The accurate and timely knowledge of a network's internal state is essential for various network management operations like routing, resource allocation, or even intrusion detection. This especially holds true for highly flexible, programmable networks that quickly react to dynamic conditions. However, current approaches of state monitoring in such networks rely on per-rule counter information. Due to limited rule space, their granularity is strongly limited. This generally yields an aggregated and therefore altered representation of the network state. Utilizing the programmability of today's data planes, we tackle this problem and present a novel approach to increase the measurement granularity up to per-application statistics. For demonstration purposes, we show how our approach greatly improves the estimation of the Flow Size Distribution.

Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility especially in high dimensions, while commonly used non-parametric methods suffer from the curse of dimensionality. A popular remedy is to construct a tree-based hierarchy of conditional bivariate copulas.In this paper, we propose a flexible, yet conceptually simple alternative based on implicit generative neural networks.The key challenge is to ensure marginal uniformity of the estimated copula distribution.We achieve this by learning a multivariate latent distribution with unspecified marginals but the desired dependency structure.By applying the probability integral transform, we can then obtain samples from the high-dimensional copula distribution without relying on parametric assumptions or the need to find a suitable tree structure.Experiments on synthetic and real data from finance, physics, and image generation demonstrate the performance of this approach.

Network state monitoring is a fundamental task for network management. However, determining the full network state in Software defined Networks requires disproportionately too many resources. This stems from the discrepancy between the established methods used for state monitoring compared to the varying contribution in terms of information obtained from every additionally monitored network node. This relationship may even become more complicated depending on the network state information of interest. One solution to overcome bottlenecks by reducing the overall monitoring footprint is the use of spatial sampling, which allows the estimation of the network state based a fraction of the overall state. In this work, we propose schemes to place a small number of measurement points in the SDN network to maximize the obtained network state information. Considering different conditions, we utilize routing information and graph theoretic centrality metrics, respectively, to estimate the amount of information a node provides. Based on this knowledge, we, furthermore, develop a mechanism to place multiple measurement points while avoiding redundant measurements. For demonstration purpose, we use the developed mechanisms to estimate the Flow Size Distribution in SDN environments. An emulative evaluation taking several known topologies shows the effectiveness of spatial sampling using the proposed scheme.