# Efficient Mobile Sink Routing in Wireless Sensor Networks Using Bipartite Graphs
## 6 Simulation Results
The results acquired for the packet delivery ratio are shown in Figure 5, which shows that the proposed mobility model obtained highly stable performance under all network sizes. The networks with 51 nodes and 76 nodes achieved the highest performance results regarding packet delivery ratio when the mobile sink speed was equal to 5, 10, and 15 m/s, consistent with the results from Figure 5. \begin{table}
\begin{tabular}{l l l l l} \hline \hline \multirow{2}{*}{**Speed**} & \multicolumn{4}{c}{**Network Size**} \\ \cline{2-5}  & **26 Nodes** & **51 Nodes** & **76 Nodes** & **101 Nodes** \\ \hline
5 & 192.12 & 31.45 & 19.33 & 78.69 \\
10 & 166.56 & 28.58 & 26.65 & 151.50 \\
15 & 633.29 & 51.74 & 30.60 & 84.37 \\
20 & 262.34 & 73.93 & 267.47 & 140.39 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average End-To-End Delay. To elaborate, since this network acquired the best results for the end-to-end delay, this will result in obtaining the highest results for packet delivery ratio due to the same reason discussed when explaining the results of Figure 1b. Additionally, from Figure 5, it can be observed that the increase in the velocity of the mobile sink to 20 m/s has affected the performance of all networks and caused a slight decrease in the performance of all networks. Thus, for small network sizes, when moving the mobile sink at high speed, frequent and rapid changes in the routing paths will take place and cause a decrease in performance. The mobile sink will also be moving at high speed, and completing data transmission between the mobile sink and the static sensor nodes will be challenging. It can also be observed that the performance of the network consisting of 101 kept increasing when the speed of the mobile sink was increased because the higher the speed of the mobile sink, the more frequently the static sensor nodes are visited; thus, data can be transmitted to the mobile sink via single hop promptly, and static sensor nodes do not suffer from buffer overflow, which results from storing sensed information for long periods when waiting to be visited by the mobile sink. On the other hand, for small network sizes, the mobile sink's anticipated mobility path is smaller than that in medium- and large-sized networks. As a result, increasing the speed of the mobile sink to 20 m/s will affect static sensor nodes and their neighbors. Thus, these nodes will not have enough time to deliver packets to the mobile sink, and packets must be routed via multi-hop routing to be delivered to the destination. Packets will also go through unnecessary and extra hops to adapt to the frequent changes in the routing path to be delivered to the mobile sink. Table 3 summarizes the result obtained for the packet delivery ratio and compares the results achieved by each network using different mobile sink speeds. The table shows that all networks achieved high-performance results in terms of packet delivery ratio, except the network consisting of 26 nodes. Table 3 shows that the 26 nodes' network performance was lower than the performance of all other networks for all the different speeds used for the mobile sink. As a result, it can be concluded that all the speeds used for the mobile sink caused frequent updates to the routing paths. Thus, packets kept circulating in the network until they were dropped. This case was made even worse when the movement speed of the mobile sink was increased because the static sensor nodes did not have enough time to communicate with the mobile sink and deliver their packets using single-hop communication. Figure 5: Packet delivery ratio. Figure 6 shows the results obtained for network throughput when the mobile sink moved following the suggested mobility model at various speeds and with varying network sizes.