Toward Efficient Virtual Cell-Based Topology Management and Adaptive Routing for Underwater Wireless Sensor Networks

Abstract

Underwater Wireless Sensor Networks (UWSNs) play a vital role in ocean monitoring and exploration. However, harsh underwater conditions and frequent topology changes caused by node and sink mobility pose significant challenges for reliable routing. Conventional routing protocols that depend on global route reconstruction and static paths generate excessive control overhead and degrade performance in large-scale underwater environments. In this paper, we propose an energy-efficient virtual cell-based mobile-sink adaptive routing (VC-MAR) protocol for UWSNs. The sensing field is logically partitioned into a three-dimensional grid of virtual cells, where a cell-gateway is elected in each cell to construct a low-overhead routing backbone. To support sink mobility, VC-MAR introduces a localized route-adjustment mechanism that updates only the affected backbone segments rather than reconstructing the entire routing structure. By confining routing updates to neighboring cells influenced by sink movement, the proposed protocol significantly reduces control packet exchanges while ensuring stable and reliable data delivery. Simulation results show that the proposed VC-MAR improves the packet delivery ratio by up to 20% and reduces routing control overhead by about 34% compared with traditional grid-based routing methods. These results confirm the suitability of VC-MAR for dynamic and realistic underwater sensing scenarios.

1. Introduction

Underwater Wireless Sensor Networks (UWSNs) have become a promising enabling technology for several marine and oceanography applications [1,2]. It plays a crucial role in applications such as underwater environmental monitoring, marine biology support, offshore prospecting, disaster prevention, and resource exploration [3,4,5]. In such networks, sensor nodes are deployed at various depths to collect and transmit environmental parameters through acoustic communication links toward the sink node. The collected sensor data aids in both underwater exploration and decision-making [6,7,8,9]. Unlike terrestrial wireless sensor networks (WSNs), UWSNs work in a more challenging environment with high propagation delay and limited bandwidth. Moreover, these environments also suffer from signal attenuation and dynamic network structures caused by water currents. These unique characteristics make the design of efficient topology management and routing protocols a critical research challenge [10,11].

Reliable and efficient data transmission management strategies in a dynamic network state are among the foremost challenges in UWSNs. The nature of the three-dimensional (3D) deployment of nodes and their passive mobility results in frequent topology changes that can impair routing performance [12,13,14,15]. Further, acoustic communication-based routing updates lead to extra control overhead and route re-establishment, thus requiring high communication costs [16,17]. Therefore, the routing protocols developed for terrestrial network environments fail to give satisfactory performance in a realistic underwater environment [18].

To address these challenges, several typical routing protocols have been widely studied in UWSNs, including depth-based routing (DBR) [19], vector-based forwarding (VBF) [20], and flooding-based approaches, such as DFR [21]. DBR depends on node depth for packet forwarding, whereas DFR improves reliability through controlled flooding. To reduce redundancy, VBF limits transmission within a virtual pipeline. However, these approaches often suffer from high control overhead, increased energy consumption, and limited adaptability to dynamic underwater environments, particularly in mobile sink scenarios.

In addition to these conventional routing strategies, several grid-based and virtual cell-based routing approaches have been proposed to improve network scalability and reduce routing complexity in 3D UWSNs [22,23]. These approaches virtually divide the underwater field into cubic cells and rely on representative nodes as cell-heads or gateways, which are responsible for data forwarding in a cell-by-cell mode [24]. By mapping the physical topology onto a virtual grid, such approaches reduce the amount of routing state information and limit control message exchanges. However, the existing grid-based routing protocols generally exhibit improvements in energy efficiency and the packet delivery ratio [25], but most of them assume static or semi-static routing paths toward fixed sinks.

The introduction of mobile sinks in UWSNs has been considered an effective strategy to reduce routing traffic congestion, prevent the energy-hole problem, and extend network lifetime [26,27]. However, exploiting a mobile sink in a grid-based infrastructure raises new challenges. Many existing solutions either restrict mobile sink movement to predefined trajectories or rely on global route reconstruction when the sink changes its position within the sensing field [28,29,30]. Such solutions raise the communication cost by increasing the exchange of control packets, which may disrupt ongoing data transmission. Therefore, a trade-off between a routing protocol that efficiently supports mobile sink movement while preserving the utility of virtual cell-based topology management is crucial. Motivated by these observations, this work develops an efficient virtual cell-based mobile-sink adaptive routing (VC-MAR) protocol for underwater wireless sensor networks. In VC-MAR, instead of reconstructing global routing paths or depending on predefined routes, the proposed protocol restricts routing updates to only the cells affected by sink movement. This localized behavior allows the network to respond rapidly to sink mobility with minimal communication overhead. As a result, routing flexibility is improved and stable data forwarding is maintained, even under dynamic underwater conditions. The main contributions of this work are summarized as follows:

• Introduces a virtual cell–based routing adjustment mechanism that utilizes face-adjacent cell correlations to adaptively update routing paths in response to sink mobility, which significantly reduces control overhead and convergence delay.
• Introduces a detecting cell-gateway-based sink discovery and validation mechanism that reduces routing adjustment updates and conserves energy.
• Develops a loop-free backtrack and forward-path optimization strategy that maintains stable data delivery and routing consistency as the mobility of the sink across the sensing field.
• Simplify routing decisions and improve network scalability by restricting routing interactions to face-adjacent neighboring cells within a 3D virtual grid.

The remainder of this paper is organized as follows. Section 2 reviews related works on grid-based routing and topology management in UWSNs. Section 3 presents the system model and assumptions. Section 4 describes the proposed virtual cell-based topology management and adaptive routing protocol, while Section 5 details the simulation settings and evaluates the performance of the proposed protocol through simulation with comparative analysis. Finally, Section 6 concludes this paper and outlines directions for future research.

2. Related Works

In Underwater Wireless Sensor Networks (UWSNs), there is a significant literature on routing and communication protocols with special focus on network topology design to overcome the tough underwater conditions [31,32,33]. To support routing decisions and extend network scalability, structured routing topologies, such as grid-based and geographic approaches, have been developed in many studies [34,35]. In this section, we survey grid-based and geographic routing protocols, highlighting their design and restrictions. The main variations among these protocols in terms of network model, routing strategy, and adaptability features are highlighted in

Table 1. Comparative summary of representative routing protocols for UWSNs.

Protocol	Routing Structure	3D Grid	Route Adaptation	Energy/Load Aware	Mobile Sink
GARP	Grid-based geographic	✓	Predefined paths	✗	✗
MGGR	Grid-based multipath	✓	Path switching	✓	✗
EMGGR	Grid-based multipath	✓	Gateway-based	✓	✗
EEGBRP	Grid-based, TOPSIS	✓	Semi-static	✓	✗
GBPR	Grid-based priority	✓	Priority-based	✓	✗
ERGR-EMHC	Grid-based, hop-based	✓	Limited	✓	✗
RQAR	Location-free QoS-aware	✗	Dynamic	✓	✓
EERBCR	Region-based cooperative	✗	Limited (predefined zones)	✓	✓
DIEER	Depth-based + adaptive routing	✗	Moderate (threshold-based)	✓	✓
DNC-MPRP	Clustering-based routing	✗	Limited (mobility pattern-based)	✓	✓
EERSDRA-GCOP	Region-based opportunistic	✗	Moderate (metric-based)	✓	✓
OCNTMS	Clustering + trajectory planning	✗	Limited (pre-planned paths)	✓	✓
Proposed VC-MAR	Grid-based adaptive routing	✓	Dynamic local adjustment	✓	✓

.

In [36], a Grid-based Adaptive Routing Protocol (GARP) was prepared for 3D UWSNs. In this work, the network was shaped as a virtual cubic grid. To obtain high routing accuracy, it relied on multiple cell–disjoint paths between the source and destination cells. Packets were forwarded along constructed routing vectors. The GARP moved to an alternative cell–disjoint path without path detection or maintenance overhead when a path became unavailable. The results showed that when the network density attained a minimum number of nodes per cell, GARP could obtain a high packet delivery ratio. However, GARP depended on predetermined routing paths, which do not uphold continuous network topology changes within the 3D sensing area.

Multipath Grid-Based Geographic Routing (MGGR) protocol for UWSNs was proposed in [37]. The MGGR arranged the network into similarly sized 3D grid cells and implemented packet forwarding cell-by-cell, utilizing various disjoint paths. Gateway nodes were selected within each cell to forward data toward a static surface sink. In contrast, standby paths were utilized to address empty cells and routing defeat. For gateway updates and path selection, the MGGR used a lightweight control mechanism. In parallel with present routing schemes, results showed that MGGR obtained improved energy efficiency, packet delivery ratio, and end-to-end delay. Despite its performance in a fixed-grid structure, MGGR lacked an explicit energy-aware mechanism in gateway selection, which could lead to uneven energy consumption and raise the issues of void holes in the routing path.

An Energy-Efficient Multipath Grid-Based Geographic Routing (EMGGR) protocol for UWSNs was proposed by the authors of [38], which extended the MGGR protocol. The network was shaped as a logical 3D grid, with data forwarded cell-by-cell via selection gateway nodes. EMGGR combined a gateway-selection mechanism that depended on node location and residual energy with an update process for neighbor gateway information. The protocol formed disjoint routing paths and contained a mechanism to treat routing holes raised by empty cells. Simulation results employing Aqua-Sim showed that EMGGR obtained improved energy efficiency, and it preserved a high packet delivery ratio. However, the EMGGR still encountered issues related to grid maintenance in highly dynamic underwater environments.

In [39], the authors proposed an Energy-Efficient Grid-Based Routing Protocol (EEGBRP) for UWSNs that integrated 3D cell division and the TOPSIS technique. The network was divided into cubic cells, and cell heads were selected at each cell. Then, multi-hop routing was formed among sensor nodes. In contrast to previous protocols, such as EMGGR, EEGBRP enhanced energy consumption through utilizing a grid-based multi-hop routing structure with TOPSIS-based gateway selection. The computational overhead of the TOPSIS mechanism increased processing complexity at the sensor node level.

A Grid-Based Priority Routing (GBPR) protocol for UWSNs was proposed in [40], which contributed a 3D logical grid structure. Data packets were forwarded via selected cell heads based on a priority-based forwarding mechanism, with neighboring cells distributed across several preference levels depending on their distances from the sink. Cells closer to the sink were given a higher preference, which reduced hop count and energy consumption. This indicates the efficiency of preference-based forwarding in 3D grid-based UWSNs using GBPR. However, the GBPR depended on node localization, which is challenging to obtain accurately in underwater environments due to the limitations of acoustic localization.

The authors in [41] proposed an efficient and reliable grid-based routing protocol (ERGR-EMHC) for UWSNs, which utilized a 3D logical cell grid and cell head nodes for packet forwarding. The ERGR-EMHC ranked neighboring cells based on the minimum hop count. Moreover, a void-handling mechanism for addressing communication voids was included. By promoting neighbor classification, forwarding efficiency, and accuracy, this protocol expanded the previous GBPR protocol. The performance of ERGR-EMHC might degrade in very sparse networks, where maintaining multiple tables for sink, neighbors, and packets introduces processing overhead.

A location-free Reliable and QoS-Aware Routing (RQAR) protocol for mobile-sink UWSNs was proposed to address accuracy and QoS affronts in tough underwater environments [42]. The RQAR used the TOPSIS multi-criteria decision-making technique to select next-hop nodes without ordering location information. To promote credible data delivery and QoS support, various parameters were considered, such as link quality, hop count, congestion level, and residual energy. RQAR raised the transmission range and preserved communication consistency to alleviate routing holes. The stimulation results showed improved packet delivery ratios and higher network throughput. The RQAR protocol improved the quality of service, but it required periodic updates for network parameters, which could increase control overhead, especially under mobility sink scenarios.

In addition to these grid-based and QoS-oriented approaches, several recent works have considered mobile sink scenarios in UWSNs. For instance, EERBCR [43] used multiple sinks moving across predefined regions, where nodes switched between sleep and active states to reduce energy consumption. DIEER [44] focused on delay-sensitive applications by combining depth-based adaptation with data aggregation and hold-forward mechanisms. DNC-MPRP [45] followed a clustering approach supported by predefined mobility patterns, while EERSDRA-GCOP [46] relied on region-based routing with opportunistic forwarding. More recently, OCNTMS [47] explored clustering and trajectory planning for mobile sinks under non-uniform traffic conditions.

In spite of these approaches, which have improved performance in different ways, many of them still depend on predefined movement patterns or relatively complex designs. This could limit their flexibility in highly dynamic 3D environments. In contrast, the proposed VC-MAR adopts a simpler and more localized routing strategy. It can better adapt to continuous sink movement.

3. System Model and Assumptions

This section outlines the network architecture, system assumptions, communication, and energy model for the design and assessment of the proposed virtual cell-based topology management and adaptive routing protocol (VC-MAR) for UWSNs. The key requirements considered in this research work are summarized below.

3.1. Network Architecture and System Assumptions

To simplify the design and analysis of the VC-MAR routing protocol, we assume a three-dimensional (3D) UWSN comprises sensor nodes that are homogeneous and randomly deployed at various depths in the surveillance fields. These nodes are responsible for sensing environmental data and forwarding it to the sink via a multi-hop acoustic communication channel. The network is divided into a series of virtual cubic cells that collectively form a 3D grid structure. A single node is dynamically elected as the cell-gateway (CG) in each virtual cell to manage inter-cell data forwarding. The mobile sink periodically moves within the 3D sensing area to gather data, and it has a random but restricted mobility pattern. The sink movement is not restricted to the area boundaries and does not guarantee that all cells are visited in each round. In contrast to underwater sensor nodes, the sink is supposed to have enough energy resources and long communication capabilities. To ensure efficient multi-hop data delivery and avoid unnecessary energy consumption, routing paths are partially and dynamically updated to invert the sink’s final station.

3.2. Communication and Energy Model

The essential means of data transmission between sensor nodes is supposed to be underwater acoustic communication. Due to the characteristics of underwater acoustic channels, energy consumption becomes a critical design factor, as it is influenced by channel characteristics such as attenuation, propagation delay, and potential interference. All sensor nodes are treated as homogeneous with respect to initial energy, transmission capabilities, and hardware configuration. Energy consumption at each node is related to packet transmission, packet reception, and idle listening situations. A standard underwater acoustic propagation model is utilized in this protocol to realistically hold transmission attenuation and energy usage. Moreover, the propagation model is based on a commonly used underwater acoustic attenuation approach that considers both distance and frequency. While interference is not explicitly modeled, its impact is indirectly captured through performance metrics such as the packet delivery ratio, delay, and energy consumption. Furthermore, communication is primarily restricted to nearby cell-gateways, which helps minimize unnecessary transmissions and reduces the likelihood of both intra-cell and inter-cell interference.

The acoustic path loss at distance d and frequency f is modeled as

$$A\left(d,f\right)=A_0{d}^k{a\left(f\right)}^d\dots$$

(1)

where A₀ is a normalization constant, k represents spherical spreading, and it is set to 2, which corresponds to ideal spherical spreading in underwater acoustic propagation, and (f) denotes the frequency-dependent absorption coefficient based on Thorp’s model [48].

The total energy consumption of a sensor node is defined as in Equation (2), the sum of energy consumed during transmission, reception, and idle states:

$${EC}_k(d,f)=(P_{0}A\left(d,f\right)+r+i_0)l_{tx}$$

(2)

where ${EC}_k$ is the total energy consumption for node k, $P_0$ is the power needed for transmitting across a distance unit, and $A\left(d,f\right)$ denotes the attenuation function that relies on the transmission distance d and the operating frequency f. The factor r represents the required energy per data unit reception, while $i_0$ is the energy consumed during idle processing. Finally, the $l_{tx}$refers to the size of the transmitted data packet.

The derived energy model is employed in the performance evaluation to assess energy depletion at nodes under different network conditions. Moreover, by restricting routing updates to a localized set of virtual cells, the proposed protocol aims to reduce transmissions and control overhead.

4. Detailed Description of Proposed VC-MAR Protocol

The proposed VC-MAR routing protocol adopts a virtual cell-based planning to effectively trace sink mobility in underwater wireless sensor networks. The monitored area is divided into a three-dimensional grid of uniform cubic cells. In each cell, an elected cell-gateway is responsible for managing local routing decisions. Data forwarding to the mobile sink is performed in a multi-hop (cell-by-cell) manner. The routing adjustment included only face-adjacent neighbors, which limits control packet overhead and preserves sensor energy. The protocol also introduces a localized route readjustment mechanism to provide accommodations for sink mobility. It dynamically updates routing paths as the sink moves across cells, without requiring global route reconstruction. By integrating a virtual 3D cell structure with sink detection, route validation, and localized path optimization, the proposed VC-MAR protocol ensures stable and loop-free data delivery even under harsh underwater conditions. The design details of the protocol are presented in the following subsections.

4.1. The Virtual 3D Structure Construction

A three-dimensional mobile sink UWSN network architecture is used in the proposed protocol. In such networks, nodes are scattered randomly across a 3D space at various depths, and their locations are unpredictable due to the effects of underwater currents. Therefore, each node i is assigned a random coordinate (x_i, y_i, or z_i) within the 3D region defined by (L × W × H). However, conventional clustering methods utilized in 2D WSNs do not fully translate to underwater areas. The network spans a full 3D volume, and depth plays a significant part in communication costs, delays, and energy consumption. If we tried to make one virtual cell per node (i.e., Ncells = Nnodes), the network would be highly partitioned and raise the probability of hotspot formations. To avoid these issues, in this protocol, we take on a 3D cubic division model that partitions the sensing area into a regular grid of cubic regions. In this work, the use of a virtual cell structure is not limited to energy considerations. It also provides a structured way to organize the network and support localized routing decisions in a scalable manner. Instead of having as many cells as nodes, we place a constant number of cubic divisions, determined by the optimal number of cell-gateways (CGs). To determine the optimal number of cells, and consequently the CGs, we adopt the heuristic inspired by the 2D grid-based clustering approaches described in [49,50], where approximately 5% of the nodes serve as cell-gateways. The underwater sensor area, which comprises N nodes, is divided into K regular cubic cells, each forming a virtual cell (cluster). One cell-gateway (CG) is selected per cell, resulting in a total of K cell-gateways. To achieve a regular 3D division, the value of K is selected as a perfect cube and is calculated as:

$$K={⌈\sqrt[3]{0.05\times N}⌉}^3$$

(3)

where N is the total number of sensor nodes. The term (N × 0.05) represents the target number of cell-gateways based on the adopted heuristic. While the cube root determines the number of divisions along each dimension. The ceiling function ensures an integer value, and cubing it results in a regular 3D grid structure.

Once the number of cubic divisions (K) is specified, the next step is to arrange the underwater region into a 3D grid. Since K is consistently selected as an ideal cube, the area can be partitioned equally along all 3D spatial dimensions.

The number of cells along each spatial dimension ($n_c$) is determined by taking the cube root of K. This provides the network with a balanced grid structure: n_c cubes in the X, Y, and Z directions. With this configuration, the full sensing volume is divided into regular cubic regions whose dimensions are calculated from the physical size of the surveillance area. In Equation (5), the edge length of each cube is determined:

$$d_{\alpha }={\displaystyle \frac{D_{\alpha }}{n_c}},\alpha ϵ〔x,y,z〕$$

(4)

where D_α is the dimension of the area, and n_c is the number of cells over each axis. These values include that each cell takes an equal share of the total environment. Each cubic region can be recognized as a triplet index. A node exists at specific coordinates (x, y, or z), and is assigned to its corresponding virtual cell utilizing the simple floor process as in Equation (6):

$$i_{\alpha }=\lfloor {\displaystyle \frac{x_{\alpha }}{d_{\alpha }}}\rfloor ,\alpha ϵ〔x,y,z〕$$

(5)

where i_α is the cell indicator over dimension α, and the node coordinate is x_α, while d_α represents the edge length of the cubic cell in that dimension.

This mapping is lightweight for underwater sensors with limited processing abilities. By utilizing such virtual mapping, the proposed VC-MAR protocol ensures that each node exists within a controlled cell-gateway. In turn, these contribute directly to reducing long-range transmissions and avoiding energy bottlenecks.

The proposed cell-based structure is used as a logical way to organize the network rather than a physical cellular system. The grid is mainly used to organize routing, where all nodes share the same underwater acoustic channel without using different communication technologies for inter-cell and intra-cell communication. Communication is kept between nearby cell-gateways, which reduces unnecessary transmissions and helps keep interference low. This also makes routing simpler and reduces control overhead, especially in dynamic 3D environments with a mobile sink.

4.2. Cell-Gateway Selection

One cell head is selected in each cell to coordinate local data gathering and share in routing decisions after dividing the underwater sensing area into regular cubic cells. This structure can efficiently manage communication and preserve scalability in the 3D underwater environment. The cell-gateway (CG) election operation first depends on the residual energy of sensor nodes. The essential point in UWSNs is that nodes with higher residual energy are selected to prevent early energy loss and extend the total network lifetime.

In addition to energy, the 3D Euclidean distance between each candidate node and the geometric center of its corresponding cubic cell is also rated. Electing a node closer to the cell center decreases intra-cluster communication distances for member nodes. For a sensor node i located at (x_i, y_i, or z_i) with residual energy E_i, the cell-gateway selection metric is defined as:

$$p_i=w_E{\displaystyle \frac{E_i}{E_{max}}}+w_D(1-{\displaystyle \frac{\sqrt{(x_i-x_c{)}^2+(y_i-y_c{)}^2+(z_i-z_c{)}^2}}{\frac{\sqrt{3}}{2}d}}),w_E+w_D=1$$

(6)

where w_E and w_D are weighting factors, E_max represents the initial maximum energy of a sensor node, and d is the edge length of the cubic cell. The (x_c, y_c, or z_c) denotes the geometric center of the corresponding cubic cell. In this work, both weights are set to w_E = 0.5 and w_D = 0.5 to give equal importance to residual energy and node position. This helps avoid selecting nodes that have high energy but are far from the cell center, or nodes that are well-positioned but have low energy. Then the cell-gateway (CG) for each cell is selected as:

$$Cell\_head=arg\underset{i\in c}{max}{p}_i$$

(7)

In the proposed VC-MAR protocol, the CG is selected by maximizing a weighted priority function. This function jointly considers normalized node energy and proximity to the center of the corresponding cubic cell. The VC-MAR creates a fully balanced virtual structure and provides a credible basis for the next 3D dynamic route adjustment modification operation in a mobile sink environment.

4.3. Dynamic Routes Adjustment in VC-MAR

The dynamic network topology is complex due to sink mobility across all locative dimensions in a 3D underwater environment. Routing mechanisms should adapt continuously while preserving energy efficiency. Flooding-based approaches are not effective; therefore, they are avoided. An efficient modification strategy for virtual cell-based mobile-sink adaptive routing (VC-MAR) is proposed to handle this concern. It works on a virtual cubic structure and depends on cell-gateway (CG) coordination. Only the CGs that specify the 3D virtual backbone are accountable for preserving and updating routing paths to the mobile sink. Unlike classic 2D WSNs, where the sink proceeds along the network border, the proposed protocol supposes a mobile sink that moves inside the 3D sensing area. This reflects a realistic underwater vehicle manner; it periodically gathers data and triggers localized routing updates only within the influent regions as the sink traverses the network.

Before specifying the step-by-step procedure for adjusting the route, it is essential to depict the neighborhood model adopted by the proposed 3D VC-MAR routing protocol. Each CG is enclosed geometrically by neighboring cells in all directions within the 3D virtual grid. Although a cubic cell has up to twenty-six neighboring cells when face-, edge-, and corner-adjacent cells are considered. The proposed protocol limits routing update propagation to only the six face-adjacent neighbors along the ±X, ±Y, and ±Z directions. This design option minimizes control overhead and energy consumption while maintaining efficient connectivity. Figure 1 describes the 3D neighborhood model and highlights the six face-adjacent neighbors utilized for routing updates.

The VC-MAR carries out route updates gradually, only where necessary, to address frequent modifications raised by sink mobility. Instead of rebuilding the forwarding routes, the protocol upgrades the current route by utilizing information from nearby virtual cells. This approach minimizes overhead and efficiently handles hold data forwarding. Depending on neighborhood structure, the dynamic route adjustment to the mobile sink can be achieved through a sequence of coordinated steps, as explained below.

Step 1: Initial Route Setup

After the cell-gateway selection and the formation of adjacencies, a primary routing structure is built, assuming a static first location of the mobile sink. In the 3D cubic grid, the number of adjacent CGs is determined by the cell’s position within the sensing area. A corner CG has at a maximum of three face-adjacent neighbors. But edge and surface CGs may have four or five neighbors. An internal CG can have up to six face-adjacent neighbors. Based on these adjacencies, the group of CGs creates a 3D virtual backbone structure that backs multi-hop data forwarding to the sink. Through the primary route setup phase, each CG elects its next-hop from among its face-adjacent neighbors, which its forwarding path gradually approaches the sink position. As shown in Figure 2, a connected and structured virtual backbone is determined across the 3D sensing area, serving as the routing array before sink mobility.

Step 2: Detection and Validation

The 3D network area is organized into virtual cubic cells, and the corresponding cell-gateway is responsible for detecting its presence and initiating the necessary routing update actions. When the mobile sink moves into a new cubic region, the corresponding CG is the initial node to discover its entity. Upon discovering the mobile sink presence, the CG checks whether the mobile sink is registered as its next-hop destination in the routing table. If the sink is registered as the next-hop, the current route residue is valid, and no routing update is started. This validation step is critical for reducing excessive control message propagation and saving energy. As shown in Figure 3, when the mobile sink moves into a new area of the sensing field and is detected for the first time, the discovering CG inspects the present routing entry to determine whether a route update is required.

Step 3: Immediate Update and Notification

If the mobile sink is recently discovered or has shifted from its previous position, the detecting cell-gateway updates its routing table, designating the sink as its next-hop. The CG that detects the presence of a mobile sink then distributes this information in a planned manner to relevant neighboring nodes. The update participates with the previous CG and with all face-adjacent neighbors of the current CGs. This localized notification strategy includes that only the influenced regions of the network are informed of the sink’s current location. This notification strategy avoids network flooding and minimizes communication overhead.

Step 4: Backtrack Adjustment

Upon receiving the sink position update from the current discovering CG, the past CG does a backtrack adjustment by updating its routing entry to forward data to the current discovering CG. The backtrack adjustment mechanism is explained in Figure 4. This warranty ensures that data packets follow the most modern and ideal path to the mobile sink. When the routing topology is heavily influenced, this adjustment may propagate further over the main data forwarding path, but only to nodes that need route recalibration.

Step 5: Forward Path Optimization

As the mobile sink position update propagates through the current detecting CG, each receiving CG verifies whether its present next-hop is set to the notifying CG. The update is skipped by the receiving CG to avoid unnecessary control packet transmissions when its next-hop is already set to the detecting CG. Otherwise, the neighboring CG updates its routing table and forwards the update to its own face-adjacent neighbors. These forwarding operations continue until all influenced nodes in the 3D grid have their routes to the mobile sink’s latest location.

Through this controlled route adjustment mechanism, the proposed VC-MAR protocol efficiently adapts to sink mobility while reducing communication overhead. To provide a clear overview of the dynamic route adjustment process, the workflow of the proposed VC-MAR protocol is illustrated in Figure 5.

The complete procedure, which includes the initial route setup and the subsequent steps for dynamic route adjustment in response to the mobile sink movement, is briefly outlined in Algorithm 1.

Algorithm 1: Dynamic Route Adjustment in VC-MAR

Input: Deployed sensor nodes, mobile sink (MS) Output: Efficient routing paths toward MS

Initialization:

Partition the 3D sensing field into uniform cubic cells and assign one cell-gateway per cell.

1. Establish face-adjacent neighborhood relationships among all cell-gateways.

2. Assume an initial static position of the mobile sink (MS) within the sensing field.

3. Each CG initializes its routing table by selecting a face-adjacent CG as its Next_Hop toward the MS.

4. The set of cell-gateways collectively forms a connected 3D virtual backbone.

MS Trigger: (MS is detected in a new cubic region)

5. A cell-gateway detects the presence of the MS.

6. The detecting cell-gateway is designated as the detecting cell-gateway (DCG).

7. If DCG.Next_Hop ≠ MS then

8.  Set DCG.Next_Hop ← MS.

Backtrack Adjustment:

9. If a previous detecting cell-gateway (Prev_DCG) exists then

10.  Set Prev_DCG.Next_Hop ← DCG.

Forward Notification:

11. For each face-adjacent neighboring cell-gateway (NCG) of DCG do

12.   If NCG.Next_Hop ≠ DCG then

13.     Set NCG.Next_Hop ← DCG.

14.     Invoke Propagate_Update (DCG).

15.   Else

16.    Terminate the update process (current route remains valid).

Propagate_Update (Current_CG):

17. For each face-adjacent downstream cell-gateway FCG ϵ neighbor (Current_CG) do

18.   If FCG.Next_Hop ≠ Current_CG then

19.    Set FCG.Next_Hop ← Current_CG.

20.    Invoke Propagate_Update (FCG).

21.   Else

22.    Drop the update message (route already optimal).

23. End.

5. Simulations and Results

The execution of the proposed VC-MAR through overall simulations is evaluated in this section. This section assesses the performance of the proposed VC-MAR through conducting a comprehensive simulation test. Simulations are performed to validate the proposed routing protocol in handling mobile sink movement and adaptive route adjustment mechanisms in 3D UWSNs. To ensure an unbiased comparison, all simulation results are performed under similar environmental and network situations.

5.1. Simulation Setup

The simulations are performed utilizing a MATLAB (R2024a)-based simulator to model underwater-acoustic communication patterns with a 3D network deployment. To act as a realistic underwater monitoring volume, sensor nodes are randomly deployed in a 3D underwater sensing area of (900 × 900 × 900 m³). The number of sensor nodes ranges from 500 to 1000. Each sensor node is supposed to be homogeneous in its primary energy and communication abilities. The sink follows a random and constrained 3D mobility pattern simultaneously. Underwater communication depends on an acoustic channel pattern with a bandwidth of 10 kbps. All nodes use the same underwater acoustic channel. Although interference is not explicitly considered, its impact can be observed indirectly through metrics such as the packet delivery ratio (PDR), delay, and energy consumption. The data and control packet sizes are adjusted to 128 and 32 bytes. The nodes communicate utilizing a broadcast MAC protocol over radio waves.

The simulation parameters are chosen based on common settings in the literature and the characteristics of underwater sensor networks. The network size and node density are set to reflect realistic 3D deployment conditions, while communication parameters, such as bandwidth and packet sizes, follow typical underwater acoustic constraints. Energy values are selected to support continuous operation and allow fair comparison. Some parameters are also adjusted through initial simulations to ensure stable and reliable results.

Table 2. Simulation parameters.

Simulation Parameter	Value	Description
Deployment area	900 × 900 × 900 m3	Represents a realistic underwater sensing environment
Number of sensor nodes	500–1000	Evaluates scalability under varying node density
Number of sinks	1 mobile	Considers a single mobile sink with unlimited energy
Deployment model	Random 3D	Reflects realistic underwater node distribution
Channel model	Underwater acoustic channel [51]	Standard underwater transmission medium
Bandwidth	10 kbps	Typical limitation of underwater channels
Data packet size	128 bytes	Balanced between overhead and payload
Control packet size	32 bytes	Reduces routing overhead
Initial energy (sensor nodes)	25 J	Ensures sufficient energy for sustained network operation
Transmission power	1 J	Represents energy cost of acoustic transmission
Reception power	0.35 J	Represents the energy cost of packet reception
Idle power	5 mJ	Accounts for idle energy consumption
Packet generation rate	15–60 packets/s	Tests performance under varying traffic loads
Communication range	200 m	Reflects practical underwater communication range
Sensing range	40 m	Represents typical sensing capability
Sink mobility model	Random constrained 3D mobility	Simulates realistic sink movement
Number of simulation runs	10	Ensures statistical reliability

refers to the key simulation parameters and their settings, with a brief justification for their selection.

5.2. Performance Evaluation

In order to evaluate the efficiency of the proposed VC-MAR protocol, we conducted a comparison with two grid-based routing protocols, GARP and ERGR-EMHC. These protocols are adopted in this comparison because they share a common basis with the proposed protocol for 3D grid modeling and cell-based packet forwarding. Two simulation experience states were designed. In the first experience state, the sink velocity changes, while the node density is kept fixed at 1000 nodes. This test case shows the efficiency of the routing mechanism in adapting to the sink mobility, as shown in Figure 6. In the second experience state, to estimate the scalability of the proposed VC-MAR, the sink velocity remains constant, and the node density changes, as presented in Figure 7. The main performance metrics considered in this assessment are the routing control overhead, packet delivery ratio, structure construction cost, and average end-to-end delay. The results are averaged over 10 simulation runs, and the error bars represent the standard deviation, indicating stable performance.

The routing control overhead of GBPR, ERGR-EMHC, and the proposed VC-MAR, with different mobile sink velocities and a constant network size, is shown in Figure 6a. In this assessment, the overhead is the overall number of control packets transmitted, except data packets. When the sink velocity rises, all protocols exhibit a higher control overhead transmission due to more frequent route adjustments. The proposed VC-MAR shows high performance at higher mobility, achieving an overhead almost 34% lower than GBPR and about 26% lower than ERGR-EMHC at 20 m/s. Unlike GBPR and ERGR-EMHC, which depend on wide update propagation, VC-MAR takes a first step toward localizing the route adjustment mechanism to limit control message diffusion to only the influenced virtual cells.

The packet delivery ratio (PDR) of GBPR, ERGR-EMHC, and the proposed VC-MAR is compared under various mobile sink velocities in Figure 6b. Due to frequent additional route disconnections and increased packet loss during topology modification, the PDR of all protocols progressively reduces as the sink velocity grows. GBPR is the most affected because it depends on a priority-based forwarding mechanism, which requires frequent neighbor reassessment. ERGR-EMHC obtains enhanced consistency compared with the GBPR protocol through using lower-hop-count forwarding. However, its periodic updates may still lead to transitory delivery obstruction. In contrast, the proposed VC-MAR preserves the efficient PDR through all sink mobility levels by imposing route adjustments to the influenced virtual cells only. VC-MAR improves PDR by up to 20% compared with GBPR and by 8% compared with ERGR-EMHC at maximum sink velocities. This explains its robustness for a dynamic underwater environment.

The overall construction costs of GBPR, ERGR-EMHC, and the proposed VC-MAR are assessed in Figure 6c. In this assessment, the construction cost is the energy used by sensor nodes in forming and maintaining the virtual 3D cell and related route adjustments information. This comprises energy used for control packet transmission, reception, and idle listening. The energy cost for all protocols rises as sink velocity grows; this is due to frequent topology updates. The results reflect that the GBPR protocol has the maximum cost for the route structure, while ERGR-EMHC obtains adequate savings. On the other hand, the proposed VC-MAR minimizes route construction cost by 37% compared with GBPR and by 25% compared with ERGR-EMHC. This achievement is enabled by VC-MAR’s localized route adjustment mechanism, which reduces control message dispersion to only the influenced virtual cells.

The average delay for the compared protocols is demonstrated in Figure 6d. Generally, the delay increases as network dynamics intensify, and more frequent route updates are required due to sink movement. The GBPR shows the maximum delay as the sink mobility increases. This returns to the adopted mechanism in repeated priority evaluations and control packet transmission. With hop-count-based forwarding, EGR-DMHC exhibits less delay compared with GBPR, but periodic route maintenance still adds latency. In contrast, the proposed VC-MAR keeps the minimum delay by limiting route adjustments to the influenced virtual cells. This becomes rapid data forwarding and minimizes needless processing.

In the second experiment case, the node density ranges from 500 to 1000 nodes, and the sink velocity is fixed to assess the scalability of the proposed protocol across various network simulation test cases.

In Figure 7a, the results show direct proportionality of the control packet overhead with node density across all assessed protocols. This is due to more nodes involved in routing communication and forwarder path maintenance. However, the proposed VC-MAR shows the minimum overhead across all densities. In contrast to GBPR, VC-MAR decreases control overhead by 31% while obtaining a 20% improvement over ERGR-EMHC as the network size increases from 500 to 1000 nodes. This outperforms VC-MAR’s localized route adjustment strategy, which limits control message dissemination to influence virtual cells to sink movement rather than depending on periodic or network-wide updates. These results assure that in dense underwater sensor deployments, VC-MAR shows outstanding scalability and efficiency in control packet exchange.

Figure 7b exhibits the packet delivery ratio (PDR) for GBPR, ERGR-EMHC, and the proposed VC-MAR. Due to promoted connectivity and the availability of various forwarding paths, the PDR increases across all protocols as node density grows. In dense underwater sensor networks, the proposed VC-MAR achieves the maximum PDR by enabling localized route adjustment within virtual cells, which decreases packet drops. The VC-MAR progresses PDR by 11% compared with GBPR and 4% compared with ERGR-EMHC at higher densities.

The total cost for route construction is presented in Figure 7c. Due to the growth in control messaging and coordination overhead, overall energy consumption increases during backbone route construction for all protocols. However, the VC-MAR minimizes construction costs by limiting topology updates to only influential virtual cells. The proposed VC-MAR decreases the construction costs by 35% compared with GBPR and by 27% compared with ERGR-EMHC at high network density.

Figure 7d demonstrates the effect of node density on the average delay for the proposed VC-MAR, GBPR, and ERGR-EMHC protocols. The proposed VC-MAR keeps the minimum delay, decreasing it by 35% compared with GBPR and by 23% compared with ERGR-EMHC. This is due to its localized virtual cell routing, which decreases the route reconfiguration overhead.

6. Conclusions

This paper establishes bounds for routing adjustment in sensor networks with mobile sinks. An effective virtual cell-based topology management and adaptive routing protocol (VC-MAR) is developed to handle mobile sink movement in a dynamic UWSN. The adopted virtual cell frame supplies a stable platform that extends topology management and efficiently forwards data. It enables localized and adaptive route adjustments to face-adjacent neighbors in response to sink mobility while avoiding costly global route reconstruction and reducing control overhead communication. Unlike traditional grid-based routing protocols that depend on static paths, the proposed VC-MAR integrates initial sink discovery, validation, localized notification, backtrack adjustment, and forward path optimization to maintain stable and efficient data forwarding paths under dynamic conditions. These properties ensure that the proposed VC-MAR protocol can adapt to sink movement without interrupting ongoing data transmission or wasting excessive energy. In the presence of mobile sinks and dynamic network conditions, the simulation outcome reveals that the proposed protocol outperforms conventional grid-based routing protocols by reducing control traffic overhead, stable routing performance, and low average delay. Recent mobile sink approaches in UWSNs often rely on predefined movement or complex designs, whereas VC-MAR provides a simpler and more adaptive solution for dynamic 3D environments. Future work will focus on prolonging the proposed protocol to support multiple mobile sinks and combining real-time traffic awareness with validation executions across a large-scale deployment network.