This paper studies time scaling and queuing behavior of aggregate traffic that is asymptotically self-similar and also exhibits small time-scale irregularities introduced via a cascade construction. The main contribution of the paper is to provide some insight into how to choose an appropriate cascade construction in order to obtain desired scaling and queuing properties. It is found that the largest time-scale of mass redistribution has far more influence on queuing behavior than the number of stages in the cascade. Thus, appropriate queuing behavior can be achieved by using one or two stages of mass redistribution, perhaps derived from the actual network dynamics.
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