# Analyzing Zone-Based Registration Using a Three Zone System: A Semi-Markov Process Approach
## 1 Introduction  
The awareness of the location of user equipment (UE, or mobile phone) should always be maintained so as to be able to connect any incoming calls to that UE anywhere within that mobile network. Location registration is the process by which a UE registers its location and status to a network database (DB) whenever it enters a new location area. If location registration is not performed properly, the network cannot know the location of the UE exactly and may need to page many cells in the network to find its location [1, 2].  
Many methods of registering location have been proposed, such as movement-based [3, 4, 5], timer-based [2], distance-based [2, 5, 6, 7], zone-based [1, 2, 8, 9, 10, 11, 12] and tracking area list-based [13, 14, 15, 16, 17, 18, 19] registration. In particular, several studies on tracking area list-based registration and the corresponding performance improvement have been conducted in recent years [13, 14, 15, 16, 17, 18, 19] since current specifications do not provide any details on how to define tracking area lists and allocate them to UEs.  
Among the methods mentioned above, most mobile networks have adopted zone-based registration due to its superior performance and ease of implementation. In this kind registration, the mobile network is split into zones consisting of several cells. UE is required to register new location information to the network whenever it moves to a new zone, this is called location registration. When a call arrives on the UE, the network sends paging messages to all of the cells in the UE's zone to identifythe cell to which the UE belongs and then connects the call. This process is called paging. Generally, as the number of cells in a zone decreases, the registration load increases but paging load decreases. Therefore, the trade-off between the registration and paging load is used to determine the optimal operating scheme for zone-based registration.  
Although recommendations for mobile networks state that multiple zones can be stored, actual mobile networks employ a zone-based registration that only stores a single zone (1Z). Due to this some studies have been conducted on zone-based registration that investigated a system with multiple zones. However, most of these studies consider only two zones (2Z) [1, 9, 10, 11] or have found the results of using three zones (3Z) to be too complicated [12]. In this study, through the development of a semi-Markov process approach, we present a new mathematical model for zone-based registration using three zones. In addition, research results on zone-based registration with one, two and three zones are used to suggest an optimal management scheme for zone-based registration.  
The structure of the paper is as follows: Section 2 introduces zone-based registration with multiple zones. Section 3 proposes a new mathematical model based on the semi-Markov process theory, to analyze the accurate performance of the 3Z system. Section 4 carries out a numerical study to investigate the performance of the zone-based registration with multiple zones. Finally, Section 5 concludes this paper.