The shape of the loss curve and the impact of long-range dependence on network performance

M.R.H. Mandjes, Nam Kyoo Boots

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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 with LRD properties, a next question is: what is their impact on network performance? To assess this issue, we consider a generic source model: traffic generated by an individual user is modeled as a fluid on/off pattern with generally distributed on- and off-times; LRD traffic is obtained by choosing 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 deviations analysis says that the (steady-state) overflow probability decays exponentially in n; we call the corresponding 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 most significant properties of the loss curve. Strikingly, for small B, the decay rate depends on the distributions only through their means. For large B there is no such insensitivity property. In case of heavy-tailed on-times, the decay of the loss 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 the performance metrics to the probabilistic properties of the input, we compute the loss curve for a number of representative examples (voice, video, file transfer, web browsing, etc.), with realistic distributions and parameters. Our conclusions on the impact of LRD on the performance can be summarized as follows: (1) If the maximally tolerable delay is relatively small, there is hardly any difference between heavy-tailed and light-tailed inputs; this gives a theoretical handle on observations that appeared in the literature. Only for very delay tolerant applications the above-mentioned large B results kick in. (2) The level of aggregation is a significant factor. If the ratio between the link rate and the peak rate of a single source is high, a high utilization can be achieved, while at the same time the delay requirements are met; this holds even if the delay requirements are stringent.
Original languageUndefined
Article number10.1078/1434-8411-54100215
Pages (from-to)101-117
Number of pages17
JournalAEÜ International journal of electronics and communications
Issue number2
Publication statusPublished - 2004


  • Heavy-tailed distributions
  • Buffer overflow
  • Long-range dependence
  • Queueing Theory
  • Large deviations asymptotics
  • Packet networking
  • IR-70509
  • METIS-220829
  • EWI-17709

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