## 4 Results
### Performance of Wireless Link Lifetime Prediction and One-Hop Channel Delay Prediction Using DNNs
The test data sets for one-hop channel delay prediction consisted of 700,000 samples, each for high-contention and low-contention scenarios. The low-contention scenario yielded a loss of 0.00000051 and an RMSE of 0.00071. The high-contention data set yielded a higher loss of 0.000019 and an RMSE of 0.00434. As the delay values were normalized on a scale of 100,000 us, the RMSE of the one-hop channel delay prediction DNN under low contention mapped to an error of 71 us, which was smaller than the 100,000 us time scale, while the 434 us error of the DNN predicting one-hop channel delay under high contention was significantly higher. This higher loss in a high-contention scenario occurs as a result of random contention delays caused by random backoff delays during the contention period. Thus, under high-contention scenarios, the one-hop channel delay prediction is more erroneous, so the routing algorithm should switch to distance mode. Next, we analyzed the computational complexity of wireless link lifetime prediction for the DNN-based approach and the optimization-based approach. In this experiment, we varied the total number of wireless links and calculated the average computational time per wireless link per data gathering cycle (\(T_{com}\)) using Equation (38). We computed the average value over 600 data gathering cycles. However, for the reader's better understanding, we have shown the 95 % confidence interval variation of the computational time in Figure (b)b. Note that the computational time of the DNN-based approach includes the data pre-processing (computing 2 nd-8 th-order terms and normalization) time along with prediction time. It is crystal clear, as is evident from Figure (b)b, that the average computational time per data gathering cycle increased for both the DNN-based approach and the optimization-based approach with the increment in the number of links. However, the increment was very low for wireless link lifetime prediction using the DNN, while a directly proportional relationship between computational time and number of links was observed for the optimization-based approach. This is because we can observe that, when the number  
Figure 15: Training curves of DNNs and computational complexity comparison of wireless link lifetime prediction models: (**a**) Training curves of DNNs, (**b**) Computational complexity comparison of two approaches for wireless link lifetime prediction. of links doubles, the computational time per data gathering cycle also doubles for the optimization-based approach. On the other hand, for the DNN-based approach, the increment in computational time with the number of links is much smaller compared to the optimization-based approach. For instance, the average computational time for the DNN-based approach increased from 33.85 ms to 55.93 ms when the number of wireless links increased from 1 to 512. The computational time for the optimization-based approach was lower than the proposed DNN approach only when the number of links was less than two, as is evident from Figure 15b. However, vehicular networks consist of a large number of vehicles and RSUs, so the number of links that have to be predicted within a given data gathering cycle is usually large. Therefore, in large networks, as the number of links is high, we can conclude that the optimization-based wireless link lifetime prediction approach fails as the average computational time per data gathering cycle extends to thousands of milliseconds; thus, it will not be able to predict wireless link lifetimes, ensuring the latency requirements of vehicular networks. On the other hand, for the proposed wireless link lifetime prediction using a DNN, the average computational time was 55.93 ms when the number of links was 512. Furthermore, even if the number of links was much higher than 512 (say, 2000), according to the gradient of the graph, we can expect the average computational time for wireless link lifetime prediction using DNN to be less than 100 ms, thus successfully satisfying latency requirements for vehicular communication.