In this study, we consider movement-based registration (MBR), improved MBR (IMBR) 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/IMBR and DBR. Especially, we focus on the derivation of the registration cost of DBR scheme by using analytical method and then show that DBR always outperforms not only MBR but also IMBR.