## 1 Introduction  
In recent years, with the rapid development of internet and multimedia technology, increasingly more users have gained access to high-speed internet, and the service of online video-on-demand (VoD) [1] has been rapidly developed. Currently, one of the most common methods to support video-streaming services is peer-to-peer (P2P) networks. In P2P-based VoD systems [2], each peer can download and watch videos from the server or other peers, and provide the downloaded video segments to other requesting peers, which can improve the system's service capabilities and reliability and reduce the server load and network construction costs. Compared with the live video system, a significant feature of the VoD system is that it can support the users to perform video cassette recorder (VCR) operations [3] (e.g., randomly dragging the progress bar for seeking, pause, fast forward, and rewind). In the P2P-based VoD system without data-prefetching technology, the users may experience significant playback delay after frequent video cassette recorder (VCR) operations, which seriously affects the users' viewing experience. Hence, the most serious challenge in the design of P2P-based VoD systems is to find a suitable segment selection algorithm to reduce the playback delay after the VCR operation. A data-prefetching strategy was proposed, i.e., if residual download bandwidth remains, the peer can prefetch a part of non-urgent data after the urgent data has been downloaded. The urgent data can ensure the video is continuously played in the next several minutes, and the non-urgent data is used to reduce the playback delay after the users perform VCR operations. In this strategy, the peer uses the residual bandwidth to download the data ahead of the current playback point, which can reduce the playback latency and effectively improve the viewing experience of users [4]. In [5], [PERSON] et al. analyzed the VCR operation behaviors of users in large-scale VoD systems, and proposed a strategy to reduce the playback delay after the VCR operation by prefetching videos with high play counts. This strategy assumes that all users in the system have identical preferences, so they attempt to predict the video that is most likely to be played in the next few minutes by analyzing a large volume of user viewing logs. However, the assumption has drawbacks. For example, the viewing preferences of users vary for different times. Hence, inaccurate predictions will cause a low bit rate of prefetched data and waste bandwidth resources. In [6], the authors proposed an anchor-prefetching strategy. The anchor is distributed throughout the video file with a fixed interval (5 min), and each anchor consists of 10 continuous seconds. This traditional anchor-prefetching strategy can effectively reduce the playback delay after the VCR operation and avoid the problem of bandwidth waste caused by inaccurate prediction. The authors of [7] developed a prefetching strategy of API by prefetching both anchor points and popular segments of the video. This approach is complementary to the anchor-prefetching strategy, which can reduce the playback delay and improve the user satisfaction. However, to implement this strategy, it is necessary to detect the video segments that are currently played by each online P2P node, which will consume many extra bandwidth resources. In [8], the authors measured and analyzed the rules of VCR operation when the user watches the video. The forward- and backward-jump lengths have been modeled with a Weibull distribution. The forward and backward distances have different parameter values of Weibull distribution. In addition, for different lengths of video files, the Weibull distribution parameter values also vary. This is the theoretical basis of our study on the data-prefetching strategy. A new strategy to determine the most reasonable anchor interval is proposed in this paper by considering two factors of playback delay and positioning satisfaction.