# An Energy Balance Clustering Routing Protocol for Intra-Body Wireless Nanosensor Networks
## 3 Clustering Routing Framework
### Clustering and Cluster Head Updating
The calculation formula is:

\[S_{k}=w(m)\frac{E_{res\_k}}{E_{max}}+\left[1-w(m)\times\frac{d_{\sum}\ -d(v_{k},h(v_{k}))}{d_{\sum}}\right] \tag{14}\]8

where \(R_{suc}\) is the data packet transmission success rate, \(F_{t}\) is the number of data packets sent by the nano nodes in the network and \(F_{r}\) is the number of data packets received by the nano control node. #### 4.2.4 The Proportion of Control Overhead

The proportion of control overhead refers to the proportion of packets used for nano-node control information to total data packets in the network. It can be written as:

\[S_{k}=w(m)\frac{E_{res\_k}}{E_{max}}+\left[1-w(m)\times\frac{d_{\sum}\ -d(v_{k},h(v_{k}))}{d_{\sum}}\right] \tag{14}\]9

where \(N_{control}\) is the data packets for control information, \(N_{service}\) is the data packets for service information and the total data packets are the sum of \(N_{control}\) and \(N_{service}\). The larger the value, the greater the proportion of control overhead. #### 4.2.5 Average End-to-End Delay

There is a processing delay, queuing delay, propagation delay and transmission delay in the transmission of packets. Average end-to-end delay \(\overline{T}\) is defined as mean of the time a packet takes from being generated to received successfully at the control node, it can be written as:

\[h^{\prime}=argmax(S_{k}) \tag{15}\]0where \(T_{pr}\) is the processing delay; \(T_{qi}\) is the queuing delay; \(d_{i}\) is the distance between the node transmitting the data packet and the control node; \(L_{data}\) is the size of the data packet sent by the sensing node, in this paper \(L_{data}\) of all nodes is the same; \(v\) is the propagation speed of the signal in the medium; \(C_{s}(d_{i})\) is the channel capacity corresponding to the node \(v_{i}\); \(N_{rec}\) is the number of packets successfully received at the control node. #### 4.2.6 Effective Throughput

The effective throughput is defined as the number of bits of the data packet successfully received by the destination node per unit time, which can be expressed as:

\[h^{\prime}=argmax(S_{k}) \tag{15}\]1

where \(Th_{avg}\) is the network average throughput, \(N_{bit}\) is the number of bits in a single packet, \(l_{N}\) is the number of data packets during \(\Delta T\) and \(R_{suc}\) is the data packet transmission success rate. ### Simulation Parameters

The simulation scenario in this paper considers the nano-nodes deployed in the skin dermis of the hand to construct a nanonetwork. According to [27], the molecular absorption factor of the skin is 110, the refractive index is 1.73, and the system parameter \(\kappa\) in Equation (16) is set to 0.5, the residual energy threshold \(\eta\) in Equation (18) is set to \(1.4\times 10^{-13}\)[21], which represents the energy consumption required to receive unit bit data when the transmission distance is 0.002 m. The simulation scenario is shown as \[h^{\prime}=argmax(S_{k}) \tag{15}\]2 Nano-nodes are randomly distributed in the area. The remaining specific simulation parameters are set as Table 1 is shown. Please notice that in Figure 10, we change the number of nano-nodes in the network lifetime simulation, but in other simulation we use 100 nano-nodes to simulate. In the simulation that considers the data packet generation interval as an independent variable, we change the interval in the range of 1 to 10 s, in other simulation, we use a fixed data packet generation interval 0.1 s to simulate. \[h^{\prime}=argmax(S_{k}) \tag{15}\]3 Simulation Scenario. ## 5 Simulation Results and Analysis

### Network lifetime

In Figure 9, the network lifetime is analyzed by simulating the number of dead nodes in the network. The simulation time is represented by rounds (each round is 120 s). In Figure 10, the time when the first node is dead is compared. In the simulation, the time refers to the number of iteration round. FND is the abbreviation for First Node's Death.