Hajek and Zhu recently showed that the BitTorrent protocol can become unstable when peers depart immediately after downloading all pieces of a file. In light of this result, Zhou et al. propose bundling swarms together, allowing peers to exchange pieces across different swarms, and claim that such "universal swarms" can increase BitTorrent's stability region. In this work, we formally characterize the stability region of universal swarms and show that they indeed exhibit excellent stability properties. In particular, bundling allows a single seed with limited upload capacity to serve an arbitrary number of disjoint swarms if the arrival rate of peers in each swarm is lower than the seed upload capacity. Our result also shows that the stability region is insensitive to peers' upload capacity, piece selection policies and number of swarms.

Hajek and Zhu recently showed that the BitTorrent protocol can become unstable when peers depart immediately after downloading all pieces of a file. In light of this result, Zhou et al. propose bundling swarms together, allowing peers to exchange pieces across different swarms, and claim that such "universal swarms" can increase BitTorrent's stability region. In this work, we formally characterize the stability region of universal swarms and show that they indeed exhibit excellent stability properties. In particular, bundling allows a single seed with limited upload capacity to serve an arbitrary number of disjoint swarms if the arrival rate of peers in each swarm is lower than the seed upload capacity. Our result also shows that the stability region is insensitive to peers' upload capacity, piece selection policies and number of swarms.

This paper focuses on the stationary portion of file download in an unstructured peer-to-peer network, which typically follows for many hours after a flash crowd initiation. The model includes the case that peers can have some pieces at the time of arrival. The contribution of this paper is to identify how much help is needed from the seeds, either fixed seeds or peer seeds (which are peers remaining in the system after obtaining a complete collection), to stabilize the system. The dominant cause for instability is the missing piece syndrome, whereby one piece becomes very rare in the network. It is shown that stability can be achieved with only a small amount of help from peer seeds-even with very little help from a fixed seed, peers need dwell as peer seeds on average only long enough to upload one additional piece. The region of stability is insensitive to the piece selection policy. Network coding can substantially increase the region of stability in case a portion of the new peers arrive with randomly coded pieces.

Peer-to-peer (P2P) communication in networks for file distribution and other applications is a powerful multiplier of network utility, due to its ability to exploit parallelism in a distributed way. As new variations are engineered, to provide less impact on service providers and to provide better quality of service, it is important to have a theoretical underpinning, to weigh the effectiveness of various methods for enhancing the service. This paper focuses on the stationary portion of file download in an unstructured P2P network, which typically follows for many hours after a flash crowd initiation. The contribution of the paper is to identify how much help is needed from the seeds, either fixed seeds or peers dwelling in the system after obtaining the complete file, to stabilize the system. It is shown that dominant cause for instability is the missing piece syndrome, whereby one piece becomes very rare in the network. It is shown that very little dwell time is necessary--even if there is very little help from a fixed seed, peers need to dwell on average no longer than it takes to upload one additional piece, after they have obtained a complete collection.

Typical protocols for peer-to-peer file sharing over the Internet divide files to be shared into pieces. New peers strive to obtain a complete collection of pieces from other peers and from a seed. In this paper we identify a problem that can occur if the seeding rate is not large enough. The problem is that, even if the statistics of the system are symmetric in the pieces, there can be symmetry breaking, with one piece becoming very rare. If peers depart after obtaining a complete collection, they can tend to leave before helping other peers receive the rare piece.