Streaming media (e.g., music or video) data access has been a research problem over the past few years, and the problem becomes tougher when the clients are mobile devices whose limited storage spaces prevent the clients from holding a large cache. A practical solution for the cellular system is to buffer the streaming data on the base stations, serving as the "cache" to the mobile devices. However, when mobile devices move from one cell to another, the cached data should also be migrated to the corresponding base station in order that users can view the media smoothly. When the number of requests increases, stations may face heavy data migration and storage burden. In this paper, we propose a statistical buffering mechanism by adapting SAA search which makes use of prior knowledge (statistical data) to predict the trend of user movement among cells. Experimental studies show that, with an acceptable complexity, our algorithms can obtain good performance on buffering streaming media data.