# Data Aggregation Based on Overlapping Rate of Sensing Area in Wireless Sensor Networks
## 5 Performance Evaluation  
### Network Configurations  
We evaluate the performance of AggOR scheme on OPNET Modeler [26] network simulation platform. The network configurations are listed in Table 2. Note that sensor nodes are evenly distributed in the monitoring field.  
We select a typical scheme EEUC and a newly proposed scheme HEER to be our comparisons. EEUC is a distributed cluster mechanism where cluster heads are elected by localized competition. Through a function of the competition range \(Rcomp\) which is decided by the distance to the base station, several tentative cluster heads are elected to compete for final cluster heads. After the cluster head selection, other nodes join in their closest cluster heads. HEER, as a chain-based protocol, constructs clusters like LEACH, and establishes a Hamilton Path in each cluster to set an order for sensors to transmit data. In order to evaluate different gathering node selection methods, we take a variation of  
Figure 6: An example of AggOR implementation.  
AggOR as comparison, in which the gathering nodes are only selected from candidate parent nodes (not considering the neighbor nodes), named AggOR-CP.  
Note that the data sizes after aggregation are not the same in different schemes. In AggOR, after a gathering node aggregates \(x\) data packets, the amount of output data is \(p(0<p<x\cdot d)\), which is decided by the overlapping rates of sensing area in this gathering area. Since the data aggregation function only removes duplicated data relevant with the overlapping sensing area, the whole data obtained by the sink are complete and accurate. However, in EEUC and HEER, a packet with a fixed amount of data is output by aggregating several data packets.  
The following metrics are used for the performance evaluation.  
1. Network lifetime: the time interval from the beginning of the network to the death of the first node.
2. Transmission overhead: the total amount of data transmitted in one data transmission round. It indicates the energy consumption of data sending and receiving in the whole network.
3. Maximum number of hops to the sink: the maximum number of hops from sensor nodes to the sink in the network. More hops mean a longer time for which the sink has to wait to collect all the data in the scenario. Hence it implies the data delivery delay.
4. Information accuracy: the ratio of the amount of information collected by the sink to the amount of information in all raw data.  
Considering that sensor density may influence the performance of data aggregation, we will discuss about this issue in Section 5.3.1. In addition, the threshold of overlapping rate of sensing area is a significant factor affecting the size of gathering area and the energy efficiency of AggOR scheme. Therefore, we will analyze the influences of this threshold in Section 5.3.2. Moreover, we consider three scenarios corresponding to different shapes of monitoring field and different locations of the sink in the network. In Scenario SP, the nodes are deployed in a pyramid field, of which the top is the sink. In Scenario SC, the sink is placed at the center of a circular field. Scenario SS has a square field with the sink in the top-left corner. Note that in all the scenarios, sensor nodes are uniformly deployed. We will analyze the sources of gathering nodes in AggOR and AggOR-CP with different \(OR_{T}\), in Section 5.3.3.