Filtering and forecasting problems for aggregate traffic in Internet links

An important problem in bandwidth allocation and reservation over a communication link is to estimate the traffic bit rate in that link. This can be done by using specific tools for measurements of the traffic bit rate. However, the obtained measures are affected by some noise. Moreover, one might be interested in future traffic forecasting, when a prediction is needed. In this paper, an iterative filtering procedure is proposed for updating the traffic estimate upon the arrival of a new measurement. A birth and death stochastic model is assumed for the traffic bit rate to provide dynamical equations for the average behavior in the absence of information carried by measurements. Approximate solutions of the same updating problem are also given under the assumption that the posterior distribution of the traffic bit rate belongs to a specific class (beta or Gaussian distribution). This leads to approximate filtering procedures, which are expected to provide significant computational advantages. Finally, results obtained by processing simulated and real data are presented; stressing that the practical behavior of the approximate filters is quite satisfactory.