## 4 Proposed Scheme
### Holding Time Estimation
On the other hand, the normalized energy value is higher for the node which has higher residual energy for itself as well as for its expected PFN at the second hop than the specific threshold. Figure 9 is plotted by varying the distance of the PFN from the edge of the transmission range and its normalized energy. The \(E_{f}\) factor decreases when the residual energy of the nodes increases and the distance from the edge of the transmission range decreases. The node with the highest residual energy among all the PFNs has a \(E_{f}\) value approximately equal to zero. The second factor \(P_{f}\) in holding time calculation brings directionality and shows the placement of the node with respect to the virtual pipeline. The node nearer to the vector connecting sender and sink is preferable for forwarding the packets. Nodes that are not within the virtual pipeline directly drop the packet. The \(P_{f}\) is calculated as:  
\[P_{f}=\tan\left(\frac{P_{a}}{W}\right) \tag{12}\]  
\[P_{a} =\left(2\times Z\right)/D_{Sk}^{\mathrm{S}},\] \[Z =\sqrt{fr\times\left(fr-D_{Sk}^{\mathrm{S}}\right)\times\left(fr -A_{Sk}^{\mathrm{A}}\right)\times\left(fr-D_{Sk}^{\mathrm{A}}\right)},\text{ and}\] \[fr =\left(\frac{D_{Sk}^{\mathrm{S}}+D_{Sk}^{\mathrm{A}}+D_{Sk}^{ \mathrm{A}}}{2}\right).\]  
The \(P_{f}\) increases when the distance \(P_{a}\) from the virtual pipeline increases resulting in increasing the holding time of the forwarding node (see Figure 10). \[CultivatePacketAdvancement=\overbrace{2-\left(PrimeGap+inferierGap\right)}^{\delta} \tag{13}\]  
Figure 9: Ef vs. Normalized Energy. The last factor _Cultirate Packet Advancement_ represents the advance distance to be covered from the source node to PFN at the second hop of the forwarding packet. The factor _Cultivate Packet Advancement_ of all the nodes is in the range [0,1]. \[CultivatePacket Advancement=\overbrace{2-\left(\frac{D_{Sk}^{\text{S}}-D_{Sk}^{A}\cos( \theta_{a})}{T_{r}^{\text{S}}}\right)+\left(\frac{D_{Sk}^{A}-D_{Sk}^{B}\cos( \theta_{b})}{T_{r}^{\text{S}}}\right)}^{\delta} \tag{14}\]  
The nodes nearer to the sink have a lesser value of _Cultivate Packet Advancement_. The packet is advanced by the distance D1 from the source node when we select node A for forwarding. On the other hand, if node B is selected as a forwarder, the packet on the first hop is advanced by a lesser distance than node A. However, on the second hop, node B is more favorable. The factor \(D_{Sk}^{\text{B}}\cos(\theta_{a})\) gives the distance from the sink node to the projection point of node A on the center of the pipeline. Similarly, \(D_{Sk}^{\text{B}}k\cos(\theta_{j})\) gives the distance up to the projection point of B on the center of the pipeline. Here, \(\theta_{a}\) and \(\theta_{b}\) are represented as:  
Figure 7:0  
Figure 7:1  
Consider the nodes shown in Figure 8, ESEVBF will select node A for forwarding because it fulfills all the factors successfully as compared to node B at the first hop. However, Node B covers more advance distance from source node S to node D at the second hop. Therefore, the proposed system will select node C for forwarding the packet, resulting in lower end-to-end delay and energy consumption.