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This paper presents a new analytic framework for dynamic location management of PCS networks. Based on the theory of hexagonal cellular patterns, a novel two-dimensional Markov walk model with six states is proposed to characterize the dynamic behavior of the intercell movements for a mobile station. We discover a broad class of isotropic processes having an identical uniform steady-state distribution of the six directions, but distinct circulant transition probability matrices. Six special isotropic processes exhibiting IID, directional, turning, ping-pong, h-spin, and t-spin mobility patterns are identified for performance comparison. We also generalize the selective paging strategy by introducing the concept of probabilistic selective paging (PSP) to reduce the paging cost. A unified analysis using recursive computations is carried out to compute the exact probability distribution for the number of per-call location updates. We calculate the location profile with respect to an incoming call and derive an exact expression of the average paging cost for PSP. With its ability to distinguish subtle performance variations and unveil new features of various dynamic location management schemes, our analytic framework is demonstrated to provide more precise and insightful results than conventional analysis.
Date of Publication: Jul-Sep 2002