## 5 Performance Evaluations
### Efficiency of Convex Hull Based Geocasting  
The performance of the GeoCHT and GEAR is evaluated and compared in both static and mobile scenarios in our previous work [6]. The details of the GEAR protocol can be found in Section 2.2. In this section, we briefly summarize the results of this comparison to show the efficiency of GeoCHT. The simulation results show that GeoCHT performs quite well in static scenarios. AQDD and NL of GeoCHT are much lower than GEAR while GeoCHT has higher ER and lower FIR in most of the cases. Figure 7 shows the comparison of ERs of GeoCHT and GEAR in a static WSN with varying density. Note that an execution ratio of 1 means that every node inside the target region has received and executed the corresponding query packet. Since we focus on the mobile WSNs in this work, we present the comparison of GeoCHT and GEAR in a mobile scenario in the following discussion. To show the effectiveness of the convex hull based geocasting (_i.e._, GeoCHT), this set of simulations are perfomed in a 2,500 \(\times\) 2,500 \(m^{2}\) deployment area with 200 sensor nodes and 6 sinks. We evaluate the effects of different number of mobile nodes in the network, namely 1% to 20% of the network nodes are moving. The average speed of the mobile nodes is 5 m/s. Global updating is used in this set of simulations to construct geocast structure. The queries are sent from sinks at a random time after the geocast structure is updated by the global updating mechanism. Figure 7: Execution Ratio of GeoCHT and GEAR in a static WSN. Figure 8 shows the routing accuracy performance of the protocols. Simulations show that the False Execution Ratio of queries in mobile networks is zero for both GEAR and our protocol GeoCHT, therefore not shown in the graphs. The reason of this FER result is that when a mobile node, which was in the target region before starting to move, receives a query, it first checks its current position and if it is not inside the area of interest anymore, it does not execute the query. In Figure 8, we see the ER results of GEAR and GeoCHT. GEAR slightly outperforms GeoCHT when we increase the mobility rate (_i.e._, number of mobile nodes). This is mainly due to the fact that we used tree-based shortest path routing to connect nodes to sinks in GeoCHT simulations. In mobile sensor networks, tree-based approaches require frequent reconfigurations. This result has motivated us to focus on mobility handling in convex hull based geocasting in this paper. The following sections evaluate the performance of two methods, _i.e._, global and local updating to achieve efficient and on time reconfiguration of the geocast structure. Figure 8 presents the FIR results of GEAR and GeoCHT. The FIR of GEAR is higher than the FIR of GeoCHT in this mobile scenario. When we increase the mobility rate in the network, the FIR of GEAR slightly increases. GeoCHT also has a slight increase in FIR when the mobility rate is increased. This means that although convex hulls of sensors encapsulated in the convex hull of a sink are affected by mobile nodes, the coverage areas of sinks are not much affected by the mobile nodes. Only the movement of the nodes which are closer to the boundary of the convex hull of a sink may change the coverage area of this sink if they move out of the current convex hull of the sink. Figure 8: Routing accuracy performance with varying mobility rate. Figure 9: Networking performance with varying mobility rate. Figure 9 shows the networking performance of the protocols. In Figure 9(a), we show the query delivery delays of both protocols. The delays are not affected much by the increasing number of mobile nodes in the network. The delay in GeoCHT is smaller than the delay of GEAR because GeoCHT discards the queries of sinks which are very far from the area of interest. Only the sinks that are close to the area of interest inject their queries; however, in GEAR, even if a sink is very far from the target region, it still injects its query so the average query delivery delay of GEAR is getting higher.