Experimental Tests to Identify the Best Length of Each Window

To identify the best architecture (in term of each window size, and the number of hidden neurons) for the neural network, we carried out the following experiment. From the ENSTB trace, we created a set of training and testing databases. Each database is characterized by the length of the now-, yesterday-, and week-window sizes. We varied the now window from 2 to 5, the yesterday window from 0 to 3, and the week window from 0 to 3. For the neural network architecture, we varied the number of hidden neurons from 1 to 10. We trained and tested each case of the 36 networks with the different training and testing databases, and repeated that for the different architectures obtained by varying the number of hidden neurons. As it is known that the initial values of the neural network weights (generally chosen randomly) affect the overall performance of the neural network, we initialized the random seed generator to the same value every time we created a new network. For each trained neural network, we used it to predict all the samples of the next two weeks. We reported the number of hidden neurons, the size of each window and the MSE value. The minimum number of the hidden neurons that gives the best performance is 2. The optimal values of the window size is that 3 for the ``now'', 2 for ``yesterday'', and 2 for the ``week'' windows. For these optimal values we got MSE=0.0041. These values illustrate the effectiveness of our model. The yesterday and the last-week windows as well as the date and day, when used, improved the performance of the NN to predict and to learn the traffic process. After choosing the best windows sizes, we show in Figure 9.2 the selected NN architecture for our model.

Figure 9.2: Our best architecture employing both short- and long-range dependencies in traffic prediction for the ENSTB Network.