## 4 Proposed Scheme
### Holding Time Estimation  
The acoustic sensor nodes are deployed to monitor the underwater environment. The sensor nodes persistently originate data packets and forward them to the centralized station. When the source node broadcasts the data packets, all nodes lying in its transmission range receive them. If all the forwarder nodes take part in forwarding the packets, then it will result in the overhead and higher energy consumption. To increase the network lifetime, we propose a holding time mechanism (see Algorithm 2) to reduce the number of forwarding nodes to lower the energy consumption, but at the same time, ensure reliability. Once the required processing time is passed, the node extends the holding time value on the second hop by setting the timer according to the holding time value. In that case, the packet is forwarded only upon the timer's expiry and no duplicate of the packet is received, otherwise, it is dropped. The following equations have been derived from [32] and processed further for the holding time mechanism of node A, as depicted in Figure 8.  
\[HT_{p}^{A}=E_{f}+P_{f}+CultivatePacketAdvancement \tag{10}\]  
The parameter energy factor (\(E_{f}\)) represents the distance of the PFN from the edge of the transmission range scaled with the inverse normalized energy of the PFN at the first hop as well as at the second hop, i.e.,  
\[E_{f}=e^{(-E_{A})}\left(\frac{T_{r}^{S}-D_{S}^{A}}{v_{s}}\right) \tag{11}\]  
where  
\[E_{A} =\frac{\left(e_{A}+e_{B}\right)-\left(emin_{hp1}+emin_{hp2}\right) }{\left(emax_{hp1}+emax_{hp1}\right)-\left(emin_{hp1}+emin_{hp1}\right)}\] \[e_{min} =min\left(e_{j}|\forall j\in\chi_{i}\right)\] \[e_{max} =max\left(e_{j}|\forall j\in\chi_{i}\right)\] \[E_{A} \in[0,1]\] \begin{table}
\begin{tabular}{c c c c c} \hline
**Struct1** & **Node A** & **Node B** & **Node C** & **Node D** \\ \hline ID & 1 & 2 & 3 & 4 \\ \(HT_{1 st}\) & 17 msec & 10 msec & 15 msec & 30 msec \\ \(HT_{2 nd}\) & 70 msec & 55 msec & 35 msec & 45 msec \\ \(HT_{r}\) & 30 msec & 17 msec & 10 msec & 15 msec \\ \hline \end{tabular}
\end{table} 
Table 2: Packet Forwarding Scenario after the nodes received the CP Packet. Figure 7: Forwarding Scenario. ```
function [\(Struct_{2 nd}\) nforwrwrdrs NBCount] = CFRWDRRS3(S,forwID, sink1, W, R, v, PFNS, NFORWD) S1=source(x,y,z), D=Destination(x,y,z), Find \(Emin_{hp1},Emax_{hp1}\) for\(P\gets 1\)to\(number\) of PFNs of Sby\(1\)do  Get location of PFN(P), Find \([PERSON]_{hp2},Emax_{hp2}\) for\(K\gets 1\)to\(number\) of PFNs of P by\(1\)do  Ej=Get the energy of the second hop PFN \(Ek=\frac{Ej-Emin_{hp2}}{Emax_{hp2}-Emin_{hp2}}\) \(HT_{2 nd}\)=Find minimum holding time at the second hop \(HT_{1 st}\)=Find holding time of node P at the 1 st hop, \(Struct_{1 st}\).\(ID=P\) \(Struct_{1 st}\).\(HT=HT_{1 st}\) \(Struct_{2 nd}\).\(ID=P\), \(Struct_{2 nd}\).\(HT=HT_{1 st}+HT_{2 nd}\)  Sort both \(Struct_{1 st}\) and \(Struct_{2 nd}\) with respect the holding time (HT) for\(m\gets 1\)to\(nodes\) in \(Struct_{2 nd}\)by\(1\)do \(m\_element\) of \(Struct_{2 nd}\).\(HT=m\_element\) of \(Struct_{1 st}\).\(HT\);  S=Find the node with minimum HT for\(t\gets 1\)to\(nodes\) in \(Struct_{2 nd}\)by\(1\)do  F1=node t coordinates from struct, F2=minimum HT coordinates, Find Propagation distance if Propagation distance < Holding time of F1 - Holding time of F2 then  Suppressed, remove from the \(struct_{2 nd}\) ifnumber of nodes in \(struct_{2 nd}\)==1 then \(struct_{2 nd}\).\(HT=0\)
```  
**Algorithm 2**Estimation of the Holding time. Figure 8: Holding time estimation. The energy of the node is normalized in neighbors of the source node. The normalized energy is between 0 and 1. The node with maximum residual energy will have lower normalized energy value. The \(e_{A}\) and \(e_{B}\) represent the residual energy of nodes A and B, respectively. The \(emin_{hp1}\) and \(emin_{hp2}\) are the minimum energy of the PFN at the first and second hop respectively, the converse is true for \(emax_{hp1}\) and \(emax_{hp2}\).