## 6 Performance Evaluations
### Simulation Results  
In this section, we simulate a total of 500 rounds of data transmission. In addition, we suppose that before transmitting data to the destination in each round, every CH checks whether it has enough energy according to the distance to the destination. If a CH has no enough energy for data transmission, a cluster failure will occur and this CH will discard the data packet in the current round. In addition, as the CH in each cluster has a dedicated relay node (RN) in protocol P-29, cluster failure means a RN has no enough energy to relay data. We adopt four metrics to evaluate the performance of MENC, including Average Cluster Failure Times per Round (ACFTR), Average Network Throughput per Round (ANTR), Average Network Throughout per Second (ANTS) and Average Energy Consumption per Round (AECR). Here we define ANTR as the average number of data packets successfully collected by BS per round, and ANTS is the average number of data packets successfully collected by BS per second. We first evaluate the performance of MENC under the case that sensor nodes are uniformly deployed in a circular sensor field with area 4\(\times\)10\({}^{4}\) m\({}^{2}\), and the data transmission cycle ranges from 0.4\(\cdot\)_T_ to 2\(\cdot\)_T_. Here \(T\) is the minimum network data transmission cycle calculated by Equation (39). As node density \(\rho\) is 1 node/100 m\({}^{2}\), the total number of sensor nodes is 400. In addition, according to Equation (38), the number of units is 4. Figure 5 gives the comparison of Average Cluster Failure Times per Round (ACFTR) among the six clustering protocols for different data transmission cycles. This figure shows that with the increase of data transmission cycle, the ACFTR of all the six protocols decrease until to the minimum value 0. This is because that each CH or RN has more time to harvest energy from the ambient environment with the increase of data transmission cycle. In addition, this figure also shows that MENC outperforms other five protocols in terms of ACFTR. This owes to the energy neutrality constraint considered in MENC. Under this constraint, a sensor node is not eligible to be CH until it harvests enough energy from the environment, and the number of sensor nodes within a cluster is not beyond the expectation of the CH. The protocol ENC adopts a Cluster Head Group (CHG) mechanism to allow that several sensor nodes serve as the CH in turn within a cluster to share the traffic load. It has smaller ACFTR than EP-LEACH, AEHAC, P-29 and LEACH. However, a sensor node with less energy may be selected as a member of CHG, which increases the probability of cluster failure. Then ENC has poorer performance than MENC in terms of ACFTR. With the increase of data transmission cycle, EP-LEACH firstly has bigger ACFTR than P-29, and then it has smaller ACFTR than P-29. This is because that the protocol P-29 selects a dedicated RN for the CH within each cluster so that the traffic load within a cluster is shared by RN and CH. Then P-29 has smaller probability of cluster failure than EP-LEACH when sensor nodes have not enough time to harvest energy from the environment. In addition, when sensor  
nodes have more time to harvest energy, EP-LEACH has less ACFTR than P-29 since sensor nodes with more available energy have bigger probability to be the CH in EP-LEACH. In AEHAC, an energy threshold is introduced to ensure that sensor nodes with too little energy switch to sleep mode for saving energy. Moreover, the sensor nodes with more available energy have bigger probability to be the CH. Thus, AEHAC has smaller ACFTR than EP-LEACH and P-29. The comparison of Average Network Throughput per Round (ANTR) among the six clustering protocols for different data transmission cycles is given in Figure 6. From this figure, we can see that with the increase of data transmission cycle, the ANTR of all the six protocols increase until to the maximum value. This is because the ACFTR decreases with the increase of data transmission cycle for the six protocols.