Mobility-Assisted Digital Twin Network Optimization over Industrial Internet of Things

Abstract

Many real-world networks for the Industrial Internet of Things (IIoT) have diverse connectivity characteristics and real-time constraints imposed by industrial processing. In the context of digital twin networks (DTNs), a large number of IIoT devices may access the network and have a tremendous volume of data. A crucial element of these IIoT devices is mobility, which cannot be effectively solved because the number of IIoT devices connected is extremely large. IIoT devices in DTNs suffer from poor data transmission and link quality because of their mobility. In this paper, device-to-device (D2D) communication-based mobility-assisted digital twin networks are proposed, where edge computing is introduced to design an efficient mapping between the physical and virtual space. Then, we propose the architecture of data transmission for the D2D network to maximize the data rate for reliable connectivity among multiple mobile nodes based on IIoT. A Markov decision process (MDP) is formulated to maximize the data rate for multiple mobile nodes while maintaining the D2D communication link quality. The simulation results demonstrate the superiority of the proposed scheme over other comparable models.

1. Introduction

The evolution of information and communication technology has introduced various emerging technologies, such as the Industrial Internet of Things (IIoT), into smart factories [1]. In the context of intelligent manufacturing for smart factories, the application of IIoT-based devices has given many advantages including operation, scalability, and reliability [2]. Intelligent manufacturing should guarantee re-configurable manufacturing units and production lines for data acquisition because a lot of data are generated from IIoT-based devices and collected to use for real-time operation management [3]. The IIoT integrates a wide variety of devices, including sensors, actuators, and robots, into industrial environments, generating a massive amount of real-time data [4]. These devices must support stringent requirements for timeliness and reliability to ensure efficient and intelligent operations within smart factories [5]. However, the mobility of these devices introduces additional challenges, such as unstable routing and frequent handoffs, which must be addressed to maintain reliable communication and data transmission.

Digital twins (DTs) can be deployed to improve the monitoring and control of physical systems for the intelligent factory [6]. A DT is a network system that distributes functions and wireless connectivity between smart physical devices, providing sensing and actuating. Furthermore, the DT paradigm is proposed to connect physical machines with virtual systems to optimize manufacturing processes and is a state-of-the-art Industry 4.0 revolution facilitated by advanced data analytics and IIoT connectivity. Furthermore, a digital twin network (DTN) is an emerging network that uses DT technology to design the virtual twins of physical objects [7]. A DTN is defined as a virtual representation of a physical network that can analyze, simulate, and control the physical network based on data and models to establish an efficient mapping between the IIoT and digital systems [8]. A DTN models a group of devices with multiple interactions and allows network operators to design network optimization solutions.

The stochastic communication latency and the continuously growing data in the IIoT network make it hard for edge servers to collect and analyze data, including the channel state information, from IIoT devices [9]. IIoT networks also bring a lot of challenges to be solved, such as mobility issues. Although mobility is a critical feature of IIoT devices, current research on IIoT routing cannot effectively support the mobility issues in intelligent manufacturing systems because the number of IIoT devices connected is extremely large [10]. With such a tremendous number of IIoT devices, a lot of data are generated and transmitted in the network systems, and then, it is easy for congestion to happen, which may significantly affect the network performance. The mobility of IIoT devices exacerbates network congestion and introduces frequent changes in topology, leading to difficulties in maintaining stable communication [11]. These challenges require the development of new frameworks to ensure real-time communication and reliable data transmission in dynamic industrial environments [12]. Therefore, resource allocation for mobile devices is necessary to support real-time communication [13]. To address these challenges, e.g., computing is leveraged to reduce communication latency by processing data closer to the source rather than relying on centralized cloud services. This approach not only improves real-time decision making but also enhances scalability by distributing the computational load across multiple edge servers.

Device-to-device (D2D) communication enables IIoT devices to support sensing and collecting data. Collected data from different mobile devices can improve quality management, product planning, and resource prediction for manufacturing cells. Therefore, the mobility problem can be solved using D2D communication between IIoT devices. In D2D communication, devices can directly communicate between two nearby devices without routing data through a base station (BS). Compared with traditional communication methods, D2D communication can offer higher communication quality for the physical devices connected. In addition, D2D communication has been proposed for applications such as extending network coverage, offloading networks, D2D relaying, etc. [14]. Device relaying makes it possible for IIoT devices in a network to function as transmission relays for each other and configure a massive mesh network. In order to effectively implement D2D communication, several challenges must be addressed, such as service and peer discovery, resource allocation, mode selection, channel quality estimation, relay selection, and power usage [15,16]. Additionally, parameters like connectivity, link capacity, packet loss, delay, and throughput are all dependent on the temporal and spatial behavior of the mobile nodes.

In the D2D network communication system, mobile devices affect the network topologies, which are easily broken. To handle these problems, we propose an architecture of D2D communication with a Markov decision process (MDP) to design an efficient mapping between IIoT devices and network systems. In addition, we formulate the optimization of network connectivity as an MDP, which allows for dynamic decision making under uncertainty. By modeling the decision process of mobile nodes as an MDP, we derive policies that optimize data transmission rates and maintain link quality, adapting to the changing network environment in real time.

We address connectivity issues with a mobility-supporting data transmission scheme for the D2D network to maximize the data rate for reliable connectivity among multiple mobile robots. In the proposed scheme, we formulate the reliable connectivity problem in various connectivity environments to support mobility. Finally, we design an algorithm to derive an optimal solution. The main contributions of this paper are summarized as follows.

(1)

This paper introduces a novel connectivity construction framework for mobility-based D2D networks, specifically designed to maximize the data rate in dynamic industrial environments.

(2)

We propose a method to support mobility by maximizing the data rate while maintaining the number of D2D links between multiple mobile and relay nodes in a manufacturing system.

(3)

A Markov decision process (MDP) is employed to formulate the system model, and we derive the optimal policy for the D2D network. Additionally, we present an optimization algorithm using linear programming (LP) to achieve the optimal policy.

(4)

We conduct extensive performance evaluations of the proposed model across various environments, demonstrating its effectiveness in maintaining connectivity and maximizing data rates. Specifically, we show that the proposed model improves performance as the number of mobile nodes increases, achieving superior average data rates and link quality compared to existing methods.

The rest of this paper is organized as follows. Section 2 introduces related work about the D2D network for the IIoT. Section 3 presents our system model for DTNs. In Section 4, the MDP model is proposed and formulated in detail. Then, performance analysis and its results are explained in Section 5. Finally, the conclusions and future work are shown in Section 6.

2. Related Work

Many routing problem studies have been presented based on the IIoT [17,18,19,20]. Long et al. [17] proposed a routing scheme to enhance energy consumption and end-to-end delay for large-scale IIoT systems. The proposed system uses large-scale systems where data were acquired by various clusters from the sink, and data can be relayed to the destination on the optimal path. Naeem et al. [18] presented a software-defined network based on an analytical parallel routing framework to optimize multiconstrained QoS parameters in the IIoT and considered loss sensitivity, delay sensitivity, and jitter sensitivity for QoS applications in healthcare traffic. Yu et al. [19] proposed an intelligence-driven green resource allocation to guarantee high reliability for the IIoT based on 5G networks. Furthermore, a deep reinforcement learning algorithm was presented to solve an energy-efficient model within the framework in dynamic environments. Liang et al. [20] proposed a 5G-enabled intelligent IIoT system to support credible mobile vehicles with disseminated code and opportunistic routing. In the proposed framework, an optimization algorithm was presented to obtain the code waiting to be verified in the limited conditions from the selected devices. 5G networks for IIoT are expected to support a wide range of applications, such as robots, actuators, and many nodes. However, studies about IIoT resource allocation to solve routing problems have not supported mobile nodes. The real-time constraints caused by industrial environments make mobility support largely challenging. Thus, a novel framework supporting mobility features is needed for IIoT routing problems.

Mobility support mechanisms for the IIoT have been studied in the literature [21,22,23,24,25]. Farag et al. [21] introduced a reliable mobility-aware routing protocol to support mobile IIoT networks based on the quality of the link. This protocol utilizes a dynamic mobility detection mechanism with an adaptive timer to manage the transmission rate and energy consumption. Singh et al. [22] formulated a stochastic integer programming model for mobility-aware relay selection in 5G D2D networks and developed a distributed greedy metric to control packet loss and delay for the mobile nodes. Moreover, graph-based network-assisted and device-controlled relay selection algorithms were proposed. Zhao et al. [23] formulated a unified routing metric for industrial networks with dynamic connectivity and solved the adaptive routing problem using an integer linear programming optimization with static and dynamic network scenarios. Bello et al. [24] introduced software-defined networking (SDN) to manage transmission scheduling and node mobility in the IIoT, providing bounded end-to-end delays, and presented the detailed design of the forwarding and time-slotted channel-hopping scheduling over SDN with a real scenario. Orozco-Santos et al. [25] proposed mobile multicast forwarding with SDN, using an SDN solution protocol that exploits time-slotted channel-hopping synchronism in dynamic industrial environments. Furthermore, the proposed protocol managed energy consumption and quality of service with multicast scheduling for the mobile nodes.

The proliferation of IIoT devices causes massive data traffic, which is expected to affect the design of the 5G D2D communication system with ultra reliable low-latency communication (URLLC). 5G D2D network systems with resource allocation have been proposed in the literature [26,27,28,29,30]. Orsino et al. [26] considered a D2D system for a 5G IoT network and examined the effects of heterogeneous devices with mobility for the mission-critical machine-type communications within multiconnectivity. Sun et al. [27] proposed social-aware incentive mechanisms for D2D resource sharing in the IIoT. One-hop-based and relay-based mechanisms were introduced to achieve a higher resource utilization ratio while supporting truthfulness. Sarma et al. [28] formulated resource allocation for a 5G D2D network in an IIoT environment for minimizing interference and increasing the data rate. To optimize a D2D 5G network, a channel assignment and power optimization problem was proposed and simulation results were presented. Khoshnevisan et al. [29] investigated 5G networks for industrial factory automation to guarantee ultra reliable low-latency communication (URLLC) wireless communication and presented coordinated multipoint communication to support a time-sensitive network including time synchronization and quality of service (QoS) for 5G networks. Huang et al. [30] focused on how to coordinate multiple energy-harvesting mobile devices with limited battery capacity to execute computation tasks in D2D networks. Also, the proposed D2D network aimed to minimize the long-term system cost, which is defined as the weighted sum of the average latency of task processing, the number of dropped tasks, and the battery energy penalty.

Many real-world networks for IIoT applications have diverse connectivity characteristics that make routing protocols difficult. In the literature about mobility in IIoT environments, although routing protocols have been introduced with various scenarios, there is no mechanism to support a lot of mobile nodes and their link quality for a reliable and real-time-supported industrial environment. In our work, we have developed a MDP model for supporting mobility in the industrial environment. Our proposed model manages reliable connectivity with maximum data rate communication to maximize the data rate between IIoT devices. Furthermore, we present an algorithm to derive an optimal solution for the MDP model.

3. System Model

3.1. Digital Twin Networks

The proposed digital twin network (DTN) architecture consists of physical, digital twin, and edge layers, as shown in Figure 1. IIoT devices in the physical layer are mapped to the digital twin layer. Then, the connectivity construction framework is designed for time-sensitive applications to maximize the data rate communication in the edge layer. In a smart factory, mobile devices need to connect with each other frequently for real-time manufacturing systems. Time-constrained communication for handling devices in the manufacturing cells and logistics sectors is one of the important demands to avoid faults and improve overall manufacturing automation efficiency for a smart factory. Thus, reliable and connective communication among devices should be constructed to support mobility.

3.2. Communication Model

To assist communication between the mobile and relay nodes, D2D links are established, as in Figure 2. The physical layer consists of various types of IIoT devices, including industrial mobile robots and various machines. The relay nodes connected to the mobile node receive the sensing data and transmit them to the edge server. Then, the relay nodes can communicate with the edge server through wired communication to relay information or data. The edge server sets up DTNs for IIoT devices within its coverage area. In the edge layer, DTNs can construct a network, which mirrors the real physical network with the corresponding DT. Therefore, the DTs can communicate information with each other through inter-twin communication. In addition, interaction communication management enables real-time communication between a physical device and its corresponding DT. In this paper, we consider a network scenario consisting of a manufacturing cell. In the manufacturing cell, multiple mobile and relay nodes directly establish D2D links to transmit data to each other. To guarantee the channel quality of cellular links, the signal-to-interference plus noise ratio (SINR) between the mobile node and relay node must be bigger than the threshold k. We can obtain the SINR function, which can be defined as

$$\begin{array}{c}\hfill SINR={\displaystyle \frac{D^{-\alpha }·T·{\left|g\right|}^2}{{\sigma }^2+I}},\end{array}$$

(1)

where g is the channel response of the mobile node, ${\sigma }^2$ is the variance of the additive white Gaussian noise (AWGN), and T is the transmission power of the mobile node. I is the interference of the mobile node.

4. Markov Decision Process

We formulate an MDP model to maximize the data rate for the mobile node. The MDP is defined by five tuples: (1) decision epoch, (2) state space, (3) action space, (4) reward and constraint function, and (5) transition probability. In the MPD model, the mobile node is the agent. The important notation for the model is summarized in

Table 1. Summary of notation.

Notation	Description
S	State space
$S_t$	State at the decision epoch t
D	State for representing the distance between the mobile and the relay node
M	Memory buffer state space of the mobile node
A	Action space
$A_t$	Action chosen at the decision epoch t
g	Channel response of the mobile node
$\sigma$	Variance of the AWGN
T	Transmission power of the mobile node
I	Interference of the mobile node
$\gamma$	Iterations
B	Bandwidth
${\eta }_T$	Average data rate
${\eta }_C$	Average of the SINR
${\delta }_C$	Threshold of the constraint

.

4.1. Decision Epoch

The time epochs at which the agent makes successive decisions are $T=\{1,2,3\dots \}$. $S_t$ and $A_t$ represent the state and the action chosen at the decision epoch $t\in T$, respectively.

4.2. State Space

S is a state space of the mobile node. In the manufacturing cell, the mobile node connects to the relay node for the cellular link. The state space of the mobile node is defined as

$$\begin{array}{c}\hfill S=D\times M,\end{array}$$

(2)

where D is the distance between the mobile node and the relay node. M is the memory buffer state space of the mobile node, which can be represented as $M=\{0,1,\dots ,M_{max}\}$. The mobile node moves around the manufacturing cell and collects data, which can be stored in the memory buffer M.

4.3. Action Space

A is a local action space of the mobile node, which can be defined as

$$\begin{array}{c}\hfill A=\{0,1\},\end{array}$$

(3)

where $A=0$ means that the mobile node does not connect to the relay node, whereas $A=1$ represents that the mobile node connects to the relay node.

4.4. Constraint Function

To guarantee the channel quality of cellular links, the signal-to-interference plus noise ratio (SINR) between the mobile node and relay node must be bigger than the threshold k. We can obtain the constraint function C, which can be defined as

$$\begin{array}{c}\hfill C={\displaystyle \frac{D^{-\alpha }·T·{\left|g\right|}^2}{{\sigma }^2+I}},\end{array}$$

(4)

where g is the channel response of the mobile node. ${\sigma }^2$ is the variance of the additive white Gaussian noise (AWGN) and T is the transmission power of the mobile node. I is the interference of the mobile node.

4.5. Reward Function

We define the reward function R to maximize the sum data rate while satisfying the defined constraint. To calculate the data rate according to the SINR, we use a modified Shannon capacity formula [31]. The data rate of the mobile device can be denoted as

$$\begin{array}{c}\hfill R={\displaystyle \frac{1}{N}}\sum _{\gamma =1}^{N}Blo{g}_2(1+{\displaystyle \frac{D^{-\alpha }·T·{\left|g\right|}^2}{{\sigma }^2+I}})\end{array}$$

(5)

where $\gamma$ and B represent the number of iterations and the bandwidth of the mobile node, respectively.

4.6. Transition Probability

$P\left[S^{\prime }\right|S,A]$ is the probability of transition from the current state S to the next state $S^{\prime }$ when the mobile device chooses action A. The transition probability from the current state $S=[D,M,A$] to the next state $S^{\prime }=[D^{\prime },M^{\prime },A^{\prime }]$ can be denoted by

$$P\left[S^{\prime }\right|S,A]=P\left[D^{\prime }\right|D]\times P\left[M^{\prime }\right|M,A].$$

(6)

When the mobile device i has no connection to the relay node ($A=0$), data in the memory state space M do not decrease. On the other hand, data in the memory state space M decrease if the mobile device connects to the relay node. Therefore, the corresponding probabilities can be represented as

$$P\left[D^{\prime }\right|D,M,A=0]=\left\{\begin{array}{c}1,\mathrm{if}{M}^{\prime }=M\hfill \\ 0,\mathrm{otherwise}\hfill \end{array}\right.$$

(7)

and

$$P\left[M^{\prime }\right|D,M,A=1]=\left\{\begin{array}{c}1,\mathrm{if}{M}^{\prime }=M-1\hfill \\ 0,\mathrm{otherwise}.\hfill \end{array}\right.$$

(8)

4.7. Optimization Formulation

The average data rate can be defined as

$${\eta }_T=\underset{t\to \infty }{lim}sup{\displaystyle \frac{1}{t}}\sum _{t^{\prime }}^{t}E\left[R(S_{t^{\prime }},A_{t^{\prime }})\right],$$

(9)

where $S_{t^{\prime }}$ and $A_{t^{\prime }}$ are the global state and action at time t, respectively. In addition, sup represents the least upper bound.

Moreover, the average of the SINR for the D2D link is defined as

$${\eta }_C=\underset{t\to \infty }{lim}sup{\displaystyle \frac{1}{t}}\sum _{t^{\prime }}^{t}E\left[C(S_{t^{\prime }},A_{t^{\prime }})\right].$$

(10)

The MDP model can be defined as follows:

$$\underset{\pi }{max}{\eta }_T$$

(11)

$$\mathrm{s}.\mathrm{t}.{\eta }_C\le {\delta }_C$$

(12)

where $\pi$ is the policy that represents the probability of taking an action in a certain state. In addition, ${\delta }_C$ represents the threshold of the constraint. To acquire the optimal policy for the mobile node i, we formulate an optimization problem that can be represented by LP. $\theta (S_i,A_i)$ is the stationary probability of state S and action A. The LP model can be expressed as

$$\underset{\theta (S,A)}{max}\sum _S\sum _A\theta (S,A)r(S,A)$$

(13)

$$\mathrm{s}.\mathrm{t}.\sum _S\sum _A\theta (S,A)C(S,A)\le {\delta }_{max},$$

(14)

$$\sum _A\theta (S^{\prime },A)=\sum _S\sum _A\theta (S,A)P\left[S^{\prime }\right|S,A],$$

(15)

$$\sum _S\sum _A\theta (S^{\prime },A)=1,$$

(16)

and

$$\theta (S^{\prime },A)\ge 0.$$

(17)

The objective function in Equation (13) maximizes the sum data rate for the mobile node i. The constraint in Equation (14) maintains the number of D2D links between the mobile node i and the relay node. The constraint in Equation (15) satisfies the Chapman–Kolmogorov equation. The constraints in Equations (16) and (17) are for the probability properties. When the LP problem is feasible, the optimal policy of the mobile node i can be obtained as

$${\pi }^{*}(S,A)={\displaystyle \frac{{\theta }^{*}(S,A)}{{\sum }_{A^{\prime }}{\theta }^{*}(S,A^{\prime })}}.$$

(18)

4.8. Optimization Algorithm

The algorithm of the MDP can be applied to update the policy of the mobile node, as shown in Algorithm 1. Each mobile node initializes its policy and transmits its state S to the edge server. The edge server calculates the reward function R and the constraint function C for each mobile node. Then, the edge server solves the LP to derive the optimization solution. The results are inserted into A and sent to the mobile node. This process is repeated for all the mobile nodes until all the optimization solutions are acquired.

Algorithm 1 MDP algorithm

1: Initialize the policy for the agent   2: for S do   3:      $S=\left[get\right(D),get(M\left)\right]$   4:      $r(S,A)$ = RewardFunction()   5:      $c(S,A)=\left[getSINR\right]$   6:      Solve $R(S,A)$ and $C(S,A)$ by the LP   7:      $List.add\left[R\right(S,A\left)\right]$ // Add a result of the LP to $List$   8: end for   9:  $A^{*}=Solution\left(List\right)$ 10: for A do 11:      Send A to the agent // Send a result for ResourceAllocation 12: end for

5. Performance Evaluation

5.1. Experiments for D2D Link Connection

In this section, we evaluate the performance of the proposed system. The number of mobile nodes ranges from 1 to 5, and the number of relay nodes is 5. The mobile node and the relay node are set up in a single manufacturing cell measuring 50 m by 50 m. Each mobile node initially selects a random position and stays in that position for 10 s, then moves to another random position. The maximum distance between devices that establish direct D2D links ${\delta }_{max}$ is 30 m. All mobile nodes have a transmission power of 23 dBm. The carrier bandwidth is set to 180 kHz. The D2D path loss exponent $\alpha$ and the D2D path loss factor for a distance in meters are set to 4 and 0.0173, respectively. In addition, the noise power spectrum density is set to −174 dBm/Hz. The performance of the proposed system is evaluated under a dynamic environment based on the parameters shown in

Table 2. List of operation parameters.

Notation	Description
Deployment area	50 m × 50 m
Number of mobile nodes i	[2, 5]
Number of relay nodes	5
Max D2D link range ${\delta }_{max}$	30 m
Transmission power $\left(T\right)$	23 dBm
Bandwidth (B)	180 kHz
D2D path loss exponent $\left(\alpha \right)$	4
Noise power spectrum density	−174 dBM/Hz
D2D path loss factor for a distance in meters	0.0173

.

We compare our algorithm with two schemes: random and distance [32]. Random means that the core network randomly selects the relay node. Distance considers the shortest distance between the mobile node and the relay node.

5.2. Effect of Iterations

Figure 3, Figure 4 and Figure 5 show the average sum data rate and the average number of links obtained with different iterations for the mobile node. In each iteration, the number of mobile and relay nodes is set to five. Figure 3 shows the average sum data rate with respect to the number of iterations. It can be observed that each algorithm converges in more than 100 iterations. Furthermore, it is observed that the proposed model yields the highest sum data rate among the comparison models. This is because the mobile nodes are connected to the relay nodes with the highest data rate to maximize the data rate at each iteration. Figure 4 shows the average number of links for the mobile node with each iteration. Although the number of mobile nodes is set to five in each iteration, the average number of links is less than five. When the mobile node tries to connect to the relay node, it should satisfy the distance threshold being less than ${\delta }_{max}$. If the distance between the nodes cannot satisfy the distance threshold, they are not connected. Furthermore, the proposed model connects to as many relay nodes as possible to increase the data rate. Therefore, the proposed model shows the highest number of links. In the distance scheme, the average number of links is lowest because this model only connects to the relay node that is near the mobile node. Figure 5 shows the seconds required for convergence. For 100 iterations, the times of the proposed, random, and distance schemes are 12.43, 12.57, and 20.34 s, respectively. Our results show that the proposed model converges within a few seconds for up to 100 iterations or equal. For 10,000 iterations, the times required for the proposed, random, and distance are 241, 242.98, and 407.70 s, respectively. These results demonstrate that the proposed model can be applied to real environments without high overhead for calculating optimization problems on the edge layer (i.e., server).

5.3. Effect of the Number of Mobile Nodes

Figure 6 and Figure 7 show the effect of the number of mobile nodes on the average sum data rate and the average number of links, where each simulation corresponds to the average value of 10,000 iterations. Figure 6 shows the average sum data rate for the mobile node. It can be demonstrated that as the number of mobile nodes increases, the average sum data rate increases. However, the average sum data rate of the random and distance models increases slowly and is lower than that of the proposed model. This is because not all the mobile nodes are connected to the relay node, as shown in Figure 7. On the other side, the proposed model connects to as many of the relays as possible to maximize the data rate, as shown in Figure 7. Thus, the proposed model not only maximizes the data rate but also guarantees the quality of the link.

6. Conclusions

In this paper, we design a mobility support data transmission scheme for D2D networks in terms of data rate and link quality. In the proposed system, multiple mobile nodes move around for sensing and collecting data and relay data to the relay node by D2D communication. We formulate the proposed system using the stochastic game theory to support multiple mobile nodes and derive the Nash equilibrium. The evaluation results demonstrate that mobile nodes in the proposed system yield a high sum data rate and maintain the quality of the D2D link. Furthermore, the simulation results show the effectiveness of our proposed scheme compared to other methods. These results have significant implications for practical industrial environments. For example, in a smart factory setting, the proposed method could improve the reliability of data transmission between mobile robots and IIoT devices, reducing downtime and ensuring more consistent real-time communication. In addition, the ability to maintain a high data rate under varying network conditions directly supports the efficiency of data-intensive operations, such as predictive maintenance and real-time monitoring in industrial systems.

However, there are several limitations in the current study. First, while our simulation results show promising improvements, they are based on idealized scenarios that may not fully capture the complexities of real-world industrial environments. Factors such as unpredictable interference, hardware constraints, and real-time operational dynamics were not fully modeled in the simulations, and these factors could potentially affect the performance of the proposed scheme in practice. Additionally, our evaluation primarily focuses on performance metrics such as data rate and link quality, leaving room for further investigation of other important parameters like energy efficiency, scalability under varying network sizes, and security aspects of D2D communication.

In future work, more extensive real-world testing and practical comparisons are proposed. We will improve our approach based on real-life feedback and further demonstrate the effectiveness of the proposed method in dynamic industrial environments. Furthermore, energy consumption can significantly affect long-term sustainability and performance. Thus, we will expand our study to address energy use more comprehensively. We will explore energy-efficient communication protocols and optimization strategies that reduce power consumption while maintaining high data rates and reliable connectivity.