Distributed protocols for peer to peer file sharing, streaming video, and video on demand have revolutionized the way the majority of information is conveyed over the Internet. The peers are millions of computers, acting as both clients and servers, downloading and uploading information. Information to be shared is broken into chunks, and the chunks are traded among peers in the network. There can be turnover in the set of chunks of information being collected and/or in the set of peers collecting the information. Coding, in which groups of chunks are combined to form new chunks, can enhance the collection process. The systems are distributed and scalable. The theory for understanding peer-to-peer systems has lagged far behind our ability to mathematically model, predict, and optimize system performance.
In this talk I shall discuss stochastic models, mathematical results, and challenges relating to the performance of peer to peer communication in large networks.