# Fault Tolerant Spectral/Spatial Optical Code Division Multiple Access Passive Optical Network
## 5 Reliability Analysis
\(CP_{RN_{EN}}\) is used to represent the first coupler of the RN that receives the incoming signal and splits it for distribution towards the feeder level ring and ONTs at the distribution level. The unavailability of this coupler is represented as \(UA_{CP_{RN_{IN}}}\). \(UA_{2:2 CP_{RNsLD1,1}}\) is used to represent the unavailability of the first coupler and is used to initiate the spatial decoding process at the RN. Whereas \(UA_{1:2 CP_{RNsLD2,1}}\) and \(UA_{1:2 CP_{RNsLD2,2}}\) are used to give the unavailability of the coupler employed at the second stage of the spatial decoding process as per Figure 3.  
\(UA_{DF}\) and \(UA_{ONTs}\) are used to represent the unavailability of the OF medium employed at the distribution level and ONT modules, respectively. Mathematically, they can be expressed as follows:  
\[UA_{DF}=D_{DF}UA_{OF} \tag{6}\]  
\[UA_{ONT_{Total}}=UA_{FIL_{SE}}+UA_{TDU}+UA_{ONT} \tag{7}\]  
Figure 10 shows the connection availability of the network components for the tree-based architecture given in [5] against the proposed ring-based network. The given analysis is conducted for the system parameters given in Table 5, and the length of the OF medium is considered as 10 km for the feeder level in both the tree- and ring-based proposed architectures. Furthermore, 2 km OF medium is considered to be deployed between the RNs of the ring topology in the proposed architecture. At the distribution level, 3 km and 5 km OF media are considered for the proposed and conventional architectures, respectively. The analysis of the connection availability of the different system components demonstrates promising results for the proposed ring-based architecture. It can be observed that the availability of the components housed inside the CO, RN, and ONT modules is well above the acceptable range of 99.999% for both networks. Figure 10 shows a significant difference between the connection availability readings at the feeder level and distribution level where the OF medium is deployed and is considered as the most sensitive part of the network in terms of failures and maintenance. The analysis shows that the proposed ring-based architecture provides acceptable results in terms of connection availability for the feeder level OF medium. This improvement can be attributed to the fact that the OF medium employed at the feeder level of the proposed architecture is protected via a ring-based topology, which is capable of facilitating the flow of traffic in both clockwise and counterclockwise directions. Consequently, if a fault occurs at any point inside the ring, the switch at the switching arrangement moves from port 1 to 2 and restores the flow of traffic to the nodes beyond the point of failure. Thus, the proposed  
Figure 10: Connection availability of different system components for the proposed and conventional setups. \begin{table}
\begin{tabular}{l c} \hline
**Component** & **Components Unavailability** \\ \hline Optical line terminal & \(5.12\times 10^{-7}\) \\ \hline Optical coupler (1:2, 2:2) & \(3\times 10^{-7}\) \\ \hline Optical coupler (1:N, 2:N) & \(7.2\times 10^{-7}\) \\ \hline Time delay units & \(4\times 10^{-7}\) \\ \hline Optical switch & \(1.2\times 10^{-6}\) \\ \hline Mux/ De-Mux filters & \(1\times 10^{-7}\) \\ \hline Optical network terminal & \(5.12\times 10^{-7}\) \\ \hline OF/km & \(2.8\times 10^{-6}\) \\ \hline \end{tabular}
\end{table} 
Table 5: Unavailability \(\left(\frac{Failure}{10\text{th}}\right)\) for system components. ring-based topology provides redundancy at the feeder level, which significantly elevates the overall availability of the network. In contrast, the tree-based architecture utilizes a single feeder fiber to carry traffic from the CO toward the RN with no redundancy against the failures across the feeder fiber. Consequently, a single failure across the feeder fiber in the tree-based architecture can disrupt the flow of traffic between the CO and receiving nodes.