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.