## 5 Performance Evaluation
### Performance Analysis of Our Proposed Method  
There are many variables that may affect the traffic flow, namely, the number of lanes, speed and distance between vehicles. The correlation between variables of multiple regression analysis and traffic flow is obtained by computation, and the variables with low correlation are deleted to reduce the amount of computation. Therefore, there are comparisons between one variable and three variables. The R-squared and test results are shown as the following Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Speed** & **Lanes** & **VEH-Distant** & **Speed+Lanes+Veh-Distant** \\ \hline R-squared & 0.1362 & 0.0067 & 0.0015 & **0.1383** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: R-squared comparison among variables. According to Equation (7), it is obvious that the correlation between the vehicle speed and traffic flow is much higher than the others, and the R-squared is less than 0.25. The highest is 0.1383, which is Speed+Lanes+Veh Distance. Therefore, in preprocessing of the traffic flow, the vehicle speed is firstly calculated as a conclusive variable affecting the traffic flow for data preprocessing, and then, the following operations are performed. We ran it five times for each set of experiments, following a step-by-step procedure for each experiment, and obtained the average values as the results. During the experiments on each baseline, we adjust the parameters to appropriate sizes to ensure that they do not overfit or underfit. The variables are brought into the MVHS-LSTM model, and epoch, learning rate and window length are iterated through the heuristic algorithm, and then, the following results are, respectively, obtained to obtain their effects on MAPE and time. The error and time data are normalized to obtain an intersecting point, and the nearby point is the best neutralization point. We take the midpoint data as the final result. Users can make a humanized adjustment on those points. Figure 4 shows the MAPE and time with an increasing number of iterations with other variables held constant. As the model is trained to be more suitable for data with the increase in iteration. So with the same learning rate and window length, the model becomes progressively better for the learned data as the number of iterations increases. It results in a decrease in the value of MAPE and an increase in the computing time required for learning. When the number of iterations was 1000, the MAPE was 0.0941, and the running time was 187.88 s. However, when the number of iterations increased from 1000 to 2000 and 4000, the MAPE decreased by 29.8% and 33.2%, and the running time increased by 193% and 492.8%. It can be seen that as the number of iterations increases, the error decreases while the learning time increases very quickly, but consuming 300% of the time to reduce the error by 3.4%. It is not worth wasting abundant computing time to acquire the tiny relative improvement in prediction accuracy in practice. As the number of epochs increases, the accuracy (MAPE) improves and becomes smaller, but the computation time increases. This is because the increase in the number of iterations leads to more learning cycles, resulting in improved learning capability. However, this improvement in learning comes at the cost of increased computational time. During the training process, we substitute the calculation error and time into the Formulas (14) and (15), and we obtain that when the epoch value is 1500, the ARG value is the smallest. Therefore, we choose the epoch of 1500 as our final result. Figure 5 shows that MAPE increases with the learning rate when other variables remain unchanged. The learning rate is a hyperparameter that guides us how to adjust  
Figure 4: The degree of epochs affecting MAPE and time. In summary, the model not only realizes the heuristic selection of parameters and variables but also gives the comprehensive value considering both MAPE and computing time.