# A Real-Time Data Delivery for Mobile Sinks Group on Mobile Cyber-Physical Systems
## 1 Introduction  
As Cyber-Physical Systems (CPS) are collectively a technology for managing systems that interlink real-world assets, such as various sensors and actuators, with computing power in the information world [1], and it has recently become a key research area in industry, which utilized in various applications such as smart factory, digital manufacturing, and digital twin [2]. For example, CPS exploit sufficient computing resources to process information that has not been addressed in the physical world in the past to promote economic benefits such as improved energy efficiency and productivity in the industry [3]. In addition, by transferring the experimental environment of the physical world to the virtual world, various prototypes could be tested in the virtual environment in advance as performing error diagnosis, predictive maintenance, and product performance measurement very efficiently [4]. Nowadays, with the development of pervasive mobile devices, Mobile Cyber-Physical Systems (MCPS) have attracted more and more attention. MCPS have extended the application domains by exploiting the advantages of CPS through mobile devices [5]. In other words, MCPS could embrace not only CPS, which mainly deal with static equipment and stable networks, but also a network consisting of a number of mobile devices, such as vehicle networks. As the networks with mobile devices are unstable, unlike the networks assumed by the CPS, and the computing power of each mobile device is very different, many studies have been proposed from various aspects for their efficient cooperation. In particular, the timeliness of the data is very important because delay and failures due to bottlenecks, etc., which could be caused by variable network environments, adversely affect the entire system [6,7]. In addition, the various mobile equipment and groups of workers (Mobile Sink Groups (MSG)) performing the collaboration should be able to receive data within a valid time because they must be operated in a mutually collaborative manner. In the past, the spatiotemporal approach was exploited for real-time data transmission [8,9]. The spatiotemporal approach forwards data with the required delivery speed. The end-to-end delay is proportional to the distance between the devices. By maintaining the delivery speed across the network, this approach could provide a predictable real-time service according to the distance. For multihop communication, each node selects one node among its neighbor nodes, which has faster delivery speed than the required delivery speed. To apply the spatiotemporal approach, per-hop data forwarding requires the delivery speed, the coordinates of the specific destination, and the progress to the destination by each of the 1-hop neighbor nodes. This traditional spatiotemporal approach has been able to successfully transmit data for individual mobile sinks through virtual infrastructure; however, data dissemination to a group of mobile sinks causes duplicated location management of all sinks and duplicated data delivery to all sinks. Therefore, the group mobility support scheme, divided into two steps, has been proposed: member information gathering and data forwarding to group members [10, 11, 12]. Typically, a leader gathers the location of member sinks and reports the representative location of the group (i.e., center point and radius) as the location information of each members might be changed frequently. After gathering, M-Geocasting [10] causes data packets to be flooded into the region (a circle) for active data delivery. In [10], a source node sends its data toward the center point of the movable area of a group. Once one of the boundary nodes gets the data, it starts flooding them only in the area. Flooding data could reduce the cost for trivial movement of sinks within the region. The authors of [11] exploit the internal movement of each member sink. They put data in a virtual rectangular area passing the center point of the group so that member sinks passively get the data when the sinks encounter the area.