## 4 Timer Value Methodology of a Forwarder Node for the Proposed Scheme
In the event that the PFN does not change its position at any point in the locality, then in the case of real life, in the simulation, a single node will be chosen every time the source broadcasts the packet. Because of the repeated selection, the currently chosen node will enter a dead state after a certain amount of time has passed. Therefore, the sensor nodes move around and their positions change in a random pattern. These nodes are qualified to act as forwarding nodes if the current source node is shallower, and if the distance between them is closer together than the transmission distance. The Neighbor Request Packet is broadcast by the source node in order to locate the forwarding nodes that it needs. To determine which is the best next hop, every node maintains its own corresponding neighbor table, which is for the for the purpose of keeping a record of their fellow community members: \(Neighbor_{table}(id,residual_{energy},d,Tinter_{value},Update_{time})\), where id is the neighbor node unique number, \(residual_{energy}\) is the residual energy of the node, d represents the Depth information, \(Tinter_{value}\) is the timer value of the node, and \(Update_{time}\) stands for the time required to update the neighbor entry. ``` for\(i\gets 1\)toTotalNodes by 1 do \(b\_id=S(i).id\)Total\(PNs=S(S(i).id).\_PFN\)Ch\(\_Flag\)  whileFlag==Truedo for\(j\gets 1\)toCentralized\(\_\)Stationsby 1 do  finddistance\(D\)]with Centralized\(\_\)station(j) if\(D\)\(<t\_\)rangethen  DATAPacket Received \(Chk_{F}lag=0\) Break and Generate Another Packet if\(PFNs==0\)then \(b\_id=b\_id-Transmitting\_Energy\) N\(\_\)S\(umps=S(S(i).id).\_N_{S}\)\(\mu\)S\(\_\)IF\(N\_\)S\(\mu\)\(\emptyset\)then  Chk\(\_\)PSUP\(0\)  for\(k\gets 1\)to\(N\_\)S\(\_\)UPS\(1\)do  Calculate Fitness Function\((FF_{\_\_}{



## 5 Simulation Results and Analysis

The proposed work is simulated against different parameters, i.e., packet delivery ratio (PDR), end-to-end delay, Average Accumulated Propagation Distance (APD), and energy tax. Packet Delivery Ratio (PDR) is defined as the ratio of the successful transmission of packets from the source node to the destination node that is the sink or centralized station. PDR can be expressed with the following equation:

\[E_{tax}=\frac{E_{total}}{ForwardingNodes\times Data_{packets}} \tag{1}\]3

The results of PDR for the proposed work (BDREA) are plotted against the DBR, WDFAD-DBR, and DOW-PR routing protocols, as shown in \[E_{tax}=\frac{E_{total}}{ForwardingNodes\times Data_{packets}} \tag{1}\]4 The results are obtained by varying the total number of nodes in the network, ranging from 100 to 500 nodes. There is an increasing trend in PDR when increasing the number of nodes in the network. This is due to the fact that by increasing the number of nodes in the network, it also increases successful delivery to its destination, i.e., lowering the probability of packets dropped. As from Figure 7, for 100 nodes in the network, the PDR is approximately 40%, which shows a higher probability of packets dropped for the WDFAD-DBR and DOW-PR protocols. PDR is gradually increased by increasing the number of nodes in the network, and for about 500 nodes, it approaches the highest peak PDR values with the aid of a higher packet overhead and a higher total energy consumption. WDFAD-DBR and DOW-PR consider the total packet advancement at the first and second hops. Therefore, by considering the first- and second-hop potential forwarding nodes of the source node, WDFAD-DBR and DOW-PR reduce the packets dropped probability and show a higher PDR--refer to \[E_{tax}=\frac{E_{total}}{ForwardingNodes\times Data_{packets}} \tag{1}\]5 Our proposed BDREA routing protocol not only considers the packet advancement over the first two hops from the source node, the traffic congestion, and the distance from to the surface station, but it also considers the inverse normalized energy tax values of the potential forwarding zones of the source nodes, and therefore, balances the total energy in the network.