A predictability analysis of network traffic
This paper assesses the predictability of network traffic by considering two metrics: (1) how far into the future a traffic rate process can be predicted with bounded error; (2) what the minimum prediction error is over a specified prediction time interval. The assessment is based on two stationary traffic models: the auto-regressive moving average and the Markov-modulated poisson process. In this paper, we do not aim to propose the best traffic (prediction) model, which is obviously a hard and arguable issue. Instead, we focus on the constrained predictability estimation with assumption and discussion about the modeling accuracy. The specific time scale or bandwidth utilization target of a predictive network control actually forms the constraint. We argue that the two models, though both short-range dependent, can capture statistics of (self-similar) traffic quite accurately for the limited time scales of interests in measurement-based traffic management. This argument, in mathematical terms, simply reflects the fact that the summarized exponential (correlation) functions may approximate a hyperbolical one very well. Our study reveals that the applicability of traffic prediction is limited by the deteriorating prediction accuracy with increasing prediction interval. From both analytical and numerical studies, we explore the different roles of traffic statistics, either at the 1st-order or the 2nd-order, in traffic predictability. Particularly, the statistical multiplexing and proper measurement (e.g. sampling/filtering) of traffic show positive effects. Experimental results suggest promising backbone traffic prediction, and generally enhanced predictability if small time-scale traffic variations, which are usually of less importance to bandwidth allocation and call admission control, have been filtered out. The numerical results in the paper provide quantized reference to the optimal online traffic predictability for network control purposes.
prediction self-similarity time-scale arma mmpp