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Personal Communication Services (PCS) standards such as the IS-41 and the GSM use a location management scheme which is based on registration areas (RA). Overlapping of registration areas has been proposed to reduce the overhead of location updates in such systems. Overlapping provides multiple choices for the selection of a registration area, a feature which does not appear in environments of nonoverlapping RAs. In this paper, we demonstrate how the choice of a registration area affects the number of subsequent registrations and define the problem of optimal choice based on minimization of subsequent registrations. We study two versions of the problem: 1) the deterministic (or offline) version, in which the entire trajectory of the mobile unit is known a priori, and 2) the stochastic (or online) version, in which the trajectory of the mobile unit is not known a priori, but the system has the knowledge of the mobility pattern of the mobile. The mobility pattern is modeled as a random walk across coverage area. In the deterministic case, the method presented computes an optimal solution to the registration problem. In the stochastic case, we present a method that determines the registration which minimizes the expected number of registrations by looking ahead in the probable future paths of the mobile unit. The algorithm's time complexity has exponential dependence on the length of the look-ahead. The cost of search is independent of the choice, therefore the algorithm does not increase the search cost. We also consider an alternative cost model for the stochastic case and propose a preemptive and a nonpreemptive approach each of which incurs different numbers of hard and soft registration operations. Simulation results show a reduction of 25-30 percent in number of registrations over a random-choice scheme. This can be translated to 5-20 percent effective location management load reduction for most cases, subject to the call-to-mobility ratio (CMR) of a mobile unit and search-cost-to-update-cost ratio (CCR) in the network.
Index Terms- Location management, mobile communication network, cellular network, online algorithm, optimization, overlapping registration area.

G. Varsamopoulos and S. K. Gupta, "Optimal Offline and Online Registration Techniques for Location Management with Overlapping Registration Areas," in IEEE Transactions on Mobile Computing, vol. 4, no. , pp. 474-488, 2005.
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