemma: a heuristic making use of machine learning (ML) predictions inside the NC analysis. While results of this work were promising in terms of delay bound quality and computational effort, there is little to no insight on when a prediction is made or if the trained algorithm can achieve similarly striking results in networks vastly differing from its training data. In this paper, we address these pending questions. We evaluate the influence of the training data and its features on accuracy, impact and scalability. Additionally, we contribute an extension of the method by predicting the best $n$ contention model alternatives in order to achieve increased robustness for its application outside the training data. Our numerical evaluation shows that good accuracy can still be achieved on large networks although we restrict the training to networks that are two orders of magnitude smaller.

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arXiv2020

Sublinear-Time Non-Adaptive Group Testing with $O(k \log n)$ Tests via Bit-Mixing Coding

The group testing problem consists of determining a small set of defective items from a larger set of items based on tests on groups of items, and is relevant in applications such as medical testing, communication protocols, pattern matching, and many more. While rigorous group testing algorithms have long been known with runtime at least linear in the number of items, a recent line of works has sought to reduce the runtime to ${\rm poly}(k \log n)$, where $n$ is the number of items and $k$ is the number of defectives. In this paper, we present such an algorithm for non-adaptive probabilistic group testing termed {\em bit mixing coding} (BMC), which builds on techniques that encode item indices in the test matrix, while incorporating novel ideas based on erasure-correction coding. We show that BMC achieves asymptotically vanishing error probability with $O(k \log n)$ tests and $O(k^2 \cdot \log k \cdot \log n)$ runtime, in the limit as $n \to \infty$ (with $k$ having an arbitrary dependence on $n$). This closes a recently-proposed open problem of simultaneously achieving ${\rm poly}(k \log n)$ decoding time using $O(k \log n)$ tests without any assumptions on $k$. In addition, we show that the same scaling laws can be attained in a commonly-considered noisy setting, in which each test outcome is flipped with constant probability.

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arXiv2019

Cross-Sender Bit-Mixing Coding

Scheduling to avoid packet collisions is a long-standing challenge in networking, and has become even trickier in wireless networks with multiple senders and multiple receivers. In fact, researchers have proved that even {\em perfect} scheduling can only achieve $\mathbf{R} = O(\frac{1}{\ln N})$. Here $N$ is the number of nodes in the network, and $\mathbf{R}$ is the {\em medium utilization rate}. Ideally, one would hope to achieve $\mathbf{R} = Θ(1)$, while avoiding all the complexities in scheduling. To this end, this paper proposes {\em cross-sender bit-mixing coding} ({\em BMC}), which does not rely on scheduling. Instead, users transmit simultaneously on suitably-chosen slots, and the amount of overlap in different user's slots is controlled via coding. We prove that in all possible network topologies, using BMC enables us to achieve $\mathbf{R}=Θ(1)$. We also prove that the space and time complexities of BMC encoding/decoding are all low-order polynomials.

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arXiv2017

Quality and Cost of Deterministic Network Calculus - Design and Evaluation of an Accurate and Fast Analysis

Networks are integral parts of modern safety-critical systems and certification demands the provision of guarantees for data transmissions. Deterministic Network Calculus (DNC) can compute a worst-case bound on a data flow's end-to-end delay. Accuracy of DNC results has been improved steadily, resulting in two DNC branches: the classical algebraic analysis and the more recent optimization-based analysis. The optimization-based branch provides a theoretical solution for tight bounds. Its computational cost grows, however, (possibly super-)exponentially with the network size. Consequently, a heuristic optimization formulation trading accuracy against computational costs was proposed. In this paper, we challenge optimization-based DNC with a new algebraic DNC algorithm. We show that: (i) no current optimization formulation scales well with the network size and (ii) algebraic DNC can be considerably improved in both aspects, accuracy and computational cost. To that end, we contribute a novel DNC algorithm that transfers the optimization's search for best attainable delay bounds to algebraic DNC. It achieves a high degree of accuracy and our novel efficiency improvements reduce the cost of the analysis dramatically. In extensive numerical experiments, we observe that our delay bounds deviate from the optimization-based ones by only 1.142% on average while computation times simultaneously decrease by several orders of magnitude.

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