The Joseph And Noah Effects And High-speed Network Traffic

Benoit Mandelbrot gave the Biblical stories of Joseph (the Joseph of the \´seven fat years and seven lean years\´) and Noah (of "Noah\´s ark" and the \´big flood") modern-day interpretations relevant for mathematical modeling; namely \´long-range depen- dence" and "the infinite variance syndrome". By long-range dependence we mean autocorrelations that decrease very slowly (like a power instead of geometric), by infinite variance syn- drome we mean distribution functions which have \´heavy tails" (Pareto-like tOs rather than exponential tails). Cu\´rrently used traffic modeling and performance analysis tech- niques fail to account for the Joseph and Noah Effects in a par- simonious manner. Based on extensive analyses of real-time traffic measurements from a number of different working packet networks, I win demonstrate why the Joseph and Noah Effects can be expected to play a major role not only in characterizing traffic in future high-speed networks but also in designing, con- trolling and managing these networks.