# Efficient Mobile Sink Routing in Wireless Sensor Networks Using Bipartite Graphs
## 6 Simulation Results  
This part shows and discusses the results of applying the simulation scenarios in Section 5.1. Each scenario was executed ten times to produce more detailed findings. The results of the 10 runs for each example were averaged to acquire the simulation results. Figure 4 displays the average end-to-end delay results for various network sizes and mobile sink movement speeds. Networks with 51 and 76 nodes achieved the best overall results regarding the end-to-end delay, especially when the mobile sink speed was equal to 5, 10, and 15 m/s. The reason behind such behavior is that these speeds are considered low or moderate speeds of the mobile sink, which results in extensive multi-hop communication through long routes, which is the primary factor affecting the end-to-end delay results obtained for this case. Figure 4: Average end-to-end delay. For other network sizes, it can be seen that the proposed mobility model obtained low and consistent end-to-end delay results, especially when increasing the speed of the mobile sink to be equal to 5, 10, and 15 m/s, which can be regarding the frequent use of single-hop communication because the mobile sink is moving at moderate speeds and visits static sensor nodes frequently. The network consisting of 26 nodes was an exception when the mobile sink speed was increased to 15 m/s. As is clear from Figure 4, the performance of this network increased dramatically because the network size is small and the speed of the mobile sink is relatively high, which may cause frequent changes and updates to the routing paths. Thus, multi-hop communication is used more frequently, and packets must go through extra and unnecessary hops to be delivered to the mobile sink. On the other hand, when increasing the speed of the mobile sink to 20 m/s, these networks obtained higher end-to-end delay results because 20 m/s is considered a high speed and may cause frequent changes in the routing paths used to convey messages to the mobile sink. As a result, a packet may go through unnecessary hops to be delivered to the mobile sink. For other network sizes, better results were obtained because the changes in the routing path did not affect all the nodes in the network. Hence, packets did not need to wander around or circulate through the network and go through some unnecessary and replicated intermediate nodes. Consequently, packets went through fewer hops until delivered to the mobile sink. As a result, smaller results for end-to-end delay were obtained. Furthermore, Figure 4 shows that networks comprising 26 and 101 nodes obtained the worst performance compared to all other networks. This can be regarded as a result of the frequent use of multi-hop routing for the packets to be delivered to their destination. To put it in another way, the path to be adopted by the mobile sink is relatively short. As a result, the motion of the mobile sink will affect the routing paths for most of the static sensor nodes. Thus, packets sent from static sensor nodes will go through multiple hops, and some of these hops result from the changes or updates to the routing path. Therefore, those packets might have been routed more than once from the same node to adapt to changes in the routing path until they are delivered to the mobile sink. Furthermore, Table 2 compares the results obtained for the average end-to-end delay for different network sizes and speeds of the mobile sink. It can be observed that medium-size networks, namely 51 and 76 node networks, performed better than other networks, especially when the mobile sink was moving according to low speed and moderate speeds equal to 5, 10, and 15 m/s. It can also be observed that the 51 nodes network obtained more consistent results than those obtained for 76 nodes for all speeds of the mobile sink. As a result, the mobility model proposed in this paper is more suitable for use with medium-sized networks when we aim to achieve low end-to-end delay.