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In this study, we deal with a Distance-Based Registration with Implicit Registration, which is an enhanced scheme of the Distance-Based Registration in mobile-cellular networks. In comparisons with other Location Registration schemes, various studies on the Distance-Based Registration scheme and performance have been performed. However, a real network hierarchy has not been properly reflected in the performance evaluation of the Distance-Based Registration. To accurately evaluate the registration and paging costs of the Distance-Based Registration, a real network hierarchy should reflect that a mobile network is made up of many Visitor Location Register areas. Furthermore, we use an embedded Markov-Chain model in the Visitor Location Register hierarchy, which can reflect not only the Implicit Registration effect of the outgoing calls of user equipment but also cell staying time of the user equipment that may follow a general distribution. Without consideration of the Visitor Location Register, the paging cost decreases due to a small paging area, but the location registration cost rises because of frequent inter Visitor Location Register. The numerical results according to the various conditions show an accurate evaluation of the Distance-Based Registration performance in a real network hierarchy and the general cell staying time. Generally, the total signaling cost will increase when we consider the Visitor Location Register. However, for more appropriate evaluation of the Distance-Based Registration performance, it is necessary to consider the Visitor Location Register hierarchy.

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