# A New Resource Allocation Protocol for the Backhaul of Underwater Cellular Wireless Networks
## Average surplus capacity of the UBSC
#### 4.2.2 Scenario 2  
Here, we investigated the four performance measures for different \(\mu_{UBSmax}\) adjustment parameter \(\beta\) and the number of mobile UTs \(N_{MN}\). As described in Table 3, \(\mu_{UBSmax}\) is expressed as a function of \(\beta\) as \(\frac{\mu_{UBSmax}}{N}+\beta\). We changed the value of \(\beta\) from 0 to 4, and that of \(N_{MN}\) from 1 to 2. The burst traffic, generated from each mobile UT, arrives at the UBS with Poisson arrival rate 30. And the average packet arrival rate of each UBS, denoted by \(\lambda\), is changed from 3 to 20.  
Figure 11 shows the average packet drop rate for this case. As shown in the graph, the average packet drop rate increases as the average packet arrival rate \(\lambda\) increases and the \(\beta\) increases. In the graph, we can find that the average drop rate is different dependent upon the number of mobile nodes (or terminals) \(N_{MN}\).  
Figure 12 shows the average resource utilization for this case. As shown in the figure, the average resource utilization approaches to almost 99% as the packet arrival rate \(\lambda\) increases. Note that when \(N_{MN}=1\) and \(\lambda<7\), the average resource utilization is high for \(\beta=0\), and when \(N_{MN}=1\) and \(7<\lambda<10\), the average resource utilization is higher for \(\beta=2\) and \(\beta=4\) than \(\beta=0\). This can be interpreted as follows. When \(\lambda<7\), the packet arrival rate of a UBS is small. So, resource utilization becomes higher for \(\beta=0\) since each UBS will have \(\mu_{UBSmax}=10\), and this capacity can support the small packet arrival rate sufficiently. However, when \(7<\lambda<10\), since the packet arrival rate is a little  
Figure 11: Average Packet Drop Rate for different \(\mu_{UBSmax}\) adjustment parameter (\(\beta\)) and the number of mobile UTs (\(N_{MN}\)).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Description** & **Values in SLS** \\ \hline \(M\) & The number of SLSs with the same parameters & 10 \\ \(n\) & The index of discrete time per one SLS & 0–10,000 \\ \(N\) & The number of UBSs & 10 \\ \(K\) & The maximum queue length & 100 \\ \(\mu_{UBSC}\) & The capacity of a UBSC & 100 \\ \(\mu_{UBSmax}\) & The maximum backhaul capacity of a UBS & \(\frac{\mu_{UBSC}}{N}+\beta\) \\ \(\beta\) & \(\mu_{UBSmax}\) Adjustment parameter & 0–5 (default: 0) \\ \(\mu_{i}(n)\) & The backhaul capacity of UBS \(i\) at time \(n\) & \(0<\mu_{i}(n)<\mu_{UBSmax}\) \\ \(\lambda\) & Average packet arrival rate of a UBS generated from normal UTs & 3–20 \\ \(\rho_{LIM}\) & Under-utilization limit & 0.3–0.8 (default: 0.5) \\ \(N_{MN}\) & The number of mobile UTs (or nodes) generating burst traffic & 1–4 (default: 1) \\ \(\lambda_{b}\) & Average packet arrival rate of a UBS generated from mobile UTs & 10–60 (default: 30) \\ \(\omega\) & Window size for average traffic calculation & 1–10 (default: 1) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameters used in the System Level Simulations.  
high, it requires more backhaul capacity than 10. So, by setting \(\mu_{UBSmax}=12\) and \(\mu_{UBSmax}=14\) for \(\beta=2\) and \(\beta=4\), respectively, some UBSs with higher packet arrival rates than the average can have higher resource utilization.