Resilient Tree-Based Video Streaming with a Guaranteed Latency

In this paper, we propose a method to organize a tree-based Peer-to-Peer (P2P) overlay for video streaming which is resilient to the temporal reduction of the upload capacity of a node. The basic idea of the proposed method is: (1) to introduce the redundancy to a given tree-structured overlay, in such a way that a part of the upload capacity of each node is proactively used for connecting to a sibling node, and (2) to use those links connecting to the siblings to forward video stream to the siblings. More specifically, we prove that even if the maximum number of children of a node temporally reduces from m to m − k for some 1 ≤ k ≤ m − 1, the proposed method continues the forwarding of video stream to all of m children in at most 2x hops, where x is the smallest integer satisfying m − k ≥ m/2x. We also derive a sufficient condition to bound the increase of the latency by an additive constant. The derived sufficient condition indicates that if each node can have at least six children in the overlay, the proposed method increases the latency by at most one, provided that the number of nodes in the overlay is at most 9331; namely the proposed method guarantees the delivery of video stream with a nearly optimal latency.