# A New Resource Allocation Protocol for the Backhaul of Underwater Cellular Wireless Networks
## 4 Simulation and Performance Analysis Results
### Simulation Results and Performance Analysis
#### 4.2.1 Scenario 1  
Here, we investigated the four performance measures for different under-utilization limit (\(\rho_{LIM}\)) and the number of mobile UTs (\(N_{MN}\)). To do this, we changed the value of \(\rho_{LIM}\) from 0.3 to 0.7, 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 (i.e., the mean inter-arrival time is given as \(\frac{1}{30}\)s). And the average packet arrival rate of each UBS, denoted by \(\lambda\), is changed from 3 to 20. Figure 7 shows the average packet drop rate for this case. (In the following four graphs, \(\rho_{LIM}\) is simply denoted by \(\rho\) for convenience sake.) As shown in Figure 7, the average packet drop rate increases as the average packet arrival rate \(\lambda\) increases. In the graph, we can find that the average packet drop rate is notably different dependent upon the number of mobile UTs \(N_{MN}\); the average packet drop rate performance becomes worse as the value of \(N_{MN}\) increases. However, the average packet drop rate is almost the same for different values of under-utilization limit \(\rho_{LIM}\). Figure 8 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. We can find the different resource utilization values when \(\lambda\) is small (i.e., \(\lambda<10\)). In addition, when \(\lambda\) is small such as from 5 to 7, average resource utilization for the case \(N_{MN}=1\) is much lower than the case \(N_{MN}=2\). This is obvious since there are more packet arrival in the case \(N_{MN}=2\), and the burst traffic is a more dominant factor when \(\lambda\) is small. When \(N_{MN}=1\) and \(\lambda=5\), the average resource utilization becomes higher as \(\rho_{LIM}\) increases. The reason is as follows. As \(\rho_{LIM}\) increases the UBS returns the backhaul resource more frequently to the UBSC if its resource is under-utilized. So, the average resource utilization becomes higher, and the message overhead due to the return procedure increases. This phenomenon can be observed in Figure 9.  
Figure 9 shows the average message overhead for this case. It is shown that the message overhead of the UBSI resource allocation protocol is remarkably small because control signaling message mostly occurs when the UBSC reallocate backhaul resources for the UBSs according to their requests. As described in Section 3, this reallocation is caused by the two cases. The first case is when the resource of a UBS is under-utilized, and the second case is when a UBS has packet drop due to the  
Figure 8: Average Resource Utilization for different under-utilization limit (\(\rho_{LIM}\)) and the number of mobile UTs (\(N_{MN}\)). Figure 7: Average Packet Drop Rate for different under-utilization limit (\(\rho_{LIM}\)) and the number of mobile UTs (\(N_{MN}\)). shortage of the backhaul capacity. When the average packet arrival rate \(\lambda\) is small, message overhead is mainly caused by under-utilization. Thus, we can observe that situation as illustrated in Figure 9. In the figure, when \(\lambda\) is small (e.g., \(\lambda=5\)), average message overhead becomes larger as \(\rho_{LIM}\) becomes higher and \(N_{MN}\) smaller. As \(\lambda\) becomes larger, the average message overhead fluctuates. This fluctuation occurs because the resource reallocation in the UBSC is mainly triggered by packet drops in the UBSs. And this packet drop randomly occurs in the UBSs since the total backhaul capacity is limited and the packet arrival rate is much higher than the backhaul capacity  
Figure 10 shows the average reserved capacity of the UBSC, denoted by \(\mu_{e}\) for this case. We can observe that \(\mu_{e}\) increases when the packet arrival rate \(\lambda\) is small. And it approaches to almost zero as \(\lambda\) becomes large. When \(\lambda\) is small (e.g., \(\lambda=5\)), \(\mu_{e}\) becomes larger as \(\rho_{LIM}\) becomes higher and \(N_{MN}\) smaller.