This paper aims at improving the distance-based location management scheme for mobile communication networks. In location management, a mobile terminal (MT) is tracked based on its location-update area (LA). The improvement is brought about by joint optimization of LA center and LA size. For LA center optimization (LCO), we determine the optimal center position of the LA given the initial position of the MT upon each location update. The investigation of optimal LA center has eluded research to date. Based on the popular continuous-time random walk (CTRW) mobility model, we propose an analytical framework that uses a diffusion equation to determine the optimal LA center that minimizes the total cost of location management, consisting of the location update cost and terminal paging cost. This framework allows us to easily model the non-Markovian movement of the MT and evaluate the impact of various measurable physical parameters (such as length of road section, angle between road sections, and road section crossing time) and LA center. In particular, we show that proper LA center can significantly reduce the total cost. For example, for the circular LA and low Poisson call-arrival rate, optimizing the LA center alone has the potential of reducing the cost by up to 37 percent. Joint optimization of the LA center and terminal paging scheme can reduce the cost even further. Simulations results match the theoretical analysis to a gap within 3 percent, indicating that our theoretical model is very accurate.
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