## 3 Proposed Scheme
### Problem Statement  
When a node \(S\) transmits the data packet (either that data packet is generated by that node or received from the downstream sensor nodes), all the neighboring nodes within its \(T_{r}^{S}\) and in the \(PFZ\), receive that packet. Now, the question arises that which node(s) has(ve) to further transmit or relay the packet in upstream direction? The answer to this question is the holding time, \(HT\). Upon successful reception of packet \(p\), a node \(i\) computes the \(HT_{p}^{i}\) and starts the timer. During \(HT_{p}^{i}\) is on, \(i\) does not forward the packet. However, node \(i\) can receive data packets from its neighboring nodes, which may be copies of \(p\) or other data packets. When node \(i\) receives additional one or more than one copies of \(p\) while \(HT_{p}^{i}\) did not expire, then it suppresses the transmission of \(p\). On the contrary, if \(HT_{p}^{i}\) expires and no copies of packet \(p\) have been received during the \(HT_{p}^{i}\) period, then \(i\) forwards the packet \(p\). This simple phenomenon alleviates the extra broadcast overhead, which is necessary for the UASN scenario where energy and bandwidth are the scarce resources. However, UASN has an added feature that must be considered while designing the holding time, which is the long propagation delay. Consider a scenario where multiple nodes in the \(PFZ\) receive \(p\), then all nodes in \(PFZ\) will calculate their respective holding time \(HT_{p}^{i}\). If the number of nodes in \(PFZ>1\), then the difference between their holding times must be greater than the propagation delay between them. Let, holding time of nodes 1 and 2 in \(PFZ\) for data packet \(p\) is \(HT_{p}^{1}=1.2\ s\) and \(HT_{p}^{2}=1.3\ s\), refer Figure 1. And let the propagation delay between both the nodes 1 and 2 is \(\frac{D_{p}^{1}}{v_{s}}=0.2\ s\), where \(v_{s}\) is the acoustic signal speed in the aquatic environment. In this scenario, node 1 will forward the packet after 1.2 s, however, due to a long propagation delay and the short holding time difference, 2 will not receive the copy of \(p\) from node 1 and its \(HT_{p}^{2}\) will expire. Hence, 2 will also forward the packet \(p\). Similarly, any other node(s) in the \(PFZ\) that has/ve holding time difference less than the propagation delay between them, will also forward(s) the packet \(p\). Therefore, even by applying the holding time, multiple copies of the same packet will be forwarded by the nodes in the PFZ that will impact the energy consumption as well as the packet collision at the next hop receiving nodes, e.g., \(n_{i}\) in the network scenario shown in Figure 1.  
From the above discussion, it is observed that there is a close relationship between the holding time difference between the close proximity neighbors, especially in the underwater communication scenario. This relationship is shown Figure 2. A well-established fact about the underwater acoustic networks is its long propagation delay that is one of its limitations to be considered by any packet forward scheme. The figure also shows that the propagation delay between node \(i\) and \(j\), \(\tau_{(i,j)}\), that is directly proportional to the distance between them. It is obvious that if the difference between the holding time of node \(i\) and \(j\) for packet \(p\), \(HT_{p}^{i}\)-\(HT_{p}^{j}\), is greater than the \(\tau_{(i,j)}\), then the packet suppression can be achieved. Otherwise, if the \(HT_{p}^{i}\)-\(HT_{p}^{j}<\tau_{(i,j)}\), then multiple copies of \(p\) will be broadcasted in the network. The shaded area in the figure is the duplication zone. This can easily be avoided when the holding time difference is larger than the propagation delay. One of the drawbacks of the larger holding time is the long end-to-end delay that should be avoided in holding time-based forwarding schemes.