In this paper, we investigate the role of storage management schemes designed to deal with traffic of different applications. First, we show the impact on user performance, service provider and network cost of a static per-application storage allocation using measured traffic traces. Then, we analyze the performance of this static partitioning scheme by means of simulations with synthetic traffic traces. Finally, we evaluate two mechanisms for dynamic storage management, namely strict priority and weighted fair allocation, designed to overcome static partitioning limitations in presence of content time-to-live and of dynamic traffic patterns.