Peer-to-Peer (P2P) file distribution systems can efficiently disseminate massive contents, such as disk images of operating systems, from a server to many users in a piece-by-piece manner. In particular, the BitTorrent protocol optimizes each peer's download speed by applying the tit-for-tat (TFT) strategy, where each peer preferentially uploads piece(s) to peer(s) from which it can download missing pieces faster. To the best of our knowledge, however, the optimality of TFT-based P2P file distribution has not been studied sufficiently. In this paper, we aim to understand the optimal scheduling in TFT-based P2P file distribution. First, we develop a discrete-time model of TFT-based P2P file distribution and formulate its optimal scheduling as a two-step integer linear programming problem. The first step is to minimize the average file retrieval time among peers, and the second step is to improve fairness among peers. We analyze the optimal solution obtained by the existing solver and reveal the characteristics of the optimal scheduling. Specifically, we show that it is crucial to distribute pieces from the server indirectly to peers with large upload capacity via those with small upload capacity.

Some major P2P file distribution systems adopt Tit-For-Tat exchange strategy, which means "initially cooperate, then respond in kind to a previous opponent's action, i.e. cooperative or not." However, when sharing a file on such P2P systems, the random peer selection has a problem in that each peer cannot download the file enough efficiently. The peer selection method that groups peers according to their rate has been proposed to solve this problem. This method is supposed to be able to alleviate the difference in performance among peers because it lets peers with similar transmitting rate connect to each other. However, when reduction in peer performance or link one occurs, which is often observed on today's Internet, some problems will emerge, such as it takes a long time for the existing method to reconfigure groups; 2) immediate reconstruction of neighbor peers has not been taken into account when peers detect deterioration in downloading performance. Therefore, we propose a method that reconfigures the group of neighbor peers once a peer notices that the performance of connected peers decreases. The proposed method is evaluated through simulation experiments using BitTorrent as an instance of Tit-For-Tat strategy. The download time of all peers and that of the peer with performance deterioration are estimated focusing on the effect of switching a degraded peer to another immediately. As a result, we confirm that our proposal can distribute files among all peers faster than the existing method keeping incentives for users to some extent. We believe that the proposal which can adapt to the sudden network deterioration is one of the most important technologies for evolution of network software.