Mobile　IM　(Instant　Messaging)　users　are　more　frequently　online　and　offline　than　fixed　users.　It　incurs　large　presence　message　traffic　that　significantly　consumes　the　limited　service　resources.　Some　studies　indicate　that　presence　delayed　update　can　effectively　reduce　the　traffic.　Firstly,　we　analyze　presence　update　process　and　research　presence　distribution.　Secondly,　we　use　mathematical　model　to　analyze　presence　delayed　update.　At　last,　we　modify　existing　simulation　methods　to　validate　the　model　in　respect　of　accuracy　and　effectiveness.