# On Connectivity and Energy Efficiency for Sleeping-Schedule-Based Wireless Sensor Networks
## 4 System Simulation  
### The Simulation Performance Index  
Table 1 shows the main simulation parameters for the network connectivity and energy efficiency algorithm, set up the monitoring area is similar to a circle, set the monitoring radius \(r=400\) m, and set the number of nodes as \(N=5000>>10\). The area of the monitoring area is about \(S=\pi r^{2}\approx 5.03\times 10^{5}\) m\({}^{2}\). The communication radius of the node is 30 m as the maximum, so the communication area of the node is \(S^{\prime}=\pi R^{2}\approx 2827.43\) m\({}^{2}\). Then, the node's communication probability \(P=\frac{S^{\prime}}{S}\approx 0.0056\ll 0.1\); therefore, the nodes thrown by the aircraft satisfy the Poisson distribution of the mean value \(\lambda=NP\). Up until now, the value range of R of the sensors nodes is higher than 30 m. However, only when the communication radius is greater than twice that of the perceived radius can the connectivity be guaranteed under the condition of certain coverage. However, the detection radius and communication radius of sensor nodes are limited by various aspects, and often coverage nodes can meet the requirements of coverage but cannot guarantee the network connectivity. Then, in a fixed region, only when how many nodes are scattered and what is the connectivity \(K\) of the nodes, can a wireless sensor network with high reliability, high connectivity probability, and long service life be guaranteed. Due to the cost and difficulty of deploying large-scale sensor networks, the current research work in this paper is carried out in the simulation environment, including the algorithm performance evaluation. For the convenience of analysis, the ideal model is used. The algorithm design uses the connected radius and the circular region, because it simplifies the analysis. The connecting radius of the sensor is different under different sending power. In the case of a certain receiving sensitivity, the relation between the wireless transmitting power \(P\) and the receiving radius \(R\) is \(P=R^{2}\sim R^{5}\), so \(P\) could be much larger than \(R^{2}\). Combined with the algorithm for judging connectivity, when calculating coverage, we use the idea of infinitesimal elements to ensure that the network is just connected, then find the minimum communication radius of each node when they are just connected. In terms of implementation, information exchange and maintenance are expensive jobs. Whether it's centralized computing or distributed computing, there is a large amount of communication overhead, and the overhead is related to the signal power of the nodes and the average node density of the network. In order to adapt to the practical application in the field of wireless sensor network, the model and theory are extended to a larger \(R\) of about 100 m as our next research item. In the previous section, a new type of network connectivity and energy efficiency algorithm is proposed to minimize the energy consumption while ensuring the maximum probability of network node connectivity \(K\) in the wireless sensor network. Using the parameters specified above, according to the experimental results, the simulation diagram of the relationship among the network node connectivity \(K\), the radius \(r\) of the monitoring area and the node communication radius \(R\) is obtained, as shown in Figure 2. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Values** \\ \hline Monitoring radius (\(r\)) & 400 m \\ \hline N & 5000 \\ \hline The communication radius of the node (\(R\)) & 30 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters for the network connectivity and energy efficiency algorithm. As can be seen from the Figure 2, when the radius of the monitoring area \(r=400\) m, network connectivity \(K\) is about 8, node communication radius \(R\) is about 16 m, and the WSN has strong characteristics of network connectivity [22].