## 2 Related Work  
In [20], a routing technique called AEERP (AUV aided energy-efficient data-gathering routing protocol) in which an AUV collects data via gateway nodes based on RSSI values of hello packets was proposed. AEERP maximizes data collecting while consuming less energy and delivering more data. In AEERP, the AUV does not have dynamic path adjustment of the elliptical trajectory when the network size increases or decreases. In [21], an AEDG routing scheme helps expand network lifetime and decrease data packet loss due to low energy consumption by using an AUV, which collects data from GNs and sends it to sink nodes. The AUV uses the SPT method to associate the least amount of MNs with the GNs based on residual energy, which helps to reduce data packet loss. The longer end-to-end delay still exists in AEDG. In [9], the data gathering protocol (DGS) in which an AUV collects data from the nodes is categorized as essential and usual data as it passes through the network. The nodes not selected as GNs send average data to GNs closer to the AUV. The protocol improves packet delivery efficiency. However, nodes relative to the AUV consume energy more quickly than nodes further away, resulting in an uneven energy consumption network. In [13], AEEDCO and approximate (AEEDCO-A) have been proposed to collect the maximum amount of data and increase network throughput time by consuming less energy and data delivery time to improve the network efficiency in UWSNs. Data collection from each cluster head makes the clusters less energy efficient and includes delay-tolerant routing protocols. In [23], based on data collection, the AUV location predictor (ALP) system was created. In this approach, the AUV collects data by moving along a predefined trajectory, and the AUV directly receives data from closer nodes, while the rest of the nodes forward data to GNs. They are more relative to the trajectory. The nodes close to the trajectory become \"hot regions\", meaning they use less energy to convey data to the AUV. In the ALP, there is no end-to-end delay model introduced for nodes to communicate with the AUV. In [24], the authors introduce the Scalable and Efficient Data Gathering (SEDG) routing protocol, which optimizes the collaboration of MNs with GNs to increase data delivery packets while consuming less energy. Furthermore, it reduces the drop data packet ratio interval time and increases network throughput time. SEDG does not address the delay model. SEDG makes paths based on the shortest path tree algorithm without considering the location and status (alive or dead) of the node. In [25], the Atomic Shaped Efficient Delay and Data Gathering (ASEDG) model, which achieved network performance indicators such as network delay, balanced energy consumption, and end-to-end delay, is examined. In [26], CARP uses connection quality information to forward packets. It uses basic topological information to prevent void and shadow zones. In [27], by using flood zone angel, the data is sent to sink nodes in UWSNs. Sensors forward packets based on flooding angle and energy condition. In [28], an enhanced hydro cast with an AUV for data collection has been proposed. The pressure levels of sensor nodes are used to route traffic to the sink in a greedy multihop method. In [29], the network considers two key factors: data packet size and transmission power utilized by sensors. By considering these factors jointly, a system has been proposed that can increase the network life using integer linear programming. In [30], a technique for data collection process in which the AUV uses Dubin curves to collect data from various 3D targets is proposed. First, it transforms 3D targets into 2D ones and builds a 2D route. Second, it changes the 2D path into a Dubin curve using ERT (Euler rotation transformation). In [31], two data-gathering schemes to reduce imbalanced energy usage and network delay time are proposed. They employ an AUV and multihop transmission.