Shaping and policing of fractal traffic

We examine the effectiveness of shaping and policing mechanisms in reducing the inherent variability of fractal traffic, with the objective of increasing network operating points. Whether a shaper simply spaces a flow or allows small bursts according to a leaky bucket, we show using analytical arguments that, i) the Hurst parameter, which describes the asymptotic variability of the traffic, is unaffected; and ii) while the traffic can be made smoother over time scales smaller than one corresponding to the shaper's buffer size, fluctuations over longer time scales cannot be appreciably altered. We further show that if shaping is used to reduce buffer size requirements at a network bottleneck, any savings here are offset by the increased buffer requirements at the shapers. Perhaps the most significant deficiency of shaping identified here is that it is necessary to model individual streams to a level of accuracy that is not feasible in practice. In contrast, statistical multiplexing can achieve reasonable network efficiencies by only requiring characterizations of aggregate traffic.