## 5 The Main Results  
We consider a transport network consisting of 5-20 nodes (cities) with several routes. Each node measures the inbound and outbound traffic. A vehicle on a road (an edge) should forecast the traffic to choose a route that is less busy to increase the transportation energy efficiency. The neural network was trained using MATLAB [29] and it was tested using a C language implementation on microcontrollers on each vehicle [15; 29]. The number of LSTM hidden layers is about 80 (our evaluation shows that increasing the number of layers does not improve the neural network performance). The numbers of processor cycles of the function that implement LSTM relation are as follows: _dot_--857 cycles, _sigmoid_--164 cycles and _tanh_--59 cycles. The execution time can be considered acceptable, as is shown in Figure 9.  
One can observe that the computational time is about 1 s for a neural network with about 100 layers. In Figure 9, the filtering is not considered, but in case of filtering, the execution time is increased by less than 10%. Considering a reasonable assumption that a decision can be made in maximum of 60 s, this framework can be used for a traffic forecasting system with about five features (that is, five adjacent nodes in each node) and an input buffer up to 600 observations. The above two scenarios were evaluated in terms of forecasting accuracy. The first and second scenario results are shown in Figures 10 and 11. The traffic is normalized to a maximum estimated traffic level. The circles in Figures 7 and 8 indicate differences between the two scenarios both with and without filtering. One can observe that the forecast accuracy is better for the second scenario. The oscillations in forecasted traffic are eliminated if filtering is involved. This is due to a better choice of analysis interval. Figure 9: Computational time vs. number of layers and number of nodes in graph [15]. Figure 11: Normalized forecasted traffic in second scenario [15]. Figure 10: Normalized forecasted traffic in first scenario [15]. To obtain a quantitative performance evaluation of the forecasting system, we compute the mean squared error as \(MSE=\sum\limits_{k=1}^{N}\left[input(k)-forecasted(k)\right]^{2}\) and take the mean MSE value as a metric to determine the forecast precision. We also consider the load of the communication network as a ratio of the reading time of the sensors and the analysis time. For the first scenario, the analysis interval is 60 min and for each analysis interval, the real inputs are read in the first 10 min. In the second scenario, after each detected traffic sensors' change, the inputs are read for 10 s. In our experiments, a real input change occurs, on average, at 140 s. The readings' intervals are smaller in the second scenario (less than 5 min per hour); therefore, the communication network load is twice as small as that in the first scenario. The detecting of changes increases the computational time by about 5%. In both scenarios, one can observe better accuracy if filtering is involved. The global evaluation of the performance is given by a score calculated as an arithmetic mean between the MSE and the load of the communication network normalized to the load of the second scenario. Figure 12 indicates the overall performance of the forecasting system. In this figure, the communication network load was normalized to the load in the second scenario. A lower score is better. One can observe that scenario 2 has better performance and filtering improves the performance in both scenarios. Filtering improves accuracy in both scenarios. Filtering leads to a greater improvement in the first scenario, which is simpler to implement. For the second scenario, which has a greater complexity, due to the necessity to detect significant changes in the input, filtering is useful, but the improvements are not so great as in the first scenario.