# Analyzing Zone-Based Registration under 2-Step Paging in Mobile Communication Network
## 1 Introduction  
To successfully track the location of user equipment (UE) in a 5G mobile communication network, it is necessary to use location registration and paging procedures. Location registration refers to a series of processes that involve continuously registering the location information in a network database to track the current location of a UE because the UE continues to move. When there is a call to a UE, the location information of the UE is first found in the network database, a paging message is then transmitted to all the cells in the location area (LA) where the UE last registered, and the call is finally connected by receiving a response from the UE. This location registration and paging procedure impose significant costs on radio channels. Therefore, performance modeling and cost analysis are essential aspects of identifying the optimal location registration method that can minimize the costs on radio channels [1, 2]. To date, many location registration strategies have been proposed to reduce mobility management costs in mobile communication networks; representative methods include movement-based registration [2, 3, 4, 5], distance-based registration [5, 6, 7, 8], and zone-based registration (ZBR) [9, 10, 11, 12, 13]. In addition, even though there have been many studies on tracking area list-based registration for 4G/5G in recent years [14, 15, 16, 17, 18], this method is not a completely new one, but rather a flexible strategy that can be implemented in the sameway as one of the traditional methods. Recently, distributed mobility management was introduced to overcome the inevitable obstacles of the existing 4G/5G, but it is still at a conceptual stage because a new design must be introduced [19]. Among the methods mentioned, the method adopted most often is zone-based registration because of its good performance and easy implementation [10; 11; 12; 13]. This study has considered the zone-based registration method. The ZBR method is mostly implemented with one-zone-based registration (1 ZR, ZBR with one zone) in which the number of zones (or LA) to be stored is one; however, there is also a possible implementation wherein the number of zones to be stored is two or more. In the case of 1 ZR, location registration occurs frequently, as it is performed whenever a UE moves to a new zone. The two-zone-based registration (2 ZR, ZBR with two zones) method has been proposed [9; 10; 11; 12] to solve this method, and it is already known that 2 ZR is superior to 1 ZR in most cases. However, existing studies comparing the performances of the two methods have a significant problem: Some studies on 2 ZR [9; 11; 12] have proposed a mathematical model to analyze the performance of a UE with two zones and compared the performance with that in which the number of zones is one. The reported studies have also demonstrated that the performance with the case where the number of zones is two is typically better. However, as per the published data, when an incoming call arrives and paging is performed, it is assumed that the zone is paged simultaneously in 1 ZR, whereas 2-step paging (2 SP) is performed in 2 ZR for the sake of performance comparison. As a result, a performance comparison was not performed properly under the same conditions. Therefore, even in the case of 1 ZR (such as 2 ZR), the performance should be compared accurately by considering 2-step paging. Moreover, in previous studies, the performance of 2 ZR was analyzed while assuming that it returned to the zone visited immediately before with probability \(\Theta\)[9; 11; 12]. In this study, even in 1 ZR, the paging cost under 2-step paging is calculated by reflecting the same mobility characteristics as in 2 ZR, defining the states of the cells constituting the zone, and calculating the steady-state probability of each state. Ultimately, we aimed to determine exactly what the best method is under the same 2-step paging and by using the same mobility model.