The Shape of the Loss Curve and the Impact of Long-Range Dependence on Network Performance

Empirical studies showed that many types of network traffic exhibit long-range dependence (LRD),i.e., burstiness on a wide variety of time-scales. Given that traffic streams are indeed endowed withLRD properties, a next question is: what is their impact on network performance? To assess thisissue, we consider a generic source model: traffic generated by an individual user is modeled as afluid on/off pattern with generally distributed on- and off-times; LRD traffic is obtained bychoosing the on-times heavy-tailed. We focus on an aggregation of many i.i.d. sources, say n,multiplexed on a FIFO queue, with the queueing resources scaled accordingly. Large deviationsanalysis says that the (steady-state) overflow probability decays exponentially in n; we call thecorresponding decay rate, as a function of the buffer size B, the loss curve. To get insight into the influence of the distribution of the on- and off-times, we list the mostsignificant properties of the loss curve. Strikingly, for small B, the decay rate depends on thedistributions it only through their means. For large B there is no such insensitivity property. In caseof heavy-tailed on-times, the decay of theloss probability in the buffer size is slower than exponential; this is in stark contrast with light-tailed on-times, in which case this decay is at least exponential. To assess the sensitivity of theperformance metrics to the probabilistic properties of the input, we compute theloss curve for anumber of representative examples (voice, video, file transfer, web browsing, etc.), with realisticdistributions and parameters.