## 3 Charging-Aware Multi-Mode Routing Protocol  
### Preliminaries and Assumptions  
The proposed method has the following assumptions. Sensors are deployed within the region of interest (RoI) randomly and are stationary after they are deployed. Their locations are reported to the sink. The sink will announce the network topology information to all sensors in the network. The coverage of sunlight only includes parts of the RoI and regularly transfers to another part after a period of time. The coverage of sunlight only transfers to a nearby area. The communication ranges of the sensors are uniform. Every sensor installs a solar panel to replenish its energy when it is under the sunlight coverage. Each sensor has a unique identity, and the location of the sink is at the center of the RoI.  
According to the energy replenish statue of sensors, they are classified into three types. The sensors covered by the sunlight are classified as the type1 sensors that they can replenish their energy. By having plenty of energy resources, these sensors can use the routing protocols which are more generous on energy consumption to reduce the data propagation delay. The cluster-based routing protocols have the fewest propagation delay can be applied for these sensors. The sensors in the area attached to the sunlight coverage are type2 sensors. These sensors cannot replenish their energy at this time. They are the sensors which the sunlight coverage just left them or will be covered by the sunlight. These sensors own good locations to communicate with the type1 sensors. The ring-based routing protocols that consider both energy usage and the propagation delay simultaneously are the candidates.  
The type3 sensors are those neither the type1 nor the type2 sensors. These sensors will endure a long time before the next time the sunlight coverage includes them. Their energy needs to be used well to prevent from exhausting their energy. The routing protocols with the best energy efficiency are the best solution. The spanning tree routing protocols are the candidates.  
Sensors periodically return their gathered data to sink. A round is defined as the sink receives the collected data of all sensors. In one round, the data propagation sequence is according to the type of sensors. The type3 sensors are the first group to propagate data; the next is the type2 sensors and so on. The next round starts when the sink receives all data of sensors.  
The radio energy model of sensors used in this article is the same as [5]. Each sensor can adjust its transmission power to the necessary energy level while sending data to its recipients. Let \(E_{dec}=50\) n/bit be the energy consumption to switch on the transmitter (or receiver) circuits to dissipate one bit of data. The energy consumption for transmitter amplifier to dissipate one bit of data is denoted as \(\varepsilon_{amp}=100\) pJ/bit/m\({}^{2}\). The radio loss is proportional to the square of the distance under the assumption of a free-space environment. Let \(E_{tx}\) (k, d) be the energy that a sensor transmits a k-bit message to a receiver with distance d. Each sensor needs to switch on the transmitter circuits and the transmitter amplifier when it sends data. \(E_{rx}\) (k) is the energy that a sensor receives a k-bit message. Each sensor needs to switch on the receiver circuits for receiving data. They are computed as (1) and (2).  
\[E_{tx}\ (\text{k, d})=E_{tx-dec}\ (\text{k})+E_{tx-amp}\ (\text{k, d}) \tag{1}\]  
\[E_{rx}\ (\text{k})=E_{rx-elc}\ (\text{k}) \tag{2}\]  
where \(E_{tx-elc}\ (\text{k})=E_{elc}\ ^{*}\ \text{k}\), \(E_{tx-amp}\ (\text{k, d})=\varepsilon_{amp}\ ^{*}\ \text{k}\ ^{*}\ \text{d}^{2}\) and \(E_{rx}\ (\text{k})=E_{elc}\ ^{*}\ \text{k}\).  
Each sensor can aggregate the received data from several sensors. The methods such as LEACH, PEGASIS, and RICA are focus on the energy consumption by reducing the average transmission distance. The CMRP approach proposed in this paper also attempts to reduce the average transmission distance and propagation delay