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A normal location area update (NLAU) and a periodic location area update (PLAU) schemes are adopted in 3GPP specifications for Universal Mobile Telecommunications System to detect presence of mobile stations. In this paper, we compare the NLAU scheme, the PNLAU (NLAU+PLAU) scheme, and a dynamic PNLAU scheme in terms of signaling and initial trunk setup cost. We analytically model cost functions of these schemes per checkpoint event. Optimality issues of the PNLAU have been studied, and optimal values are derived. The first optimality issue is to minimize the total cost of signaling and failure call setup. The second optimality issue is to minimize the signaling cost with an upper bound on failure call setup probability. Simulations are carried out to validate against analytical results.