On spectral analysis of the Internet delay space and detecting anomalous routing paths

Latency is one of the most critical performance metrics for a wide range of applications. Therefore, it is important to understand the underlying mechanisms that give rise to the observed latency values and diagnose the ones that are unexpectedly high. In this paper, we study the Internet delay space via robust principal component analysis (RPCA). Using RPCA, we show that the delay space, i.e. the matrix of measured round trip times between end hosts, can be decomposed into two components: the estimated latency between end hosts with respect to the current state of the Internet and the inflation on the paths between the end hosts. Using this decomposition, first we study the well- known low-dimensionality phenomena of the delay space and ask what properties of the end hosts define the dimensions. Second, using the decomposition, we develop a filtering method to detect the paths that experience unexpected latencies and identify routing anomalies. We show that our filter successfully identifies an anomalous route even when its observed latency is not obviously high in magnitude.

What is New about the Internet Delay Space?

The Internet delay space is a comprehensive result of the Internet topology, routing policies, and network traffic. In this paper, a large scale of measurement was carried out to measure the Internet delay space and reveal new characters of the Internet delay space today. A comprehensive analysis was made from three aspects: the relationship between delay and geodistance, TIV severity and its dimensionality. It's found that as the evolvement of the Internet, the Internet delay space is transforming from a non-metric space into a metric space. To validate our observation, a simulation experiment, complementary measurements and analysis on the former typical delay datasets were performed. The experimental results were consistent with our observation.

Investigation of Local Stability Transitions in the Spectral Delay Space and Delay Space

The stability boundaries of LTI time-delayed systems with respect to the delays are studied in two different domains: (i) delay space (DS) and (ii) spectral delay space (SDS), which contains pointwise frequency information as well as the delay. SDS is the preferred domain due to its advantageous boundedness properties and simple construct of stability transition boundaries. These transitions at the mentioned boundaries, however, present some conceptual challenges in SDS. This transition property enables us to extract the corresponding local stability variation properties in the DS, while it does not have any implication in the preferred SDS. The novel aspect of the investigation is to introduce a comparison mechanism between these two domains, DS and SDS, from the stability transition perspective. Interestingly, we are able to prove their equivalency, which provides complementary insight to the parametric stability variations.

Equivalency of Stability Transitions Between the SDS (Spectral Delay Space) and DS (Delay Space)

It has been shown that the stability of LTI time-delayed systems with respect to the delays can be analyzed in two equivalent domains: (i) delay space (DS) and (ii) spectral delay space (SDS). Considering a broad class of linear time-invariant time delay systems with multiple delays, the equivalency of the stability transitions along the transition boundaries is studied in both spaces. For this we follow two corresponding radial lines in DS and SDS, and prove for the first time in literature that they are equivalent. This property enables us to extract local stability transition features within the SDS without going back to the DS. The main advantage of remaining in SDS is that, one can avoid a non-linear transition from kernel hypercurves to offspring hypercurves in DS. Instead the potential stability switching curves in SDS are generated simply by stacking a finite dimensional cube called the building block (BB) along the axes. A case study is presented within the report to visualize this property.