## 6 Performance Evaluations
### Simulation Results
In addition, we can also find that before the ANTR of the six protocols reach the maximum value, MENC has bigger ANTR than other five protocols. This is because that MENC has the smallest ACFTR compared with ENC, EP-LEACH, AEHAC, P-29 and LEACH. In addition, MENC has higher energy efficiency than these protocols since it adopts multi-hop communication method for inter-cluster data transmission. The comparison of Average Network Throughput per Second (ANTS) among the six clustering protocols for different data transmission cycles is shown in Figure 7. From this figure, we can see that with the increase of data transmission cycle, the ANTS of MENC, ENC EP-LEACH, AEHAC and P-29 decrease, and that of LEACH increases firstly and then decreases. This phenomenon can be explained as follows: with the increase of data transmission cycle, the ANTR increases for all the six protocols. In addition, LEACH has faster increase rate of ANTR than that of data transmission cycle when data transmission cycle is smaller than 0.8 \(T\). This figure also shows that MENC has bigger ANTS than other  
Figure 5: The comparison of ACFTR among MENC, ENC, EP-LEACH, AEHAC, P-29 and LEACH for different data transmission cycles. Figure 6: The comparison of ANTR among MENC, ENC, EP-LEACH, AEHAC, P-29 and LEACH for different data transmission cycles. protocols, and the difference of ANTS among the six protocols tends to be zero when data transmission cycle increases. This is because MENC has bigger ANTR than other protocols, and the ANTR tends to be the maximum value for the six protocols with the increase of data transmission cycle. Based on the above results, we can conclude that \(T\) is the optimal data transmission cycle in MENC. This is because that on the one hand, the network-wide energy neutral state can be well guaranteed when data transmission cycle is equal to or bigger than \(T\), since the ACFTR is nearly zero and the ANTR is nearly maximal according to Figures 5 and 6; On the other hand, as the ANTS decreases rapidly with the increase of data transmission cycle, the ANTS can be maximized on the premise of guaranteeing perpetual network operation when data transmission cycle is equal to \(T\). In order to observe the energy consumption of nodes in the network, we give the Average Energy Consumption per Round (AACR) for different data transmission cycles, as shown in Figure 8. From this figure, we can find that the AACR of the six protocols have a downward trend with the increase of data transmission cycle. This is because more energy can be harvested by each node with the increase of data transmission cycle. When data transmission is smaller than 0.8 \(T\), MENC has bigger AACR than other five protocols since it has fewer cluster failure times. In addition, according to Figures 5, 6 and 8 we can conclude that MENC has the highest energy efficiency among the six protocols. This can be explained as follows: when data transmission cycle is bigger than 1.2 \(T\), MENC has smaller AACR than other five protocols and nearly the same ACFTR and ANTR with other protocols; In addition, a node has higher energy efficiency if it consumes less energy for transmitting the same amount of data. Since multi-hop communication method is adopted in MENC and other five protocols adopt the single-hop one, this conclusion is also in accordance with the case that multi-hop communication has higher energy efficiency than single-hop one. Figure 8: The comparison of AACR among MENC, ENC, EP-LEACH, AEHAC, P-29 and LEACH for different data transmission cycles. Figure 7: The comparison of ANTS among MENC, ENC, EP-LEACH, AEHAC, P-29 and LEACH for different data transmission cycles. In the following simulations, we evaluate the performance of MENC under the case that the sensor field size \(S\) ranges from \(2\times 10^{4}\) m\({}^{2}\) to \(6\times 10^{4}\) m\({}^{2}\), and the data transmission cycle is equal to \(T\) which is calculated by Equation (39).