## 3 Charging-Aware Multi-Mode Routing Protocol
### Charging-Aware Multi-Mode Routing Protocol (CMRP)
The results of RICA are similar to that of the PEGASIS+. The proposed chaining method makes the results of MCC better than that of RICA. The MSTP exhibits the best results among all evaluated methods. Sensors spend most of their energy on data gathering and propagate data in short distance. These two characteristics mean MSTP has the longest lifetime so that it has the lowest average remaining energy. The average residual energy of CMRP is 1% more than MSTP because the sensors within the sunlight coverage sacrifice part of the energy to reduce the propagation delay. Figure 8 shows the average propagation delay in a round. In this experiment, the data transmitting rate is assumed to be 1 Mbps and carry sensing is 1 ms. The PEGASIS and PEGASIS+ methods have the worst propagation delay because data need to be delivered one by one on the chain. The propagation delay is explicitly proportional to the number of sensors in the network. At most two sensors can propagate data simultaneously. For the LEACH method, sensors in each cluster need to send their data to the CH one after another. If the network has five clusters, up to five sensors can transfer data simultaneously. The RICA method divides the length of the chain in PEGASIS into two equal size chains. Data in these two chains can be delivered simultaneously so that its data propagation delay is less than the PEGASIS. Similarly, the MCC chains the sensors as the RICA but shortens the distance. Therefore, MCC has less propagation delay than the RICA. Figure 7: Average residual energy until the first node dies. The propagation length of the MSTP heavily depends on the topology. The propagation delay is slightly worse than the RICA when the sensors are less than 175. It is because the children nodes of the same parent in the tree need to send their data in turn. In addition, the MST usually constructs an unbalanced tree. The maximum depth of the tree is usually near 40% number of sensors. Thus, the propagation delay is worse than the RICA. However, densely deployed sensors can reduce the chance to construct an unbalanced MST. The propagation delay is equal or less than the RICA when the number of sensors is more than 175. The CMRP exhibits the shortest propagation delay. In the CMRP method, about 25-50% sensors use the spanning tree method, 25-50% use the ring-like method to propagate data, and 25% sensors use the cluster-based method to delivering the data. CMRP still has the lowest delay time even the number of sensors increases. The propagation delay of CMRP is less than MSTP about 21-28%. Figure 9 shows the impact of the sunlight coverage period. Three period {600, 150, 50} rounds are simulated shown in Figure 9a-c, respectively. When the period shortens, the numbers of operation rounds of all methods slightly increases except the CMRP. The improving rate of the operation rounds is no more than 5%. However, the improving rate of the CMRP is ranged from 15-29%. The CMRP adapts the routing mechanism according to the charging status of the sensors. The intelligent adapting makes it suitable for application in rechargeable wireless sensor networks. The results of the confidential interval with alpha = 0.95 of Figure 9a-c are shown in Figure 10a-c. Most of the results have no more than 0.8% error. Figure 8: Average data propagation delay. Figure 9: _Cont_. Figure 10: Confidential interval with alpha = 0.95 of Figure 9. (**a**) confidential interval of Figure 9a; (**b**) confidential interval of Figure 9b; (**c**) confidential interval of Figure 9c. Figure 3:0 Impact of the sunlight coverage period. (**a**) coverage period is 50 rounds; (**b**) coverage period is 150 rounds; (**c**) coverage period is 600 rounds. Finally, the life-delay rate is listed in Figure 3:1 The LEACH does not consider the energy and the delay time at the same time so that the LDR is far away to 1. Without effective scheduling of the adjacent sensors, the original PEGASIS exhibits worse LDR value as the LEACH. However, the LDR of the PEGASIS+ is 9-times that of the original PEGASIS.