  Measurements and data analysis have proved very effective in the study of the
Internet's physical fabric and have shown heterogeneities and statistical
fluctuations extending over several orders of magnitude. Here we analyze
performance measurements obtained by the PingER monitoring infrastructure. We
focus on the relationship between the Round-Trip-Time (RTT) and the
geographical distance. We define dimensionless variables that contain
information on the quality of Internet connections finding that their
probability distributions are characterized by a slow power-law decay
signalling the presence of scale-free features. These results point out the
extreme heterogeneity of the Internet since the transmission speed between
different points of the network exhibits very large fluctuations. The
associated scaling exponents appear to have fairly stable values in different
data sets and thus define an invariant characteristic of the Internet that
might be used in the future as a benchmark of the overall state of ``health''
of the Internet. The observed scale-free character should be incorporated in
models and analysis of Internet performance.
