On finding optimal registrations in presence of overlapping registration areas

Personal Communication Services (PCS) standards such as IS-41 and 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 [4]. Overlapping RAs form regions in which a mobile has a choice in selecting which RA to register to. The choice of current RA has implication on the number of registrations a mobile may require in the future. In this paper we investigate the problem of finding the best (or optimal) registration for a user in a cellular PCS environment with overlapping Registration Areas (RAs). We study two versions of the problem: (i) the deterministic version, where the entire trajectory of the mobile is known a-priori, and (ii) the stochastic version, where the trajectory of the mobile is not known a-priori but the system has the knowledge of mobility pattern of the mobile. The mobility pattern is modeled as a stochastic random walk across regions. In the deterministic case the method presented computes an optimal solution to the registration problem. In the stochastic case we present a method which determines the registration which minimizes the expected number of registrations by looking ahead at the probable paths which may be traversed by the mobile in future. The paper also proposes a preemptive and a non-preemptive version of the stochastic method which incur different numbers of hard and soft registration operations.