This paper presents a performance study of BitTorrent-like P2P systems by modeling, based on extensive measurements and trace analysis. Existing studies on BitTorrent systems are single-torrent based and usually assume the process of request arrivals to a torrent is Poisson-like. However, in reality, most BitTorrent peers participate in multiple torrents and file popularity changes over time. Our study of representative BitTorrent traffic provides insights into the evolution of single-torrent systems and several new findings regarding the limitations of BitTorrent systems: (1) Due to the exponentially decreasing peer arrival rate in a torrent, the service availability of the corresponding file becomes poor quickly, and eventually it is hard to locate and download this file. (2) Client performance in the BitTorrent-like system is unstable, and fluctuates significantly with the changes of the number of online peers. (3) Existing systems could provide unfair services to peers, where a peer with a higher downloading speed tends to download more and upload less. Motivated by the analysis and modeling results, we have further proposed a graph based model to study interactions among multiple torrents. Our model quantitatively demonstrates that inter-torrent collaboration is much more effective than stimulating seeds to serve longer for addressing the service unavailability in BitTorrent systems. An architecture for inter-torrent collaboration under an exchange based instant incentive mechanism is also discussed and evaluated by simulations.