Multiscale analysis and control of networks with fractal traffic

A recently introduced multiscale framework is used to develop efficient ana lysis and design techniques for networks with self-similar traffic. These a llow the interarrival density function for fractal point processes under Be rnoulli random erasure to be determined, as well as the counting process di stribution for superposition of these processes. The results suggest that f ractal characteristics are preserved under traffic branching and merging, w hich may, in turn, provide insight into the prevalence of self-similarity i n aggregate traffic broadly observed on real networks. Multiscale technique s are also developed for analyzing fractal queueing scenarios. The persiste nt memory inherent in the underlying point processes leads to substantially different behavior than is observed in traditional queueing scenarios, and important implications on resource consumption and quality of service are discussed. Finally, we show how multiscale methods can be used with dynamic programming techniques to develop efficient and practical control policies for these fractal queues, In particular, optimal server control is develop ed for a memoryless queueing system with self-similar traffic input, and op timal flow control is formulated for self-similar service of memoryless tra ffic. Exploiting recent history, these controllers are shown to achieve sub stantially better performance-both in terms of quality of service and resou rce utilization-than queueing control strategies traditionally used. (C) 20 01 Academic Press