# Mobility Management Scheme with Mobility Prediction in Wireless Communication Networks
## 2 Registration Scheme with Flexible TAL Forming  
In this study, we present a registration scheme considering mobility prediction and corresponding flexible tracking area list (TAL) forming, which is similar to that present in [10] from the viewpoint of basic concept. However, the previous study on mobility prediction and flexible TAL did not present user's accurate mobility and corresponding analytical model to evaluate its performance. Thus, we constructed user's accurate mobility and corresponding analytical model from the viewpoint of the mobility prediction and flexible TAL forming. In this scheme, we used mobility trace of certain residing area for each UE. Based on a known geographical area of the trace, its map, and statistics from previously studied results, we deployed two different cell sizes for urban and rural parts of the area as in [10]. In Figure 1, a bold frame is the initial cell (cell 1), where the UE has registered its location. In this study, it is assumed that a TA consists of one cell for convenience of analysis. Allocated TAL (or cells) for the UE is marked in colored cells and the predicted direction angle (with moving probability to the direction, \(q\)) is shown in the dotted line. In the urban area with restricted moving environments under compact road structure of small sector, the UE can move to the center cell with an angle of \(60^{\circ}\) and a predicted direction of \(q\). On the other hand, an angle of \(120^{\circ}\) is assumed for rural environments with relatively wide moving roads (big sector). In both cases, the following mobility model is considered:  
1. The UE predicts the movement direction based on the accumulated past data \"every time the UE performs location registration (or leaves the current location area)\" and configures the location area accordingly, (The UE moves to the center cell(s) of new location area with probability \(q\)). 2. When moving between cells in the location area, it moves according to the random walk model (that is, the probability of selecting one of the 6 surrounding cells is the same). First, let us consider urban environment in Figure 1.  
The UE registering in cell 1 can enter cell 3 with probability \(q\) or enter any one of the remaining five cells with probability \((1-q)/5\). If it enters one of the three neighboring cells that are not in the current TAL, it will register its location. The UE entering cell 3 can enter any one of the six neighboring cells with equal probability, \(1/6\). Similarly, the UE entering cell 2 can enter any one of the six neighboring cells with probability \(1/6\). Such a mobility model is called a (symmetric) random walk model. Note that movements of the UE registered in cell 1 are not random walks, although all remaining movements are random walks. If the UE moves to one of the neighboring cells that is not in the current TAL, it will register its location and a new TAL is set up so that entered cell is cell 1 of Figure 1.  
Next, let us consider a rural environment in Figure 1, which is very similar to an urban environment. Figure 1: TAL forming scheme depending on UE’s moving direction prediction. (**a**) Urban area (small sector, 60\({}^{\circ}\)); (**b**) Rural area (big sector, 120\({}^{\circ}\)). The UE registering in cell 1 can enter cell 2 or cell 3 with probability \(q\) or enter any one of the remaining four cells with probability \((1-q)/4\). If it enters one of the two neighboring cells that is not in the current TAL, it will register its location. The UE entering cell 2 can enter any one of the six neighboring cells with probability \(1/6\). Similarly, the UE entering cell 3 can enter any one of the six neighboring cells with probability \(1/6\). Note that the movements of the UE that registered in cell 1 are not random walks, although all remaining movements are random walks.