An adjusted ARIMA model for internet traffic

Traditional time series models such as ARIMA models have been proven to be inadequate for modelling traffic exhibiting long-range dependance. In this paper we present a new model the adjusted ARIMA model for modelling long-range dependant Internet traffic. The AARIMA model is suggested to give a quick and simple way to model Internet traffic by retaining all the properties of the ARIMA models while capturing the self- similarity. We use the Box-Jenkins methodology as a frame work for our modelling procedure. We construct our model by building the best ARIMA model possible for a trace and then adding our adjustment to obtain the equivalent AARIMA model. We show that the AARIMA model shows an evident improvement over the ARIMA model using several goodness of fit criteria, our main goodness of fit criteria is the ability to capture the Hurst parameter of the original trace being modeled. The model should not underestimate the Hurst parameter and any overestimation should be less than or equal to 20% of H parameter of the measured trace. The adjusted ARIMA model is shown to accurately predict Internet traffic for up to one hour in advance. The adjustment we propose to the ARIMA model is by introducing a feedback term made up of the first difference of the series being modeled. We used four Hurst parameter estimators to measure the self- similarity of the measured traces and both the AARIMA and ARIMA models for all measured traces. For all the estimators used the AARIMA was found to capture the long-range dependence irrespective of estimator used. We used the adjusted ARIMA model to predict three public domain internet traffic traces namely a Bellcore internet wide area network external traffic trace (length 35 hours), a Bellcore Internet Wide Area Network "purple cable" trace (length half an hour) and a MPEG-1 compressed video traffic trace (length half an hour). We show that for the public domain traces the AARIMA model gives values of H parameter which are more accurate than those given by the ARIMA model.