## 4 Timer Value Methodology of a Forwarder Node for the Proposed Scheme
End-to-End delay is another important parameter that is defined as the total time taken by a packet to travel from the source node to the sink node. This includes the transmission time delay, the holding time delay, and the propagation time delays. The end-to-end delay curve is plotted in Figure 6 for WDFAD-DBR, DOW-PR, and BDREA. DOW-PR reduces the end-to-end delay time and improves the performance by 15% illustrated in Figure 10, compared to the proposed work's BDREA. The fact can be verified from the timer calculation equation and the fitness value equation that the BDREA is more focused towards energy minimization, which also results in enhanced PDR. For the instance of time, if there exist two paths for transmission, BDREA will prioritize the one where the least amount of energy is consumed, while DOW-PR will prioritize the one where an end-to-end delay results in a minimum time. BDREA results in an 18% reduction in end-to-end delay when compared with WDFA-DBR, as BDREA also considers the distance to the surface sink in selecting the next forwarder, and therefore reduces the end-to-end delay time. Comparing BDREA with WDFAD-DBR, it improves the results by 5% and therefore results in a lower end-to-end delay. Figure 2:3 Objective Function plotting using Whale Optimization Algorithm for the proposed scheme. ## 6 Conclusions

A novel Betta and Dolphin Pods Routing and Energy Scarcity Aware (BDREA) protocol has been developed for an underwater wireless sensors network. The sensors are producing and transmitting data packets in their immediate area, while the nodes in their neighbors' networks are receiving the packets. The nodes that belong to the neighbors have the ability to act as forwarding nodes, which means that they can send data packets onwards toward centralized stations. A timer mechanism is calculated in order to prevent packets from being overheard, and to reduce the amount of energy that is consumed. The computation of the timer used by BDREA takes into account the progression of the packets during the first two hops after the source node, the volume of traffic along the forwarding path, the distance to the centralized station, and the inverse energy of the forwarding region. When compared to the benchmarks WDFAD-DBR and DOW-PR, the work that was presented had a better performance in terms of PDR, energy tax, and end-to-end latency. To be more exact, it has been determined that BDREA improves PDR by 8%, energy tax by 50% in comparison to DOW-PR, end-to-end delay by 18%, and APD by 5%, in comparison to WDFAD-DBR. Methodology, H.Z. and K.I. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The authors declare no conflict of interest. ## References

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