Power laws, highly optimized tolerance, and generalized source coding

We introduce a family of robust design problems for complex systems in unce rtain environments which are based on tradeoffs between resource allocation s and losses. Optimized solutions yield the "robust, yet fragile" features of highly optimized tolerance and exhibit power law tails in the distributi ons of events for all but the special case of Shannon coding for data compr ession. In addition to data compression, we construct specific solutions fo r world wide web traffic and forest fires, and obtain excellent agreement w ith measured data.