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Location management (LM) is an important function in a personal communication network to track movements of mobile terminals (MTs) for call delivery. It is well-known that the total signaling cost of a distance-based LM scheme is the lowest among dynamic location management schemes for PCS networks. In this paper, we derive the joint probability distribution of two random variables: the moving distance of an MT and the number of location updates resulting from the moving distances exceeding the distance threshold. As special cases, the probability distributions of an MT's moving distances and the number of location updates during an LM interval are obtained. These statistics are generally applicable to irregular cell topologies and general cell residence time distributions. Based on the derived statistics, the optimal distance thresholds for distance based LM schemes with blanket paging and sequential paging are solved analytically. Numeric results show that our optimized distance-based LM scheme outperforms some well-known LM schemes in total LM cost.