# Mobility-Assisted Digital Twin Network Optimization over Industrial Internet of Things
## 1 Introduction
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.