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IP multimedia core network subsystem (IMS) provides presence service for universal mobile telecommunications system (UMTS). In IMS, the presence server is responsible for notifying an authorized watcher of the updated presence information. If the updates occur more frequently than the accesses of the watcher, the presence server will generate many notifications. This paper uses a weakly consistent scheme (called delayed update) to reduce the notification traffic. In this scheme, a delayed timer is defined to control the notification rate. We propose an analytic model and simulation experiments to investigate the performance of delayed update. The study indicates that delayed update can effectively reduce the notification traffic without significantly degrading the valid access probability.