# Improvement and Performance Evaluation When Implementing a Distance-Based Registration
## 6 Numerical Results
When E(Tm) is 0.6, the total signaling cost is minimal when \(N\) is 7. When E(Tm) increases, \(N\) with minimal total signaling cost is gradually reduced. When E(Tm) is 1.0, the total signaling cost is minimal when \(N\) is 4. When E(Tm) is 1.2, the total signaling cost is minimal when \(N\) is 3. In other words, as E(Tm) increases, the size of the LA with the minimum total signaling cost becomes smaller and the proportion of the total signaling cost decreases. Conversely, as E(Tm) increases, the proportion of the paging cost increases and the number of cells in the LA with the minimum cost becomes smaller. Figure 14 shows the effect of an implicit registration on reduction of signaling cost. If an implicit registration is not adopted, the total signaling cost is minimal when \(N\) is 4. However, if implicit registration is adopted, the total signaling cost is minimal when \(N\) is 7. In other words, implicit registration can reduce the location registration cost, which  
Figure 12: Total signaling cost for various numbers of cells in an LA (CMR = 1). Figure 13: Total signaling cost for various E(T\({}_{\rm m}\)) (CMR = 1/3). increases the size of the LA and minimizes the total signaling cost. The effect of such implicit registration is greater when the call occurs frequently (i.e., the CMR becomes larger). Figure 15 shows the performance comparison results of DBR and ZBR. In the previous study [6], only DBR with an LA increasing on a ring-by-ring basis was considered, so performance was compared by assuming that the LA of ZBR, the target of comparison, also increasing on a ring-by-ring basis. According to the results of previous study [6], it was analyzed that the performance of DBR was superior to that of ZBR in terms of total signaling cost when the distance threshold \(D\) = 2 at which total signaling cost of DBR was minimized. In Figure 15, considering the DBR having an LA that increases on a cell-by-cell basis, and assuming that the LA of ZBR, the target of comparison, also increases on a cell-by-cell basis, the performance is compared. From the figure, when U = 8, DBR is minimized at \(N\) = 7 (\(D\) = 2) like the previous study [6] and shows bett  
Figure 14: Total signaling cost for various numbers of cells in an LA (CMR = 1). Figure 15: Performance comparison results of DBR and ZBR (CMR = 1). However, in the previous study [6], even though the ZBR was minimized at \(N=3\), the performance of DBR was compared with the result for \(D=2\) (\(N=7\)) in ZBR and concluded to be significantly better. On the other hand, when U = 4, DBR is minimal at \(N=4\) and still shows better performance than ZBR. As such, the results of accurately comparing the performance by reflecting the LA increasing on a cell-by-cell basis are new results that cannot be obtained in previous study. In the figure, the performance of DBR is always better than that of ZBR because a pure random walk mobility model [9; 11; 15; 16] is assumed. However, if a mobility model favorable to ZBR is assumed as in [6; 7], the results may change. Let us briefly consider the mobility model proposed in [6; 7]. Figure 16 represents a revised random walk mobility model of a UE for each \(N\). In the figure, \(q\) is the probability that a UE can move to surrounding cells. If a pure random walk mobility model is assumed, \(q\) is \(1/6\). However, since the boundary of the LA in ZBR is generally composed of areas such as roads, bridges, rivers and mountains where there is relatively little traffic, \(q\) can be less than \(1/6\). Figure 17 shows the total signaling cost of ZBR for various \(q\) to compare with that of DBR. In the figure, when \(q=1/12\), the performance of ZBR is better than that of DBR since the minimum of ZBR at \(N=2\) is less than that of DBR at \(N=4\). As shown in Figures 15 and 17, since the performance of the location registration method varies depending on the mobility model, network environment and so on, 4G and 5G networks adopt TAL-based location registration, which can be operated as DBR as well as ZBR [4; 21; 22; 23].