Location update for PCS networks with a fractional movement threshold

Many dynamic location update schemes, such as the time-based, movement-based, and distance-based schemes, have been studied in the location management for Personal Communication Service networks, whereas the movement-based scheme is the most practical approach. In this paper, we propose a novel fractional movement-based location update scheme, in which the movement threshold is a real number with a fraction instead of an integer. We prove analytically that there is a unique optimal fractional movement threshold that minimizes the total cost of location updates and paging per call arrival. Our study shows that the fractional movement-based scheme outperforms the pure movement-based scheme. Furthermore, we propose a hybrid location management scheme, in which when the call-to-mobility ratio is larger than another threshold, the optimal fractional movement-based scheme is adopted. Otherwise, the static location update scheme is adopted. The Newton approximation method is adopted to find the 2^nd threshold.