# Research on Networking Protocols for Large-Scale Mobile Ultraviolet Communication Networks
## 3 Network Performance Analysis
### Network Performance
#### 3.2.5 Throughput and Data Loss Rate  
By combining Equations (3), (6), (8) and (9), the probability \(P_{\text{loss}}\) of data transmission failure and data loss can be obtained.  
\[\left\{\begin{array}{l}P_{\text{success}}=P_{\text{path\_alley}}P_{\text{no \_inter}}P_{\text{matrix}}P_{\text{no\_ber}}\\ P_{\text{loss}}=1-P_{\text{success}}=1-\left[1-\exp(-\frac{A^{2}}{4\sigma^{2} \sigma^{2}})\right]^{m}(1-\frac{\pi^{2}A}{4\sigma^{2}})(1-BER)^{(n-1)N_{\text{ occupied}}B_{\text{ctrl}}}\end{array}\right. \tag{10}\]  
The average throughput of the network can be jointly represented by the number \(N_{\text{path}}\) of transmission paths established in an average complete transmission cycle and the average data volume \(B_{\text{path}}\) per transmission path.  
\[Throughput=\frac{B_{\text{path}}}{T_{\text{data}}}.N_{\text{path}} \tag{11}\]  
Only when the established transmission path does not experience interference, bit errors, or breakage during \(T_{\text{data}}\) is the data transmission valid. Therefore, when a single path successfully transmits data, the data volume it carries can be calculated.  
\[B_{path}=\frac{T_{\text{data}}}{mT_{\text{clk}}}.P_{success} \tag{12}\]  
In the limiting case where none of the transmission paths occupy Silent nodes, it follows that  
\[N_{\text{path}}=\frac{n}{N_{\text{occupied}}}=\frac{n}{(m+1)(c-1)+2}\leq\frac{n }{m+1} \tag{13}\]  
By combining the above equations, the final expression for the average throughput of the network can be obtained as follows:  
\[Throughput=\frac{n}{(m+1)mT_{\text{clk}}}\bigg{[}1-\exp(-\frac{A^{2}}{4\sigma^ {2}\sigma^{2}})\bigg{]}^{m}(1-\frac{n^{2}A}{4\sigma^{2}})(1-BER)^{\frac{(n-1)T_ {\text{data}}N_{\text{occupied}}B_{\text{ctrl}}}{T_{\text{clk}}}} \tag{14}\]  
As indicated in Equation (14), the fewer nodes occupied by each average transmission path, the more transmission paths the network can establish simultaneously, and the higher the throughput. The protocol employs a shortest path selection algorithm with high-priority nodes taking precedence, which can significantly reduce the number of nodes occupied by established transmission paths.  
Additionally, the impact of node density on network performance is also of great importance. On one hand, a higher node density results in fewer hops required for transmission paths, allowing nodes to transmit more data within \(T_{\text{data}}\). Moreover, the network exhibits a higher connectivity probability, avoiding data loss caused by the destination node not being in the same subnet. However, the number of silent nodes occupied by transmission paths also increases with higher node density, reducing the number of simultaneously establishable paths. On the other hand, when the node density is low, the network is likely to be partitioned into multiple subnets with high probability, degrading network performance.  
In mobile networks, mobility speed is one of the most critical influencing factors. An increase in node mobility speed accelerates changes in network topology, triggering issues such as interference, link breakage, or matrix expiration, which degrade network performance. Furthermore, in networks with low node density, node mobility further increases the probability of interference between different paths. When the mobility speed is high, shortening the neighbor discovery cycle and updating the connection matrix in a timely manner can mitigate the adverse effects of node mobility on network performance.