# Virtual Network Function Embedding under Nodal Outage Using Deep Q-Learning
## 7 Simulation Results
### Service Acceptance Ratio  
Netrail topology's performance is represented from Figures 13-16 for 2, 4, 8, and 12 core CPUs, respectively. Figures 17-20 illustrate the performance of the BtEurope topology for 2, 4, 8, and 12 core CPUs, respectively. \begin{table}
\begin{tabular}{c c} \hline \hline  & **Parameters** \\ \hline Hidden Layers & 2 \\ Neuron per Layer & 256 \\ Neural Network & 2 \\ Target NN update (\(\tau\)) & 10 \\ Activation function (Expect for Output Layer) & ReLu \\ Drop Probability & 0.2 \\ Optimizer & Adam \\ Learning Rate & 0.001 \\ Discounting Factor & 0.99 \\ Batch Size & 32 \\ Memory Size & 80 \\ Loss Function & Mean Square Error (MSE) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: DRL model parameters. Figure 12: Diversification of the DRL Model. Considering the performance of topologies with 0% of nodal outage from the Figures 13-20, we can state that, with the rise in the core capacity (i.e., 2, 4, 8, and 16 VNF per core) as well as nodal capacity (i.e., 2, 4, 8, and 12 core), the SAR of the topologies increases. This is due to the surge in resource availability. These highly available resources are still inadequate with the increase in the VNF-FG's complexity (i.e., VNFs per VNF-FG). The rise in the complexity induces a surge in VNF's resource demand, causing these highly available resources to be insufficient. For a smaller topology like Netrail, the model refuses deployment of all VNF-FGs after a certain point, like 8 VNFs per service for 0% nodal outage, as shown in Figure 13. This is due to the constraint depicted by Equation (2), which states that each substrate node can accommodate just one VNF, and Netrail topology consists of only seven nodes. Any VNF-FGs containing VNFs more than the total number of substrate nodes are rejected. Therefore, small topologies dismiss the complex VNF-FGs. This is not the case for the large topology like BtEurope where a sufficient amount of resources are available for the placement of the VNF-FGs, making sure that the constraint in Equation (2) is always satisfied. Because of the high availability of resources, the BtEurope's performance is much better than Netrail. For example, considering the lowest available resource scenario: 2 core CPU and 2 VNF per core (see Figures 13 and 17), the SAR for BtEurope is approximately 50%, whereas Netrail could only serve \(\sim\)15% of VNF-FGs. Figure 14: SAR: Netrail Topology with Nodal Outage—4 Core CPU. Figure 13: SAR: Netrail Topology with Nodal Outage—2 Core CPU. Now, we focus our discussion on the Netrail topology's performance with 30% and 50% nodal outage. For two VNFs per service (or two VNFs per VNF-FG. We have used the terms 'VNF per service' and 'VNF per VNF-FG' interchangeably), all arrived VNF-FGs are accepted at 0% outage. With the rise in the nodal outage, this SAR declines due to less availability of substrate nodes. For example, for 30% nodal outage, the SAR is dropped by 20% (see Figure 13). If we examine the performance of the model horizontally (i.e., along with the VNF-FGs complexity), the rejection rate increases. This performance is maintained till the resource is exhausted or the constraint in Equation (2) is not satisfied. For 50% of the nodal outage, i.e., when the topology is modified and is composed of only three nodes, there is an acceptance of only fewer VNF-FGs (see Figures 15 and 16, which show that the 8-core and 12-core cases perform better than the 2-core and 4-core cases in the presence of nodal outage due to the presence of more resources in the topology). Exploring horizontally in the Figures 13 and 15, the model's performance deteriorates slowly due to the resource depletion, especially the link availability. The probability of connectivity of links between the VNFs is based on number of VNFs per Service. With the increase of VNF's per service, the demand for link resources increases. Figure 16: SAR: Netrail topology with nodal outage—12 Core CPU. Figure 15: SAR: Netrail topology with nodal outage—8 Core CPU.