# Energy Transmission and Equilibrium Scheme in Data Communication Opportunistic Networks
## 2 System Model Design
Especially in data communication, nodes are easy to find the communication areas by moving. Then, the data packets can be transmitted. Energy consumption happens when transmitting data packets. If each data packet is transmitted by consuming the \(e\) energy unit. Then, the data packets transmitted from \(A\) to \(B\) consuming energy are:  
\[E_{<A,B>}=e\times p_{<A,B>} \tag{2}\]  
From \(B\) to \(A\) are:  
\[E_{<B,A>}=e\times p_{<B,A>} \tag{3}\]
4. Energy supply. According to step 2 and 3, if \(p-p_{ave}\geq 0\), the sending data packets are more than receiving, this node needs to supply energy from its neighbor; if \(p-p_{ave}<0\), the receiving data packets are less. For a node, in the condition of \(E\geq E_{\text{limit}}\), this node should transmit energy to its neighbor. \(E_{\text{limit}}\) is the carrying energy with the least threshold. It ensures the energy lower limit for the node. In the transmission model, if node \(A\) sends more data packets than node \(B\), at the same time, node \(B\) carries energy \(E_{B}\geq E_{\text{limit}}\). Therefore, node \(A\) consumes more energy and it needs to acquire energy from its neighbor. Hence, node \(B\) is a neighbor, it has enough energy to supply. Therefore, node \(A\) acquires energy supply from \(B\). The supply energy is:  
\[\Delta E_{<B,A>}=e\times(p_{<A,B>}-p_{ave}) \tag{4}\]  
\(\Delta E_{<B,A>}\) is the energy supply from \(B\) to \(A\). \(p_{<A,B>}-p_{ave}\) is the difference in the transmission of data packets. The more \(p_{<A,B>}-p_{ave}\), the more node \(A\) transmits data packets, then node \(A\) acquires more energy from neighbor \(B\). Formula (4) suggests that node \(A\) acquires energy from the neighbor, and then node \(B\) can keep enough energy transmitting data packets. Nodes \(A\) and \(B\) complete the energy equilibrium when they transmit data packets. Node \(A\) avoids energy over-consumption; node \(B\) acquires more data packets and supplies redundant energy to node \(A\). After they finish the data packets and energy transmitting, node \(B\) acquires more effective data packets from node \(A\). At the same time, node \(A\) not only receives data packets, but also has been supplied energy. In data communication, nodes must transmit more data packets, since they have high frequency founding communication areas. According to the energy equilibrium, active nodes extend their life-time and transmit more data packets to others; inactive nodes have more opportunity to improve communication when they supply energy. (5) Iteration energy supply in data communication. In data communication, there are a great number of nodes. A node can acquire or supply energy to its neighbors. For node \(A\) in data communication, it has many neighbors when it moves and establishes the communication area. At the beginning, node \(A\) carries energy \(E_{0}\). When it meets neighbor \(B_{1}\), they transmit data packets to each other. At this time, node \(A\) carries energy:  
\[E_{1}=E_{0}-\Delta E_{<A,B_{1}>} \tag{5}\]  
Next time, node \(A\) transmit data packets, its energy is:  
\[E_{2}=E_{1}-\Delta E_{<A,B_{2}>} \tag{6}\]  
When node \(A\) is in the data environment, after many transmissions, the iteration formula can be found as Equations (2), (5) and (6):  
\[E_{n}=E_{n-1}-\Delta E_{<A,B_{n}>}=E_{n-1}-e\times(p_{<A,B_{n}>}-p_{ave}) \tag{7}\]  
\(E_{n-1}\) represents the energy node carried the last time, \(\Delta E_{<A,B_{n}>}\) is the supply energy between the nodes. If \(p_{<A,B_{n}>}-p_{ave}>0\), node \(A\) has enough energy and supplies energy to its neighbors; if \(p_{<A,B_{n}>}-p_{ave}<0\), node \(A\) acquires energy. The iteration formula can judge how many energies a node carries and estimates its lift-time in the big communication. Moreover, the iteration formula can judge the average energy in the data environment. (6) Extend the communication life-time for nodes. In data communication, the energy equilibrium can extend active nodes, which take part in communicating high frequency life-times and avoiding energy over-consumption.