# Mobility-Assisted Digital Twin Network Optimization over Industrial Internet of Things
## 2 Related Work  
Many routing problem studies have been presented based on the IIoT [17; 18; 19; 20]. [PERSON] 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. [PERSON] 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. [PERSON] 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. [PERSON] 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]. [PERSON] 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. [PERSON] 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. [PERSON] 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. [PERSON] 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. [PERSON] 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-latencycommunication (URLLC). 5G D2D network systems with resource allocation have been proposed in the literature [26; 27; 28; 29; 30]. [PERSON] 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. [PERSON] 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. [PERSON] et al.