------------------------------------------------------------------------------- ******************************************************************************* ------------------------------------------------------------------------------- B O S T O N U N I V E R S I T Y Computer Science Department C O L L O Q U I U M Wednesday, September 25, 1996 3:00 pm (Coffee served at 2:30 pm) Seminar Room / MCS 135 ------------------------------------------------------------------------------- ******************************************************************************* ------------------------------------------------------------------------------- POWER-TAIL DISTRIBUTIONS AND THEIR SIGNIFICANCE IN THE BEHAVIOR OF COMMUNICATIONS AND COMPUTER SYSTEMS Lester Lipsky Department of Computer Science and Engineering University of Connecticut Storrs, CT 06269-3155 lester@brc.uconn.edu Power-tail distributions are those for which the probability that an event will exceed size "x" is of the form Pr(X>x) = R(x) ==> 1 / x^s for large x. Although they look well behaved, such distributions can have the singular property of infinite variance, or even an infinite mean. As pathological as these distributions seem to be, they occur everywhere in nature, from the CPU time used by jobs on main-frame computers, to sizes of files stored an discs, to size of earthquakes, to health-insurance claims. Recently there has been a spate of papers describing the highly irregular and "bursty" behavior of data transmission on various telecommunications networks. We show that such erratic behavior can be produced by renewal processes with power-tail inter-arrival times. We describe these distributions in detail, and present a class of functions which can be used for analytically modelling or simulating such traffic. We also discuss truncated power tails (distributions which have very large, but bounded domains) as models for systems which have experienced a relatively small number of arrivals. We then apply these to "buffer overflow" problems, showing how telecommunications networks with such arrival or service processes might be expected to behave over long periods of time. ------------------------------------------------------------------------------- For colloquium info, including directions, see http://www.cs.bu.edu/colloquium For more information contact Prof. David Yates -------------------------------------------------------------------------------