In a cellular network, the network coverage is partitioned into nonoverlapping areas called registration areas to facilitate location management (LM) that keeps track of the location of a user equipment (UE) unit. In the second-generation Global System for Mobile Communications (GSM) and the third-generation Universal Mobile Telecommunications System (UMTS), a registration area is called a location area (LA) in the circuit-switched domain or a routing area (RA) in the packet-switched domain. In the fourth-generation Long-Term Evolution (LTE), a registration area is called a tracking area (TA). To tackle the drawbacks of the LA/RA-based LM scheme used in GSM and UMTS, which is intrinsically a static scheme, LTE adopts a dynamic LM scheme called a TA list (TAL)-based scheme. Under the TAL-based scheme, the network allocates to a UE unit a group of TAs referred to as a TAL instead of only a single TA. The UE can move freely within the allocated TAL without performing any location updates that are called TA updates (TAUs) in LTE. Only when moving into a TA that is not included in the allocated TAL does the UE need to perform a TAU, and afterward, the network will allocate, to the UE, a new TAL. The performance of the TAL-based scheme relies on the allocated TAL. If the allocated TAL is inappropriate with respect to the UE's mobility and traffic characteristics, the TAL-based scheme may produce adverse effects. To find an optimal TAL allocation method for global UE units that exhibit weak regularity in their mobility, this paper develops an embedded Markov chain approach to analyze the signaling cost of the TAL-based scheme. This paper distinguishes itself from existing studies in the following aspects. First, this paper follows LTE technical specifications, that is, the number of TAs in a TAL can vary and, furthermore, is upper bounded, whereas existing studies partially or completely ignore this stipulation. Second, this paper emphasizes the impact of a call handling model that dictates whether a TAU occurs after the completion of a call by considering two call handling models, i.e., a call plus location update and a call without location update. Third, as for the dependence among the cell residence time, the TA residence time, and the TAL residence time, this paper proposes the use of a fluid flow model to describe this dependence, which is simple but does not compromise accuracy. Analytical formulas for the total signaling cost of the TAL-based scheme due to TAU and paging operations, as well as formulas that are useful in designing an optimal paging scheme, are derived, and their accuracy is validated through Mont Carlo simulation. Then, numerical studies are carried out to investigate the impact of diverse parameters on the signaling cost, revealing that the network can allocate, to a UE unit, an optimal TAL that is consistent with the UE's mobility and traffic characteristics to minimize the signaling cost of the TAL-based scheme.
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