## 4 System Model
### Network Model  
In the proposed protocol, SNs are randomly distributed inside a \(W\times W\) rectangle sensing field. Each SN has a distinct ID that can be anywhere between 1 and \(N\), such that SN = {SN1, SN2,..., SNN}. Along with its coordinates in relation to the field center, it also contains location information (\(x_{i},y_{i}\)). The network model's graphic representation is displayed in Figure 1. Data from SNs are received by a DFH, and are subsequently routed to the sink node, where the sink node is positioned at a specific location outside the region. The network is broken down into rounds throughout its active lifespan. Setup and steady-state are the two phases that jointly make up the first round. The steady-state phase is all that is included in subsequent rounds. It is noteworthy to mention that regrouping (DFH reselection) must take place after a certain number of rounds (i.e., batch), so the setup and steady-state phases are carried out in the following round. However, successive rounds only comprise the steady-state phase, and the process continues, as confirmed in [49]. The RTs for the proposed protocol are given in Figures 2 and 3, respectively, to ensure the efficiency of the data fusion mechanism. In the setup phase, the sink node employs the MPA to identify DFHs after dividing the sensing area into DFGs. This will be covered in more depth subsequently. In the setup phase, all SNs in the area of sensing receive a request information message from the sink node, and each SN\({}_{i}\) responds by sending an information message to the sink node. The ID, current RE, and location of a SN\({}_{i}\) are all part of this message. The sink node breaks down the area of sensing into \(H\) equal hexagonal groups after receiving this message from all SNs, where the group's radius is adaptable to the network size. Every DFG can be represented symbolically by \(DFG_{H}\) and is identified by all SNs. Furthermore, after the MPA method is executed, the sink node gathers these data into the sink node's table message, which contains crucial network information and is subsequently provided to SNs used to identify as a \(DFH_{l}\{1<l<H\}\) for each DFG. In addition, the sink node is liable for figuring out the relative RT and assigning each SN\({}_{i}\) a specific TDMA TS for packet transmission during the steady state phase. Consequently, it sends its data directly to \(DFH_{l}\). After transmission, SN\({}_{i}\) enters sleep mode to save energy. Then, a \(DFH_{l}\) collects data from all of DFGMs and delivers them directly to the sink node or the next PDFR based on the proposed protocol without routing and with multi-hop routing, respectively. When a SN\({}_{i}\) fails to provide enough energy sufficient to send a packet to the sink node or its DFH, it becomes dead. In these cases, the SN\({}_{i}\) is taken off the sink's table. A disjoin message is broadcast to all SNs in the network sensing area by a DFH when its energy level sags below a predetermined threshold. Furthermore, information about DFGMs and their corresponding RE levels is included in another disjoin message that is sent straight to the sink node. Here, the sink node realizes that, in order to bring about synchronization, the entire network's regrouping (DFH reselection) procedure is warranted. The proposed protocol involves various forms of messages, detailed as follows: (1) The Request Information Message: A broadcast from the sink node to all SNs, requesting their information. (2) The SN's information message: A unicast message is sent by each SN\({}_{i}\) to the sink node as a reply. The main fields of this message are the SN's ID, location, and RE. (3) The sink node's Table Message contains all necessary information about the SNs after network area division and running the MPA.