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Presence is a service that allows a user to be informed about the reachability, availability, and willingness to communicate of another user. Presence service has become a key enabler for many popular applications such as instant messaging and push-to-talk. However a study shows that presence service can account for 50% or more of the total signalling traffic the IMS core network handles (C. Urrutia-Valds et al., 2006). This is quite a burden for a real IMS network and need to be tackled. In this paper, a thorough analysis of the traffic load distribution reveals that notify messages account for the largest portion of the traffic load on a presence server. We propose a mathematical model of a queueing system with batch arrival and controlled vacation to describe the processing of notify messages inside a presence server. The model is then used to calculate the optimal value of the timer that controls the notify queue, which is an essential parameter to adjust in network sizing upon deploying a presence server. An approximation of the model is also provided so that the performance of a presence server can be tuned in an online manner based on real traffic statistics.