The thunder of distant Net storms

Computers and routers on the Internet send each other error messages (called ICMP datagrams) to signal conditions such as network congestion or blackouts. While these datagrams are very rare, less than 0.001% of total traffic, they hold very important global information about problems and congestions elsewhere in the Net. A measurement of the flow of such error messages in our local cluster shows a very pathological distribution of inter-message times: P (∆t) ≈ 1/∆t. This scaling extends for about seven decades, and is only punctuated by extraneously periodic signals from automatons. More than a half of these error messages were themselves generated erroneously. The decentralized and anarchich structure of the Internet has, for a long time, invited people to perform all sorts of measurements. Indeed, it has taxed and even challenged our ability to make such measurements: for instance, it’s been several years since we last knew, to any accuracy, how large the Internet actually is [1, 2]. Many types of measurements have shown “anomalous” or “pathologic” statistics, meaning that the distribution of some quantity has power-law (a.k.a. Pareto or “heavy”) tails . A power-law tail implies that the probability of an outlier diminishes very slowly with the size of the outlier, and hence measurements show strong irregularities. While anomalous from a classical statistics viewpoint, this is a very usual phenomenon in the natural sciences, and has been extensively studied [3, 4]; in particular, one of the earliest examples concerns noise in communication channels [5]. As applied to the Internet, local traffic measurements at the datagram level [6, 7, 8, 9, 10], session data [11], webserver workloads [12, 13], USENET thread length [14] and Web surfing patterns [15] all show these tails. There is ample evidence that these statistical pathologies do not come from intrinsic instabilities of the Net as a communications system, but rather stem from the way in which people use the Net. Power-law distributions are often regarded as prima-facie evidence of some