An extensive body of research deals with estimating the correlation and the Hurst parameter of Internet traffic traces. The significance of these statistics is due to their fundamental impact on network performance. The coverage of Internet traffic traces is, however, limited since acquiring such traces is challenging with respect to, e.g., confidentiality, logging speed, and storage capacity. In this work, we investigate how the correlation of Internet traffic can be reliably estimated from random traffic samples. These samples are observed either by passive monitoring within the network, or otherwise by active packet probes at end systems. We analyze random sampling processes with different inter-sample distributions and show how to obtain asymptotically unbiased estimates from these samples. We quantify the inherent limitations that are due to limited observations and explore the influence of various parameters, such as sampling intensity, network utilization, or Hurst parameter on the estimation accuracy. We design an active probing method which enables simple and lightweight traffic sampling without support from the network. We verify our approach in a controlled network environment and present comprehensive Internet measurements. We find that the correlation exhibits properties such as long range dependence as well as periodicities and that it differs significantly across Internet paths and observation times.
A comparison of Poisson and periodic sampling was carried out in @cite_18 @cite_19 . In @cite_18 the authors show experimentally, that the differences between round trip times (RTT), loss rate and packet pair dispersion estimates, obtained by either Poisson or periodic probing, are in some cases not significant. Depending on the autocovariance of the sampled process, Poisson or periodic sampling can be superior. This is shown in @cite_19 using the metric asymptotic variance.
@cite_19 @cite_18
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Active probes of network performance represent samples of the underlying performance of a system. Some effort has gone into considering appropriate sampling patterns for such probes, i.e., there has been significant discussion of the importance of sampling using a Poisson process to avoid biases introduced by synchronization of system and measurements. However, there are unanswered questions about whether Poisson probing has costs in terms of sampling efficiency, and there is some misinformation about what types of inferences are possible with different probe patterns. This paper provides a quantitative comparison of two different sampling methods. This paper also shows that the irregularity in probing patterns is useful not just in avoiding synchronization, but also in determining frequency-domain properties of a system. This paper provides a firm basis for practitioners or researchers for making decisions about the type of sampling they should use in a particular applications, along with methods for the analysis of their outputs The well-known PASTA ("Poisson Arrivals See Time Averages") property states that, under very general conditions, the fraction of Poisson arrivals that observe an underlying process in a particular state is equal, asymptotically, to the fraction of time the process spends in that state. When applied to network inference, PASTA implies that a Poisson probing stream provides an unbiased estimate of the desired time average. Our objective is to examine the practical significance of the PASTA property in the context of realistic RTT, loss rate and packet pair dispersion measurements with a finite (but not small) number of samples. In particular, we first evaluate the differences between the point estimates (median RTT, loss rate, and median dispersion) that result from Poisson and Periodic probing. Our evaluation is based on a rich set of measurements between 23 PlanetLab hosts. The experimental results show that in almost all measurement sessions the differences between the Poisson and Periodic point estimates are insignificant. In the case of RTT and dispersion measurements, we also used a non-parametric goodness-of-fit test, based on the Kullback-Leibler distance, to evaluate the similarity of the distributions that result from Poisson and Periodic probing. The results show that in more than 90 of the measurements there is no statistically significant difference between the two distributions.