Modelling of autocorrelated traffic using TES processes: New contributions to the empirical methodology

Abstract

The modelling of traffic in current telecommunication networks, and in particular of video traffic requires methods that take into account any possible strong autocorrelations in the arrival process. The presence of a strong autocorrelation, which is typical in burst traffic, makes the network performance measurements based on classical queuing models with independent arrivals non valid, producing poor estimates of delays and loss rates. Nowadays, TES (Transform Expand Sample) models [1], [2], proposed by B. Melamed, represent an attractive alternative to modelling strongly autocorrelated processes. These models can be easily implemented on a computer, they present low computational complexity and allow the approximation of a wide variety of autocorrelation functions. In this paper we suggest three modifications of the empirical methodology for the fit of TES processes [3]. The first one is a modification of the GSLO (Global Search Local Optimisation) algorithm, which significantly reduces the computation time of the algorithm. The second contribution consists of using not only the marginal distribution and the autocorrelation function of the empirical series, but also its partial autocorrelation function as a criterion for the selection of the TES model. In this way, we can considerably improve the process of selection of the parameters for the model, obtaining a much better fit to the empirical data. Finally, we propose to increase the objectivity of the modelling process by computing a residual value that measures the difference between the empirical data and the synthetic TES series generated, thus reducing the heuristic selection process that the user must realize.