Multi-Tree-Based Peer-to-Peer Video Streaming with a Guaranteed Latency

This paper considers Peer-to-Peer (P2P) video streaming systems, in which a given video stream is divided into b stripes and those stripes are delivered to n peers through b spanning trees under the constraint such that each peer including the source can forward at most b stripes. The delivery of a stripe to n peers is said to be a k-hop delivery if all peers receive the stripe through a path of length at most k. Let Bk=∑i=0k-1bi. It is known that under the above constraint, k-hop delivery of b stripes to n peers is possible only if n≤Bk. This paper proves that (k+1)-hop delivery of b stripes to n peers is possible for any n≤Bk; namely, we can realize the delivery of stripes with a guaranteed latency while it is slightly larger than the minimum latency. In addition, we derive a necessary and sufficient condition on n to enable a k-hop delivery of b stripes for Bk-b+2≤n≤Bk-1; namely for n's close to Bk.