Non-Linear Time-Series Models of Ethernet Traffic

In this paper non-linear threshold autoregressive models are examined for use in modeling the temporal variation in the byte-rate in Ethernet traffic. The model is comprised of a number of autoregressive processes each of which is to be used in a specified range of amplitude of the byte-rate. The local dynamics within each threshold range are captured by an autoregressive process. The switching between each submodel is conditioned on the amplitude of a lagged value of the time-series. To dev elop the model the Bellcore Ethernet LAN data is used. It is shown that non-linear threshold autoregressive processes can be used to capture the dynamics of Ethernet LAN traffic. This model also provides for both short and longterm prediction capability and allows us to quantitatively identify the sources of long-range-dependence features in the traffic. When the aggregate traffic is partitioned into classes based on packet sizes, certain classes of traffic follow deterministic cyclical patterns. These periodic components arise from the process switching between different amplitude regimes. Superposed on this fundamental period are longer cycles that can be localized either below or above the mean byte-rate. By constructing amplitude thresholds associated with a finite set of delay parameters, the dynamics within each threshold are captured by locally linear autoregressive processes. The aggregate process is globally nonlinear. This model is shown to provide good agreement with the marginal distributions and the correlation functions derived from the Ethernet traffic data. In addition, simulation experiments demonstrate that the loss statistics observed in finite buffer queues agree favorably with those generated by the measurements.

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