## 5 Numerical Results
### Impacts of DRL-JCBRTP NN Architectures on Beaconing Performance  
In Section 4.2, we introduced the SAC algorithm as a model-free, off-policy DRL approach that utilizes both actor and critic NNs to optimize beaconing performance in dynamic vehicular environments. The weights of both the SAC networks were initialized using the Xavier initialization method, which is effective in maintaining the variance of activations across layers, ensuring stable learning [39]. In our approach, the critic NN is structured as an MLP with two hidden layers, each consisting of 512 neurons, utilizing the ReLU activation function. To optimize the networks, we employed the Adam optimizer, which combines the benefits of adaptive learning rates (as in RMSProp) with the momentum technique to enhance convergence speed and stability [40]. Additionally, the learning rate was scheduled using Polyak averaging, which dynamically adjusts the learning rate to maintain efficient and stable training [41]. In this section, we evaluate the performance of four distinct actor NN architectures within the SAC framework: MLP, one-layer, two-layer, and three-layer LSTMs. The first actor network mirrors the critic network, employing an MLP with identical architecture and parameters. For the LSTM-based actor networks, each layer is configured with 256 hidden units and a sequence length of 10, focusing on learning and predicting sequences of beacon intervals. We then explore one-layer, two-layer, and three-layer LSTM configurations, with each additional layer following the same setup. This comprehensive comparison seeks to identify the most effective architecture for the actor NN in the SAC algorithm, with a focus on performance and the ability to learn complex sequences. We trained all these networks using prioritized replay memory and the SAC parameters in Table 1.  
**Beacon Rate and Transmit Power**: As shown in Figure 6, one-layer and two-layer LSTM models exhibit significant adaptability by adjusting their BRs in response to increased vehicle density. This dynamic response is likely a mechanism to manage channel congestion in denser environments. On the other hand, three-layer LSTM maintains a stable BR similar to the MLP, indicating a potentially less adaptive or more conservative strategy under high-density conditions. Figure 7 shows that the MLP model gradually increases its TP with rising vehicle density, which could worsen channel congestion. In addition, one-layer and three-layer LSTM models keep their TP nearly constant, suggesting their challenges in effective TP policy learning. In contrast, the TP of two-layer LSTM model starts at 28 dBm, decreasing and stabilizing at around 25 dBm as vehicle density increases. These results show that two-layer LSTM adapts its TP more effectively, better maintaining an optimal CBR and reducing beacon collisions, making it more efficient in varying traffic conditions. **Vehicle Detection Performance**: Figure 8 illustrates that two-layer LSTM consistently maintains a low detection failure probability (DFP), with only a minimal increase at higher vehicle densities, demonstrating its robust detection capabilities. In comparison, three-layer LSTM, though more stable than one-layer LSTM and MLP, exhibits a higher DFP than two-layer LSTM. Figure 9 further underscores the superiority of two-layer LSTM, which consistently achieves a significantly larger mDFD than the other models. While three-layer LSTM shows improvement, it still falls short, particularly in high-density scenarios. These results clearly indicate that two-layer LSTM is the most effective at maintaining detection reliability and distance across varying vehicle densities. Figure 6: Beacon rate vs. vehicle density. Figure 7: Transmit power vs. vehicle density.