The Missing Piece Syndrome in Peer-to-Peer Communication

TL;DR

This paper analyzes the 'missing piece syndrome' in peer-to-peer file sharing, showing that system stability depends on the seeding rate relative to peer arrival rate, with symmetry breaking causing rare pieces.

Contribution

It identifies conditions under which the missing piece syndrome occurs and proves system stability criteria based on seeding and arrival rates, including for various piece selection policies.

Findings

System is stable if seeding rate exceeds peer arrival rate.

Symmetry breaking leads to rare pieces and potential system instability.

Results hold for different piece selection policies, including network coding.

Abstract

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 investigate 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. Assuming that peers arrive with no pieces, there is a single seed, random peer contacts are made, random useful pieces are downloaded, and peers depart upon receiving the complete file, the system is stable if the seeding rate (in pieces per time unit) is greater than the arrival rate, and is unstable if the seeding rate is less than the arrival rate. The result persists for any piece selection policy that selects from among useful pieces, such as rarest first, and it persists with the use of network coding.