## 4 Performance Evaluation of ECHERP  
In order to evaluate the performance of ECHERP simulations, over 50 different 100 m \(\times\) 100 m network topologies were performed. The network architecture considered is the following:  
* A fixed base station is located away from the sensor field. * The sensor nodes are energy constrained with uniform initial energy allocation. * Each node senses the environment at a fixed rate and always has data to send to the base station (data are sent if an event occurs). * The sensor nodes are assumed to be immobile. However, the protocol can also support node mobility. * The network is homogeneous, and all the nodes are equivalent, _i.e._, they have the same computing and communication capacity. * The network is location unaware, _i.e._, the physical location of nodes is not known in advance. * The transmitter can adjust its amplifier power based on the transmission distance. The aforementioned network architecture is typical of numerous applications of hierarchical WSNs, such as in environment and habitat monitoring, surveillance and reconnaissance, home automation, biomedical applications, object tracking, traffic control, fire detection, inventory control, agriculture, machine failure diagnosis and energy management [10]. In a real application of the proposed protocol, it may be used in a fire monitoring system in a set of buildings where the sensors in each building are grouped in the same cluster that send the data to the cluster of the next building. The simulation was performed by developing a customized software environment based on Java programming language. In all the simulation scenarios examined, 500 homogeneous nodes with an initial energy of 2 J were randomly scattered within a 100 \(\times\) 100 m\({}^{2}\) sensor field. The base station was positioned at point (0, 150), so it is at least 100 m away from the closest node, and the packets sent were 500 bytes. The energy consumption due to communication is calculated using the first order energy model described in the previous subsection. We assume that each sensor node is immobile and generates one data packet per round to be transmitted to the BS. The sensor nodes were grouped into clusters consisting of cluster heads that send data to upper level cluster heads in order to finally reach the BS. Figures 4 and 5 show the average energy dissipation and the number of nodes that remain alive when LEACH, PEGASIS, BCDCP and ECHERP are applied. The Node Ratio (\(N_{\text{r}}\)), as explained in (4) is equal to 1. As these figures depict, the performance of ECHERP is considerably better than LEACH, PEGASIS and BCDCP. More precisely, in the case of LEACH, PEGASIS and BCDCP, all the network nodes are depleted by the end of the 110 th, 115 th and 120 th round, respectively. On the other hand, when ECHERP is applied, the last remaining node is depleted in the 145 th round. Additionally, the performance of ECHERP is evaluated as a function of the ratio of upper level and lower level nodes. More precisely, it is true that the upper level cluster heads not only transmit their own data to the base station, but they also forward the data of the lower level cluster heads destined to the base station. Therefore, they have higher average energy dissipation than the lower level nodes. In order to correlate the performance of ECHERP with the distribution of nodes in network topology, the node ratio \(N_{\mathrm{r}}\) is defined as follows:  
\[N_{r}=\frac{\sum n_{u}}{\sum n_{l}} \tag{4}\]  
where \(\Sigma n_{u}\) is the number of nodes at the upper level and \(\Sigma n_{l}\) the number of nodes at the lower levels. Figure 4: Average energy dissipation _versus_ the network lifetime in rounds. Figure 5: Number of nodes alive _versus_ the network lifetime in rounds. Simulation tests showed that the best energy efficiency is achieved when the BS is located 150 m away from the center of the network field and the number of upper level nodes is by 10% greater than the number of lower level nodes. This is graphically displayed in Figures 6 and 7.