# An Energy-Efficient Routing Protocol for Reliable Data Transmission in Wireless Body Area Networks
## 4 Energy-Efficient Routing Protocol for Reliable Data Transmission in WBAN
### Construction of the Maximum Benefit Function  
The maximum benefit function is to normalize the residual energy, transmission efficiency, available bandwidth and hops to the sink, and then sum them up after allocating the weighted coefficients respectively. Therefore, the node with the largest value of the function is the best next hop.  
Since the energy of nodes is limited, it is necessary to improve the energy efficiency [33]. This paper firstly considers the residual energy of the nodes, choosing the nodes with more residual energy as the best next hop and thereby can balance the overall energy consumption of the network. Formula (4) is used to calculate the residual energy \(E_{i}^{res}\) of the node. The normalized expression is as follows:  
\[\gamma_{i1}=\frac{E_{i}^{res}-E_{min-th}}{E_{i}^{initial}-E_{min-th}} \tag{5}\]  
where \(\gamma_{i1}\) denotes the normalized parameters of the residual energy, \(E_{i}^{initial}\) denotes the initial energy of the node \(i\), i.e. the maximum energy of the node, and \(E_{min-th}\) denotes the minimum threshold of the node. When the residual energy of the node is lower than the threshold, only their own data are transmitted.  
The transmission efficiency of a node is the ratio of packets forwarded successfully. The more packets forwarded successfully per unit time, the higher the transmission efficiency of the node. Selecting nodes with high transmission efficiency as the best next hop can ensure reliable data transmission between nodes. The expression of the transmission efficiency \(\eta_{i}\) is as follows:  
\[\eta_{i}=\frac{P_{i}^{success}}{P_{i}^{receive}} \tag{6}\]  
where \(P_{i}^{receive}\) and \(P_{i}^{success}\) represent the number of packets received by the node \(i\) and the number of packets successfully forwarded. The transmission efficiency \(\eta_{i}\) are normalized as follows:  
\[\gamma_{i2}=\frac{\eta_{i}-\eta_{min}}{\eta_{max}-\eta_{min}} \tag{7}\]  
where \(\gamma_{i2}\) denotes the normalized parameter of transmission efficiency,\(\eta_{max}\) and \(\eta_{min}\) represent the maximum and minimum transmission efficiency, respectively.  
The available bandwidth of a node is the bandwidth currently available. The wider the available bandwidth, the better the data transmission will be. Considering the available bandwidth of nodes can further ensure the reliable transmission of data and improve the performance of the network. The available bandwidth \(B_{i}^{av}\) of the node \(i\) is normalized as follows:  
\[\gamma_{i3}=\frac{B_{i}^{av}-B_{min}}{B_{max}-B_{min}} \tag{8}\]  
where \(\gamma_{i3}\) denotes the normalized parameters of the available bandwidth of the node, \(B_{max}\) and \(B_{min}\) denote the maximum bandwidth and minimum bandwidth respectively.  
After network initialization, the node knows the hops to the sink. Choosing the appropriate next hop node can reduce transmission delay and ensure real-time communication between nodes. \(H_{i}\) denotes the hops of the candidate next hop node to the sink and normalizes it as follows:  
\[\gamma_{i4}=\frac{H_{i}}{H_{max}} \tag{9}\]  
where \(\gamma_{i4}\) denotes the normalized parameter with the hops and \(H_{max}\) denotes the maximum hops of the candidate next hop node to the sink.  
A simple linear weighted sum of the above four normalized parameters is used to construct a maximum benefit function \(M_{i}\), which can evaluate the performance of each candidate next hop node, and then select the best next hop node. The maximum benefit function is expressed as follows:  
\[M_{i}=\alpha*\gamma_{i1}+\beta*\gamma_{i2}+\theta*\gamma_{i3}+\lambda*(1-\gamma_ {i4}) \tag{10}\]  
where \(\alpha,\beta,\theta,\lambda\) is the weight factor of each parameter, and \(\alpha+\beta+\theta+\lambda=1\), which needs to be selected according to experience in practical application.