## 3 Mobility Support Scheme Based on Decision Tree-Based Pattern Classification and Regression
### Graph Construction and Resource Allocation Based on Predicted Mobility Pattern  
In this section, we describe how to construct a graph for the mobile device and allocate resources according to the mobility pattern predicted in Section 3.1 above. However, the main idea of this paper is to construct a separate graph and allocate each resource according to the mobility pattern and cycle of the mobile device. Therefore, we focus on the graph construction and resource allocation results when the proposed scheme is applied to the scheme of [21], which is one of the representative graph construction and resource allocation schemes in WirelessHART. Figure 8 shows the examples of the network topology for each cycle and the corresponding uplink graph when the proposed scheme is applied to [21]. First, assume that device 6 in Figure 8 is a mobile device and travels close to devices 1, 2, and 3 as shown in Figure 8a. At this time, Figure 8b shows a graph for communication with device 1, Figure 8c shows a graph for communication with device 2, and Figure 8d shows a graph for communication with device 3. The initial mobile device, device 6, joined the network through a join process near devices 3 and 4, as shown in Figure 8a, and moved along a black solid line at regular intervals. Based on the results learned in Section 3.1 above, the network manager knows that the devices used by the mobile device for communication are device 1, device 2, and device 3, and knows when they are connected to each device. Therefore, at the time of TS 0, TS 400, and TS 800, a graph (Figure 8a) is generated to be used for communication with device 1. At the time of TS 100, TS 300, TS 500, TS 700, TS 900, and TS 1100, a graph (Figure 8c) is constructed to be exploited for communication with device 2. Similarly, at the time of TS 200, TS 600, and TS 1000, a graph (Figure 8d) is constructed to be exploited for communication with device 3. All of the graphs in Figure 8 could be constructed by exploiting [21], but it is difficult to know which graphs to exploit at a certain time. However, by constructing and using graphs according to time-specific access devices based on movement patterns, the proposed scheme avoids path disconnection due to the  
Figure 7: The location prediction results for unit time for mobile devices based on predictive models. movement of mobile devices, as well as the need for graph reconstruction and resource reallocation to recover them. After the graph construction is completed, the network manager allocates resources to each graph. This resource allocation reflects the network topology state according to the mobility pattern of the mobile device. Figures 9-11 are the resource allocation results according to [15; 21], and the proposed scheme for Figure 8, respectively. In each allocation table, the vertical axis represents the channel used (CH), while the horizontal axis represents time (TS). Each cell in the table, denoted as X\(\rightarrow\)Y, indicates that data are transmitted from device X to device Y. For instance, TS 0/CH. 0 in Figure 9 indicates that device 8 transmits data to device 7 via channel 1 at time slot TS 0. The shaded portion of each table represents the section assigned by the mobile device for data transmission. Based on this, Figure 9 illustrates the resource allocation when mobile device 6 connects to the network via device 3 and device 4 through the join process. In the existing scheme [21], as shown in Figure 9, resource allocation is performed based on the current position without accounting for the movement of the mobile device. As illustrated in Figure 9, resource allocation is repeated at the time of generating the graph, irrespective of the movement of the mobile device. Consequently, at TS 100 and TS 200, the mobile device cannot transfer data through the allocated resources. In the case of Figure 10, as a basic scheme to support the mobility of mobile devices, resources would be pre-allocated to devices at all locations where the mobile device is likely to be.