## 4 Efficient Data-Balancing for CPS
### Node Selection and Recruitment Module  
The objective of recruiting the sensor node and selecting legitimate actuators helps to improve throughput and decrease latency. The recruitment process is employed if the actuator hub (the cluster head node) does not discover sufficient sensor nodes in its cluster space. As a result, the actuator node starts the recruitment request from another actuator node. First, the actuator node checks its zone regions by sending a recruitment request. If the actuator does not discover the required nodes in its neighborhood, it broadcasts the multicasting message to recruit the nodes. When the actuator node comes to the nodes from its non-adjacent cluster, the pipelining-based method (which allows different practical units of a system to function synchronously) is applied to reduce the latency that could be caused by a long distance. Furthermore, the recruiting actuator first recruits the sensors from its neighbor and then recruits them from nonadjacent neighbors. Let us assume that the actuator node recruits the sensor nodes from other cluster regions. The actuator is static and gathers data about the person; thus, every monitoring point \(M_{p}\) requires sensor nodes via recruitment to gather the data from a human. The probability \(pr\) of a sensing requirement \((N_{r},P_{r})\) can be calculated as  
\[pr=\int_{N_{r}}^{n}fx(N\times\gamma,\omega)\partial N, \tag{2}\]  
where \(pr\) is the probability of the recruited sensor, and \(N_{r}\) is the recruited sensor.  
The probability of checking point \(M_{p}\) can be decided when the activity is completed at another checking point \(M_{p1}\), which is \(\partial_{p1,p}\). Thus, with the probability of having to observe point \(p\), information can be detected utilizing recruitment node \(N_{r}\), decided by  
\[N_{r(d)}=1-\sum_{p}^{p=\infty}p\Bigg{(}1-\bigg{(}\partial_{p1,p}\int_{N_{r}}^{ n}fx(N\times\gamma,\omega)\partial N\Big{(}1-\sum_{t=0}^{n}t(1-\partial_{p0,p1}) \Big{)}\bigg{)}\Bigg{)}, \tag{3}\]  
where \(N(r(d))\) is the recruited sensor sensing data, \(\partial_{p1,p}\) is the distance of the recruited sensor from its domain to the recruiting sensor's domain, and \(t\) is recruitment time.  
Once the recruitment sensor node begins to sense the data, if the sum of the data is more than the detecting capability of the deployed and recruitment node, the actuator starts the extra sensor recruitment process from neighboring and non-neighboring cluster spaces, given by  
\[A_{rec}=1-\prod_{N_{rec}}N\times 1-\sum_{p}^{p=\infty}p\Bigg{(}1-\bigg{(} \partial_{p1,p}\int_{N_{r}}^{n}fx(N\times\gamma,\omega)\partial N\Big{(}1- \sum_{t=0}^{n}t(1-\partial_{p0,p1})\Big{)}\bigg{)}\Bigg{)}, \tag{4}\]  
where \(A_{rec}\) is the recruiting actuator, and \(R\) is the cluster domain that gives the sensor as a recruitment sensor.  
After an additional sensor recruitment process, we obtain a new vector \(P_{r}^{\prime}\) that illustrates the probability of monitoring point \(M_{p}\), which needs to be covered by recruiting the additional sensor nodes.  
\[P_{r}^{\prime}=\begin{cases}\frac{P_{r}-A_{rec}}{1-A_{rec}},&\text{ if }A_{rec}\leq P,\\ 0,&\text{ otherwise.}\end{cases} \tag{5}\]  
where \(P_{r}^{\prime}\) is the new vector that indicates the probability of a grid station.