# Multiparameter Fusion Decision Routing Algorithm for Energy-Constrained Wireless Sensor Networks
## 2 System Model and Routing Evaluation Parameter
### Routing Evaluation Parameter
#### 2.2.1 Energy Equilibrium Degree  
In WSNs, the one-hop coverage area of adjacent nodes overlaps with each other. If local energy balance within the one-hop range can be achieved, the energy balance of the entire network can be approximately realized in a distributed way by using local information [37]. However, for the routing decision-making, some energy balance routing algorithms [16; 17; 18; 19] generally consider the residual energy to select the next hop. In these algorithms, the node with less residual energy has a lower chance of being chosen as the transit node. At the same time, the nodes with more residual energy are more involved in data transmission. This literature takes residual energy as one of the criteria for routing decisions. In the traditional method, energy balance is passive; that is, the residual energy may have an extreme imbalance when the data forwarding path is updated. Therefore, our paper introduces an active energy balance strategy. Before data are formally transmitted, this strategy predicts the equilibrium degree of residual energy between nodes after selecting different neighbors. In the traditional method, the energy imbalance in a local network region \(A\) is measured by the mean square error of the residual energy of the nodes. Hence, the region energy imbalance can be expressed as follows:  
\[EIB^{\prime}=\sqrt{\frac{1}{n}\sum_{i\in A}\left(E_{i}-\overline{E}\right)^{2}} \tag{4}\]  
where \(n\) is the node number of \(A\). \(E_{i}\) denotes the residual energy of node \(i\). \(\overline{E}\) represents the average residual energy of all sensor nodes. The mean square error cannot fully reflect the unbalance degree of the residual energy within \(A\). For example, if the residual energy of each node is reduced by half, then \(EIB^{\prime}\) is also reduced to half of the original. However, the energy imbalance between nodes does not change. In sociology, the Atkinson coefficient is defined to measure the inequality of income distribution. The smaller the social income gap is, the lower the value of the Atkinson coefficient will be. Here, when the Atkinson coefficient is introduced into a WSN, the new \(EIB\) is as follows:  
\[EIB=1-\left[\frac{1}{n}\sum_{i\in A}\left(\frac{E_{i}}{\overline{E}}\right)^{1 -\varepsilon}\right]^{\frac{1}{1-\varepsilon}} \tag{5}\]  
where \(\varepsilon\) is the inequality aversion index, and the commonly used value is 2.5. \(EIB\) describes the energy balance state of nodes within the single-hop range; that is, if the energy distribution in \(A\) is more balanced, the Atkinson index value will be smaller. Thus, assuming that forward neighbor \(h\) is the next hop of node \(i\), the residual energy of node \(i\) is as follows:  
\[\hat{E}_{i}^{ih}=E_{i}-e_{t}\left(l,d_{i,h}\right) \tag{6}\]  
where \(l\) is the size of the unit packet. \(d_{i,h}\) is the distance between node \(i\) and \(h\). \(e_{t}\left(l,d_{i,h}\right)\) is the energy required to transmit \(l\)_bits_ data. At the same time, the forward neighbor \(h\) needs to receive and forward the data from node \(i\). Therefore, its estimated residual energy can be expressed as follows:  
\[\hat{E}_{h}^{ih}=E_{h}-e_{r}\left(l\right)-e_{t}\left(l,R\right) \tag{7}\]  
where \(e_{r}\left(l\right)\) and \(e_{t}\left(l,R\right)\) represent the energy used to receive and send \(l\)_bits_ of data, respectively. Here, it is assumed that the distance forwarded by the forward neighbor \(h\) is the maximum communication radius \(R\). For other forward neighbors, since they do not need to consume energy to participate in the data transmission of the node \(i\), their remaining energy can be regarded as remaining unchanged, that is, the estimated remaining energy is as follows:  
\[\hat{E}_{j}^{ih}=E_{j} \tag{8}\]According to Equations (6) to (8), \(EIB\) of each candidate next hop in the set \(FN(i)\) can be estimated.