Multiscale Analysis and Control of Networks with Fractal Traffic

Abstract

A recently introduced multiscale framework is used to develop efficient analysis and design techniques for networks with self-similar traffic. These allow the interarrival density function for fractal point processes under Bernoulli random erasure to be determined, as well as the counting process distribution for superposition of these processes. The results suggest that fractal characteristics are preserved under traffic branching and merging, which may, in turn, provide insight into the prevalence of self-similarity in aggregate traffic broadly observed on real networks. Multiscale techniques are also developed for analyzing fractal queueing scenarios. The persistent 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 developed for a memoryless queueing system with self-similar traffic input, and optimal flow control is formulated for self-similar service of memoryless traffic. Exploiting recent history, these controllers are shown to achieve substantially better performance—both in terms of quality of service and resource utilization—than queueing control strategies traditionally used.