  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.
