Our Method

The structure of our predictor is illustrated is as shown in Figure 9.1. To build such a predictor, three steps need to be carried out. The first is to form a database collected from real traffic traces for a sufficiently long period and to format this database in a specific manner (as described bellow). The second is to identify a suitable NN architecture and training algorithm as described in Sec. 9.3.3. Generally, the three-layer feedforward network and any efficient training algorithm like the Levenberg-Marquardt or the Conjugate Gradient algorithms may be a good choice. The third step is to train and test this NN and to select a retraining strategy (either periodically off line whenever the performance degrades bellow certain predefined threshold, or on line), see Sec. 9.3.6 for experimental results regarding this point. Concerning the real traces, they should be collected from the network whose traffic we want to predict. The accuracy of the method will greatly depend on the network traffic used in this learning phase. Each of the training and testing databases should consist of 5 parts. The first is the ``now window'' which consists of $F(T)\ldots F(T-n)$, where $F(T)$ is the current value of the traffic and $F(T-n)$ represents the value of the $n^{th}$ previous step. The second part is the ``yesterday window'', which contains $F_y(T)\ldots F_y(T-y)$, where $F_y(T)$ is the value of the traffic yesterday at the same time as now, and $F_y(T-y)$ is that of $y^{th}$ previous step. Similarly, the third part is the ``week window'', which contains $F_w(T)\ldots F_y(T-w)$, where $F_w(T)$ is the value of the traffic in the previous week, in the same day and at the same time as now. $F_w(T-w)$ is that of $w^{th}$ previous step. Then come the ``day'' and ``date'', where the ``day'' represents the day of the week from 0 to 6, and the ``time'' represents the time of the day. The ``time'' variable takes discrete values depending on the ``step size''. For example, if the ``step size'' is one minute, the ``time'' takes values that vary from 0 to $60\times 24$. The final part is the next value of the traffic, $F(T+1)$, that is, the output of the NN. All these data should be normalized to the range from 0 to 1. This is to achieve better performance, see Sec. 9.3.2 for more details. The ``now window'' represents the short-term information of the traffic process. Both the ``day window'' and ``week window'' as well as the ``day'' and ``date'' represent the long-term information.

Figure 9.1: A black-box representation of our tool to predict in real time the future traffic, where $T\in[0,\infty]$ is the time step number, $F(T)$ is the current value of the traffic, $F(T-n)$ is that at the previous $n^{th}$ step, $F_y(T)$ is that in the same instant but yesterday, $F_w(T)$ is that in the previous week, ``Time'' is the discrete time of the day, and ``Day'' is the day of the week