## 9 Discussion  
The algebraic algorithm built into every node in the additional network to connect the second base station to the cluster heads performed well compared to its nearest pathfinding algorithm (single source shortest path). A comparison of the algorithms is shown in Table 5.  
Several pathfinding algorithms proposed in the literature have been surveyed and the same is compared with the algebraic pathfinding algorithm presented in this paper. The comparison considers the number of nodes, edges, shortest paths, path pairs and several elements. The comparison is carried out considering the network shown in the revised IoT diagram. From the table, it can be observed that algebraic methods require fewer operations for selecting a path for data transmission, given that a source node from the transmission is initiated.  
The failure rate of a base station is negligible. The success rate is around 98.0%. The entire IoT network will malfunction when a base station fails. The probability of which is 0.98. To ensure a failure-free situation (100% success rate), adding a second base station is necessary, which requires a different type of networking topology because the distance  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & & \multicolumn{5}{c}{**Preceding Devices**} \\ \cline{5-8}  & & & & \begin{tabular}{c} **Device** \\ **Rate** \\ \end{tabular} & \begin{tabular}{c} **Device** \\ **For Connection** \\ \end{tabular} & \begin{tabular}{c} **Device** \\ **Name D1** \\ \end{tabular} & \begin{tabular}{c} **Device** \\ **Name D2** \\ \end{tabular} & \begin{tabular}{c} **Device** \\ **Name D3** \\ \end{tabular} & \
\begin{tabular}{c} **Device** \\ **Name D4** \\ \end{tabular} &
\begin{tabular}{c} **Combined** \\ **Success** \\ **Rate** \\ \end{tabular} \\ \hline
10 & \begin{tabular}{c} Device Level \\ CrossBar NW \\ 11 \\ 12 \\ 13 \\ 14 \\ 15 \\ 16 \\ 17 \\ 18 \\ 18 \\ 19 \\ 19 \\ 20 \\ 21 \\ 22 \\ 23 \\ 24 \\ 25 \\ 26 \\ 27 \\ 28 \\ 29 \\ 20 \\ 21 \\ 23 \\ 24 \\ 25 \\ 26 \\ 27 \\ 28 \\ 29 \\ 29 \\ \end{tabular} & \begin{tabular}{c} **Device** \\ **Success** \\ **Rate S1** \\ \end{tabular} & \begin{tabular}{c} **Device** \\ **Name D2** \\ \end{tabular} & \
\begin{tabular}{c} **Device** \\ **Name D3** \\ \end{tabular} &
\begin{tabular}{c} **Device** \\ **Name D4** \\ \end{tabular} \\ \hline
10 & \
\begin{tabular}{c} Device Level \\ CrossBar NW \\ CrossBar NW \\ 11 \\ 12 \\ 13 \\ 14 \\ 15 \\ 16 \\ 16 \\ 17 \\ 18 \\ 19 \\ 20 \\ 21 \\ 20 \\ 21 \\ 22 \\ 23 \\ 24 \\ 25 \\ 26 \\ 27 \\ 28 \\ 29 \\ 29 \\ \end{tabular} &
\begin{tabular}{c} Level \\ 0.987 \\ 0.987 \\ 0.950 \\ 0.95  
between the cluster head and the second base station becomes a major issue.Adding one redundant base station is sufficient as it provides a 100% success rate. With the addition of more base stations, the cluster heads will become overloaded, which leads to a depletion of response time due to increased latency.  
The success rate of the revised IoT network is 0.948 when compared with an IoT network that caters for changes in the device, the fault rate of which is fixed at 0.827. A comparative analysis of improvements in the fault tolerance in the IoT network achieved with changes made into different layers of the IoT network is shown in Table 6. With the changes made to the IoT network, the fault tolerance level of the IoT network is increased by 14.63%.