# A Hybrid Control Path Planning Architecture Based on Traffic Equilibrium Assignment for Emergency
## 5 Experimental Results and Analysis
### The Availability and Timeliness of Equilibrium Traffic Assignment Prediction  
To learn the correlation between the current traffic distribution with the optimally equilibrated traffic distribution map, and to achieve the prediction of the optimally equilibrated traffic distribution in new scenarios, the ST-ETA equilibrium mapping layer uses Equation (15) for model training. In the experiments of this paper, the optimal balanced flow distribution map sample data are generated by the equilibrium assignment method with SO as the optimization objective and solved by the F-W [52] method.  
As can be seen from Figure 7a, the training RMSE, validation RMSE and MAE gradually decrease and level off over 500 iterations. The performance shown in Figure 7b can be achieved on the validation set after 500 training epochs, with an RMSE of 68.59, MAE of 41.34, and Accuracy of 78.60%. The horizontal coordinates of Figure 7c,d are shown in descending order by loads in the SO equilibrium distribution graph. Figure 7c illustrates the flow distribution between SO and ST-ETA for highly loaded sections with flows of 200-1500. It can be seen that ST-ETA captures the overall distribution pattern of SO well, but the flow loading is lower than the actual flow of SO. This suggests that ST-ETA merely captures the fact that high-traffic roads typically have a higher capacity to carry loads and can be used as critical evacuation roads in path planning. However, it cannot learn the maximum load carrying capacity of these critical roads. ST-ETA learns from multiple SO plans and \"averages\" several plans that are similar to the current scenario. When there exist SO plans that utilize certain roadways at or near-maximum capacity to accomplish evacuation, ST-ETA would allocate a small portion of the flow that exceeds the \"average\" capacity to the more critical and commonly used evacuation roads. This view can also be correspondingly corroborated from Figure 7d. This figure shows the comparison of two model flow distributions for the low-load road (0-200). Some low-load roads have slightly higher traffic volumes than the SO option. Certainly, this suggests that some travelers bear more costs in this evacuation (e.g., appropriately choosing a detour to a nearby roadway with lower loads). And the total system scheduling time increases accordingly. This is not  
Figure 6: The background load prediction error under different convolution modules.  
the absolute optimal balanced traffic distribution. But trying to achieve absolute optimality in a real large road network is unrealistic and the error is acceptable in terms of the total travel time comparison as seen in Section 5.3.  
In terms of model run times, we compare the data-driven method ST-ETA, which is mapped by the SO traffic assignment method, with the classical SO method MSA [11] and the F-W [52] method in terms of timeliness. The experiment uses the statistical OD evacuation volume and real-time calculated network capacity of the Chengdu road network from 13:00\(\sim\)14:00 on 1 November 2016. In Figure 8a, the MSA took 28 iterations to reach system optimization in 22,304.66 s, while the F-W required seven iterations in 5010.84 s. The ST-ETA was pre-trained using the neural network and took 14,257.14 s to perform 500 training iterations. The decision-making phase after training, as shown in Figure 8b, requires 843.93 s and 843.05 s for the FW and MSA allocation process based on an all-or-nothing policy, respectively. It cannot satisfy the demand of providing real-time path decision-making in emergency scenarios. The ST-ETA can provide a decision-making solution in only 101.51 s, which can effectively solve the problem of real-time decision-making for large-scale network path planning in emergencies.  
Figure 8: Comparison of the run time of different traffic assignment models.  
Figure 7: The prediction performance of ST-ETA.