## 3 Proposed Dynamical DOSS Model  
The proposed model aims to maximize the EE of the HetNet using the D-DOSS approach. This approach involves a strategic algorithm that forms small clusters throughout the network by dividing it into \(N_{C}\) equal-sized squares, each representing a cluster region. These cluster boundaries help identify the cluster each BS belongs to but do not affect UA, as users will still connect to the BS providing the maximum SINR \(\beta_{max}\). Compared to CS, the decentralized D-DOSS approach offers better ease of implementation and manageability, though it may have some performance trade-offs since CS has comprehensive knowledge of all BSs in the network, resulting in higher impact. The optimization problem is formulated considering various constraints such as delay constraints, coverage probability constraints, and SINR threshold constraints. The goal is to ensure efficient network operation while maintaining the required QoS for users. The D-DOSS approach forms clusters within the network, with each cluster managed to balance load and performance. This decentralized management scheme optimizes power consumption and resource allocation, enhancing the overall EE of the network. Table 3 lists all the parameters used in the equations for implementing D-DOSS and problem formulation. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Description** \\ \hline N & Total number of users in the network \\ \hline n & Specific value that \(N\) can take \\ \hline \(\mathrm{P(N=n)}\) & Probability of having \(n\) users \\ \hline \(\lambda\mathrm{u}\) & User density or arrival rate \\ \hline \(\lambda_{\mathrm{BS}}\) & Base station density or arrival rate \\ \hline \(\rho\) & Constant used in cell size distribution, typically \(\rho=3.575\) \\ \hline \(\Gamma\) & Gamma function for factorial generalization \\ \hline \(\mathrm{P(N\leq n)}\) & Cumulative probability of having fewer users \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters definition for equations. If \(N_{c}=1\), the CS and DS both will be identical. In a K-tier network which contains \(N\) total numbers of users. At any point X in VT, within an area of \(A\), the probability of a BS to serve a user for three different cases is given as follows:  
Case (i): \(N=n\),  
\[\mathrm{P(N=n)}=\int_{0}^{\infty}\mathrm{P[N=n|X=A]f_{x}(A)dA}\]  
\[\mathrm{th}\] \[\cong\frac{\lambda_{n}^{n}\left(\rho\lambda_{BS}\right)^{K}\Gamma \left(n=\rho\right)}{\Gamma\left(\rho\right)n!\left(\lambda_{n}+\rho\lambda_ {BS}\right)^{n+p}} \tag{1}\]  
where \(N\) is the random variable, \(\mathrm{n}\) is a specific value that \(N\) can take, \(\mathrm{P(N=n)}=\int_{0}^{\infty}P[N=n|X=A]f_{x}(A)dA\) is the conditional probability, \(f_{x}(A)\) is the probability density function of \(X\), and \(\lambda_{u}\) and \(\lambda_{BS}\) are user and small BS density, respectively. Further \(\rho\) is a constant used in cell size distribution here? \(\rho=3.575\), and \(\left(\Gamma\right)\) is a gamma function for factorial generalization. The above integral can be solved using identity [52] for the general case when a BS has few or fewer users, i.e., \(\left(N\leq n\right)\),