Fundamental delay bounds in peer-to-peer chunk-based real-time streaming systems

This paper addresses the following foundational question: what is the maximum theoretical delay performance achievable by an overlay peer-to-peer streaming system where the streamed content is subdivided into chunks? As shown in this paper, when posed for chunk-based systems, and as a consequence of the store-and-forward way in which chunks are delivered across the network, this question has a fundamentally different answer with respect to the case of systems where the streamed content is distributed through one or more flows (sub-streams). To circumvent the complexity emerging when directly dealing with delay, we express performance in term of a convenient metric, called "stream diffusion metric". We show that it is directly related to the end-to-end minimum delay achievable in a P2P streaming network. In a homogeneous scenario, we derive a performance bound for such metric, and we show how this bound relates to two fundamental parameters: the upload bandwidth available at each node, and the number of neighbors a node may deliver chunks to. In this bound, k-step Fibonacci sequences do emerge, and appear to set the fundamental laws that characterize the optimal operation of chunk-based systems.