## 4 Timer Value Methodology of a Forwarder Node for the Proposed Scheme
The number of alive nodes for the BDREA protocol is higher, by balancing the energy in the network, which means that a finding a suitable node with respect to the timer value will mostly occur. Therefore, the BDREA routing protocol reduces the packet dropped ratio while maintaining a higher PDR value, as from \[E_{tax}=\frac{E_{total}}{ForwardingNodes\times Data_{packets}} \tag{1}\]6 The timer value calculation is the major factor for improving the related objective parameters, by tuning

\[E_{tax}=\frac{E_{total}}{ForwardingNodes\times Data_{packets}} \tag{1}\]7 Packet Delivery Ratio (PDR) vs. Number of Nodes. the related metrics. The objective of this article is to improve the related parameters by considering the energies of the potential forwarding nodes in the forwarding locality. This will prolong the network life, and at each instance of time, more favorable forwarding nodes will be available for selecting the next forwarding. BDREA defeats the benchmark, DOW-PR, by an average of 8% improved PDR, and WDFAD-DBR by 10% improved PDR for the 200 nodes in the network. The total energy consumption is defined as the average energy consumed per node during the successful transfer of the packet from the source node to a sink node. It includes the sending, receiving, and idle state energy. The computation equation is the following:

\[E_{tax}=\frac{E_{total}}{ForwardingNodes\times Data_{packets}} \tag{1}\]8

where \(E_{total}\) denotes the whole network energy, and Nodes and Packets denote the number of nodes and packets successfully received, respectively. The energy tax for the all of the schemes is plotted by varying the number of nodes in the network, as shown in \[E_{tax}=\frac{E_{total}}{ForwardingNodes\times Data_{packets}} \tag{1}\]9 The general trend followed by all of the protocols is that the energy tax decreases when the number of nodes in the network is increased. For a node number of 100, the performance of the proposed work for BDREA in terms of energy tax is lower than in the conventional schemes. This is due to the fact that the conventional schemes find better nodes in terms of packet advancement, while there exists a minimum packet overhead, due to a less dense network. The performance of BDREA is better for a dense network, to save energy utilization in terms of packet overheads, and in exchanging the different packets. It can be visualized that the proposed BDREA defeats the other protocols in terms of energy tax for a dense network. This is due to the fact that the proposed work considers the energy of the forwarding zones in forwarding the packets, which balances the overall residual energies of the nodes in the network; therefore, it prolongs the network life time. For each packet transmission, the network will find the best suitable nodes in terms of the timer value parameter, and will optimize the energy performance. It can be seen from Figure 4 that the proposed work improved the energy tax of the network by approximately 50%, compared to DOW-PR and WDFAD-DBR. Figure 2:0 Objective Function plotting using Whale Optimization Algorithm for the proposed scheme. The Average Accumulated Propagation Distance is the distance covered by each packet during the hop-to-hop transmission. Actually, it is the hop distance that is measured. As there are many sink nodes in a network, so the packet distance to the shortest sink is measured as the final accumulated propagation distance. The equation of APD is defined as follows:

Figure 2:1

where the number of packets successfully delivered, and the hop number from the source to sink node is represented by s and k, respectively; \(dist_{i}^{j}\) is the propagation distance of the ith hop of the jth packet. APD is plotted for all the protocols in Figure 2:2 It can be seen from the results that DOW-PR and BDREA result in the same APD values, because both the protocols consider the distance to the surface station and the number of hops up to the centralized station.