## 4 Simulation Evaluation
### Impact of the Number of Sensor Nodes  
We evaluate the hop counts, the total number of packets, the total number of perimeter packets, the packet delivery ratio and the end-to-end delay for different numbers of sensor nodes, from 200 to 900. Figure 8 illustrates a variation of the hop counts for each protocol. In both protocols, as the number of nodes increases, the average hop count decreases. When the node density increases, each node has more neighbor nodes than before. It results that each protocol could find a shorter route under high density conditions. We also observe that the proposed protocol and BOSS show a smaller number of hops than others when the number of sensor nodes is low. It is the case that only our protocol finds a geographic route in a hop, while the other protocols cannot find a route and misunderstand that there is no appropriate forwarding node. In this case, they should change their routing mode into perimeter mode. Therefore, they have a longer route than ours. However, if the node density increases, all protocols could  
Figure 7: Data throughputs CDFs of 50 randomly-selected node pairs. have a higher probability of finding the next hop forwarder among mutually-communicable neighbor nodes. All protocols select the same neighbor as the next hop forwarding node; therefore, they have the same hop counts when there is high node density. Figures 9 and 10 show the total number of packets and the total number of perimeter packets, including data and control packets, according to the variation of the node density. As shown in Figure 9, although the total number of packets of each protocol decreases before a 700-node density, in most cases, BLR and BGR have more packets than the proposed protocol. This is because they have more routing failures than the proposed protocol. However, the graphs of both BLR and BGR rapidly decrease at increasing densities. We observe that the path of each protocol is almost similarly constructed at a density of 700. Furthermore, in this graph, we can see another fact: that the total number of packet from both BLR and BGR is slightly increasing after a density of 700. The reason is that if the node density is extremely high, this might lead to the collisions produced by neighbors forwarding the message, because the timers expire almost concurrently. However, since the proposed protocol exploits a novel collision avoiding scheme, called DACAS, it has only a few collisions. When there is a low density, BOSS shows the best performance compared to the others. However, as the number of nodes increases, BOSS generates more packets. This is because CTS collisions among a number of neighbor nodes may generate a forwarding failure, thus leading to retransmission on the hop. As shown in Figure 10, we figure out the total number of perimeter packets in detail. Generally, the proposed protocol shows a lower number of perimeter packets than others. Every protocol changes its routing mode into perimeter mode when all forwarding candidates cannot receive a data packet. Since both BLR and BGR have a lower number of forwarding candidate nodes than the proposed protocol, they have more of a chance to get changed into the perimeter mode. We observe that the proposed protocol has no perimeter packets after a 700-node density. Because, although there exist collisions in the high prioritized region due to extremely high node density, the rest of the nodes in the low prioritized region  
Figure 8: The hop counts _vs._ the number of sensor nodes. can relay data safely. On the other hand, the total number of perimeter packets of both BLR and BGR increases after a 700-node density. As mentioned above, the main reason is collisions due to high node density. In the case of BOSS, perimeter packets are generated by collisions among a high number of control packets.