## 5 Forecasting Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Predictor** & **Time Interval** & **r** & **RMSE** & **MAPE** \\ \hline \multirow{4}{*}{MLP-FFA} & t & 3.2 & 6.8 & 12.07\% \\  & t + 1 & 3.5 & 7.2 & 13.95\% \\  & t + 2 & 3.6 & 7.8 & 14.89\% \\  & t + 3 & 3.9 & 7.9 & 15.32\% \\ \hline \multirow{4}{*}{ARIMA} & t & 4.4 & 9.1 & 13.56\% \\  & t + 1 & 4.6 & 9.7 & 15.37\% \\  & t + 2 & 6.8 & 14.2 & 18.93\% \\  & t + 3 & 8.5 & 15.7 & 23.24\% \\ \hline \multirow{4}{*}{ARIMA-PSO} & t & 3.3 & 6.8 & 9.39\% \\  & t + 1 & 3.4 & 6.9 & 9.89\% \\  & t + 2 & 3.7 & 7.2 & 10.48\% \\  & t + 3 & 3.9 & 7.8 & 11.57\% \\ \hline \multirow{4}{*}{DRBM-FFA} & t & 2.9 & 6.1 & 8.75\% \\  & t + 1 & 3.1 & 6.4 & 9.63\% \\  & t + 2 & 3.4 & 6.9 & 10.31\% \\  & t + 3 & 3.5 & 7.1 & 11.12\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Traffic flow prediction results. Figure 7: RMSPE for the targeted links. Calculating the computation time (CT) taken for algorithm completion is especially necessary in the real-time IoV applications when OBU computer systems should quickly respond to any external occurrences. In this work, to obtain a fair comparison, the same computer is used for measuring the computation time (as measured by the \"tic-toc\" MATLAB function) [48; 49]. The MATLAB R2017b on an Intel Core i5 laptop with Windows 10 system is used to carry out this measurement. In this study, the stopwatch timer functions, tic and toc, are used to calculate the computation time. Invoking tic starts the timer, and the next toc reads the elapsed time in MATLAB. The CPU time returns the total CPU time (in seconds). The line graph compares the amount of computation time on the DRBM-FFA, MLP-FFA, ARIMA, and ARIMA-PSO in 30 runs. When comparing the data resulting from the plot, the average time needed for ARIMA-PSO and MLP-FFA calculation is approximately 0.6 (s). ARIMA has a high computation time of about 0.7 (s). In contrast, DRBM-FFA has the lowest computation time of 0.5 (s). Figure 9 shows changes in the computation time between the DRBM-FFA, MLP-FFA, ARIMA, and ARIMA-PSO methods. The standard deviation (SD) of the function values achieved in the experimental trials were also evaluated to determine prediction stability. Here the same initial conditions are used for all algorithms. The results in Figure 10 show that the standard deviation of the function values of all the other algorithms have larger values in comparison to the proposed DRBM-FFA approach. ARIMA-PSO is the next most robust approach, followed by MLP-FFA and ARIMA. The average of standard deviation for ARIMA is clearly the highest with values at 0.050, and hence their solutions qualities can be deduced to be less stable. Figure 8: Monte Carlo experiment results over a 60-min period. Figure 9: Average of computation time. In sum, the average of standard deviation obtained by DRBM-FFA is lower than those obtained by MLP-FFA, ARIMA, and ARIMA-PSO, so the proposed hybrid is very robust. Also, the swarm method of PSO achieves better result in standard deviation by ARIMA-PSO than MLP-FFA, ARIMA. The less the operating cost can be achieved with smaller standard deviations. To further test the effectiveness of the proposed scheme, the proposed DRBM-FFA algorithm is compared in terms of complexity with the MLP-FFA, ARIMA, ARIMA-PSO algorithms. The computational complexity of the proposed model depends on the number of training samples in datasets, the structure of the RBM, the time complexity for the initialization of the fireflies, calculating the fitness values, attraction mechanism and updating the light intensity for selecting the best firefly. So, the overall computational complexity is determined as follows:  
\[ \begin{array}{ll}O(\text{RBM},\text{FFA})=&O(\text{RBM})+O(\text{FFA})\\ &=O(\text{RBM})+O(\text{initialization})+O(\text{cost function calculation})\\ &+O(\text{attraction})+O(\text{light intensity})+O(\text{best firefly selection})\end{array}