## 3 Charging-Aware Multi-Mode Routing Protocol
### Charging-Aware Multi-Mode Routing Protocol (CMRP)
However, data propagation is not because sensors need to take turns to be the CH or leader. The sensors can operate longer if the energy consumption on data propagation can be evenly distributed to all members in the network. The lifetime is computed in the number of rounds and a round is defined as all sensors in the network finish propagating data to sink. The average number of data propagation hops evaluates whether a method can quickly deliver the data to the target through by using fewer numbers of relay processing. The average data propagation delay indicates the delay time to propagation data to the sink. Note that propagation hops does not imply short propagation delay. If sensors have the same target to receive data, they need to be queued to send data. Therefore, a routing method with fewer numbers of propagation hops does not imply it will have shorter propagation delay. Propagation delay can be reduced if multiple sensors can propagate their data simultaneously. The average remaining energy until the first node dies indicates whether a routing method can evenly distribute the power consumption on data propagation to all sensors or not. A method makes part of sensors to take the overhead of data propagation will shorten the operation time of the whole network. Therefore, the average remaining energy of sensors is high. The life-delay rate (LDR) is defined as the product of the number of rounds and the propagation delay. Both values are normalized. Let Rnd(M) be the number of rounds of method M. The normalized number of rounds of a method is defined as Rnd(M)/Rnd(M\({}^{*}\)) where M\({}^{*}\) is the evaluated method that has the maximum number of operating rounds. The definition of the normalized propagation delay is similar. A method with LDR is close to 1 means it considers both the delay time and operation lifetime. ### Environment Setups

Initially, sensors are deployed within a 400 m \(\times\) 400 m area randomly. The numbers of deployed sensors are {100, 125, 150, 175, 200}. The sink is located at the center of the RoI. The size of the data packet is 2000 bits. A sensor can propagate its data out when it receives all data that needs a route through it to the sink. The initial energy of all sensors is 1 Joule. The energy consumed on data aggregation is set to 5 nJ/bit. The energy to set up the transmitting and receiving circuits is 50 nJ/bit. The energy for the transmitter amplifier to dissipate one data bit is set to 100 pJ/bit/m\({}^{2}\). The location of sunlight coverage changes periodically. In the simulation of this paper, the sunlight coverage is assumed to be a continuous rectangle area. This area rotates from left side to right side as the daily trajectory of the sun. The default rotating period for moving sunlight coverage to the next area is 150 rounds. The periods with [50, 150, and 600] rounds are simulated to evaluate the impacts of the rotating period. The charging rate of the sensors within the charging area simulated is 0.0001 J per round. In this simulation, 500 random topologies are evaluated to compute the averaged results. ### Numerical Results

Figure 4 shows the lifetime until the first node die. The numbers of rounds of the LEACH and PEGASIS methods are lower than 200. The LEACH spends too much energy on long-distance data transmission. The original PEGASIS uses a bad chaining methodology that causes it to introduce worse

results. The PEGASIS+ is applying the proposed MCC method to chain the sensors. This chain is created by linking the sensors into a circle at first and then breaks the longest edge. The results become better explicitly. The results of the ring-based method RICA [24] is better than original PEGASIS because it has a better chaining mechanism. When the ring-based method RICA applies the proposed MCC mechanism to chain the sensors into a circle, denoted as MCC, the number of operation rounds increases about 20-30%.