## 5 Performance Evaluations
### Evaluation of Accuracy of Local Updates  
In this set of simulations, only one global update (_i.e._, sinks helloing) is performed at the beginning of the simulation to build a full geocast structure (_i.e._, the routing trees and convex hulls) in the network. Then, only local updates from mobile nodes are sent in their neighborhoods to keep geocast structure up-to-date during the simulation. Performance of local updating with different \(k\) values are compared. The parameter \(k\) affects the frequency of local updates performed by MNs. A small \(k\) results in triggering local updates more frequently. Assuming a mobility speed of 10 \(m/s\) and 250 \(m\) transmission range, when we have \(k~{}=~{}0.10\), MN sends a beacon packet for every 25 \(m\) displacement. In Figure 13 we compare the local updates with different MN beacon parameter, \(k\), values and global updating with a frequency of 5 seconds which achieves the best performance as shown in the previous set of simulations. It is observed that ER of all local updates with different \(k\) values is better than the best global update. When we increase the number of nodes in the network by keeping the deployment area fixed, the density of the network also increases. This increase results in shorter distances between parent and child nodes. Hence, as observed in the figure, for bigger number of nodes, the ER values are very close to each other for different values of \(k\) because longer MN beacon intervals still achieve on-time updating of geocast structure in dense networks. With this observation, we can redefine \(k\) as _density factor_ since it is determined by the density of the network. In Figure 14, we compare the communication overhead (CO) of local and global updating. When sensor nodes are more densely deployed in the sensor field, the CO increases for both global and local updating. However, the CO of local updating with different \(k\) values is always lower than that of global updating. This is an expected results since local updates only reshapes the branches affected by mobile nodes so the messaging is reduced in the local updating. Figure 13(b) plots the ERs of local and global updating when we increase the number of mobile nodes in the network. Local updating with \(k~{}=~{}0.05\) gives the best results of ER. While ERs of local updating with \(k~{}=~{}0.05\) are very close to local updating with \(k~{}=~{}0.10\) and \(k~{}=~{}0.20\) for networks having less than 35 mobile nodes, this behavior changes for networks having more mobile nodes. Results show that when we have more mobile nodes, more frequent updates are needed to reflect the actual geocast structure. For any \(k\) value of local updating, global updating gives worse ER results than local updating. Figure 14(b) presents the results in terms of communication overhead when we vary the number of mobile nodes. As expected if we have more number of mobile nodes, the messaging and communication overhead increases for local updating. On the other hand, CO slightly increases for global updating when we increase the number of mobile nodes since communication overhead of global updating mainly depends on the number of nodes in the network and some convex hull update messages due to timeout mechanism. However, as observed from Figures 13(b) and 14(b), it is possible to determine a \(k\) value for local updating which results in less CO and still performs better than global updating in terms of ER. If we compare the COs of local and global updating, for example for \(k~{}=~{}0.20\), when we have 40 mobile nodes in the network, COs of local and global updates are more or less the same. This number is getting smaller for smaller \(k\) values (_i.e._, COs of local and global updates are similar when we have 25 nodes for \(k~{}=~{}0.05\) and 30 nodes for \(k~{}=~{}0.10\)) of local updating because smaller \(k\) values create more beacon and update messages in the network. Figure 13: Comparison of local and global updates in terms of Execution Ratio.