An efficient mobility management for mobile stations plays an important role in mobile communication network. In this study, we consider movement-based registration(MBR) and distance-based registration(DBR). Analytical models based on 2-dimensional random walk in hexagonal cell configuration are considered to analyze the performance of MBR and DBR. Especially, we focus on the derivation of the registration cost of DBR scheme by using two analytical methods and then show that DBR always outperforms MBR. Numerical results are provided to demonstrate optimal condition under various circumstances.