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 B-k = Sigma(k-1)(i=0) b(i). It is known that under the above constraint, k-hop delivery of b stripes to n peers is possible only if n = B-k. This paper proves that (k + 1)hop delivery of b stripes to n peers is possible for any n = B-k; 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 B-k - b + 2 <= n <= B-k - 1; namely for n's close to B-k.