## 3 Charging-Aware Multi-Mode Routing Protocol
### Charging-Aware Multi-Mode Routing Protocol (CMRP)
A well adjacency methodology explicitly reduces the data transmission distance so that sensors can save their energy and the network has a longer operation time. Among all evaluated methods, the MSTP method has the longest lifetime. MSTP selects the shortest adjacent neighbor to propagate data so that every sensor can minimize the energy consumption used on propagating data to its next hop. The lifetime of the CMRP is only worse than the MSTP by no more than 1%. It sacrifices some energy to reduce the propagation delay. CMRP considers the lifetime and the propagation delay simultaneously. The sensors with plenty of energy make their effort to reducing the propagation delay, and the sensors located at the unchangeable area shorten their transmission distance to save energy. However, the CMRP exhibits better propagation delay than that of the MSTP in the later experiments. Figure 5 shows the lifetime until 1%, 25%, and 50% of nodes die in a network with 100 sensors. The cases that more than 75% of nodes die are not evaluated because sensors can replenish their energy and part of the method does not have these cases. In the cases of 1% of sensor nodes dying, the numbers of rounds in LEACH and PEGASIS methods are less than 200. However, the PEGASIS method exhibits outstanding results against the LEACH in the cases of 25% and 50% of nodes dying. The original PEGASIS method uses a bad chaining methodology to link the sensors. When those sensors which have long-distance neighbors exhaust their energy, the remaining sensors with shortening distance neighbors can operate longer. Therefore, the number of operation rounds increases explicitly. The RICA uses a better chaining method to link the sensors so that is has better results than the LEACH and PEGASIS. When the MCC mechanism is applied to chain the sensors, the PEGASIS+ and the RICA-like MCC methods address the problem of creating long-distance neighbors for sensors. Therefore, their results are improved explicitly. The MSTP greedily constructs the closest neighbors for each sensor so that every sensor can prevent wasting their energy on long-distance data propagation. Consequently, it has the best results. The proposed CMRP integrates the advantages of the MSTP, RICA, and cluster-based methods. Although its result is worse than the MSTP, it is still better than the other method. Figure 6 evaluates the average number of propagation hops. The LEACH method delivers the data to sink within two hops. Chaining the sensors into a long chain makes PEGASIS and PEGASIS+

Figure 4: Lifetime until the first node dies. methods introduce a great number of propagation hops. The RICA and the MCC methods reduce the chain of PEGASIS into two small ones with 50% length and make the sensors on these two chains operate simultaneously. The number of propagation hops used by the MSTP method depends on the topology. The average number of propagation hops is within 10-20 and increases as the number of sensors grows. By dynamically changing the data propagation target according to the recharging status of the sensors, CMRP has better results than the MSTP. Figure 7 shows the average remaining energy of the sensors until the first node dies. Sensors in the LEACH method have fewer propagation hops and have extremely unbalanced energy consumption. The average residual energy of the sensors is more than 18-30%. While the number of sensors increases, the average residual energy of sensors grows. It indicates that sensors do not efficiently share the data propagation overhead. Figure 5: Number of rounds with different dead nodes percentage. Figure 6: Average number of data propagation hops. Except the LEACH method, the average residual energy of sensors in the other methods is within 3-9%. PEGASIS exhibits the worst results because the bad chaining mechanism makes part of sensors select long-distance propagation targets. By applying the proposed MCC chaining mechanism, the average remaining energy of the PEGASIS+ reduces about 1% of the original PEGASIS. It is slightly worse than the RICA.