Modeling the initial stage of a file sharing process on a BitTorrent network

In this paper, we model the number of seeders during the initial stage of a file sharing process on BitTorrent networks. The initial stage is crucial for successfully identifying the initial seeder, who provided the source of the files on the Internet. Most existing BT models focus on different parameters in the steady state, which occurs at a later stage of a file sharing process. None of them are able to characterize the initial stage. In this study, we propose the first model on capturing the characteristics on the growth of the number of seeders during the initial stage on a BT network. Also, we derive a lower bound for the appearing time of the second seeder and the length of the stationary period. Our model suggests that the number of seeders remain stationary during the starting period of a file sharing process. When it enters the rapid-rising period, it increases more speedily as an increasing number of seeders are available for supplying the rarest pieces. The observed demarcation of the stationary period and the rapid-rising period is significant in identifying the initial seeder on a BT network. If the investigative work can be commenced within the stationary period, the chance of identifying the initial seeder is much higher. On the other hand, if the file distribution has entered the rapid-rising period, one can no longer determine which of the existing seeders is, indeed, the initial seeder.