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Presence is a service that allows a user to be informed about the reachability, availability, and willingness of communication of another user. Presence service has become a key enabler for many popular applications such as instant messaging and push-to-talk. Traffic to a presence server is resulted by user behaviors such as login/logout, online status modification, and automatic status refresh by client application. Mathematical models are proposed in this paper to study the user behaviors associated with a presence server during the time of a day such that traffic characteristics to a presence server can be inferred. The correctness of our estimation and analysis are verified by extensive simulations using Matlab. This study on the relationship between user behaviors and traffic to a presence server can help network operators to plan network capacity, optimize server performance and detect traffic anomaly.