—Peer-assisted Video-on-Demand (VoD) systems have not only received substantial recent research attention, but also been implemented and deployed with success in large-scale realworld streaming systems, such as PPLive [1]. Peer-assisted Videoon-Demand systems are designed to take full advantage of peer upload bandwidth contributions with a cache on each peer. Since the size of such a cache on each peer is limited, it is imperative that an appropriate cache replacement algorithm is designed. There exists a tremendous level of flexibility in the design space of such cache replacement algorithms, including the simplest alternatives such as Least Recently Used (LRU). Which algorithm is the best to minimize server bandwidth costs, so that when peers need a media segment, it is most likely available from caches of other peers? Such a question, however, is arguably non-trivial to answer, as both the demand and supply of media segments are stochastic in nature. In this paper, we seek to con...