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.

[1]  E. P. Miles Generalized Fibonacci Numbers and Associated Matrices , 1960 .

[2]  Bobby Bhattacharjee,et al.  Scalable application layer multicast , 2002, SIGCOMM '02.

[3]  Miguel Castro,et al.  SplitStream: high-bandwidth multicast in cooperative environments , 2003, SOSP '03.

[4]  Kien A. Hua,et al.  ZIGZAG: an efficient peer-to-peer scheme for media streaming , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[5]  Pablo Rodriguez,et al.  Performance Analysis of Peer-to-Peer Networks for File Distribution , 2004, QofIS.

[6]  Gustavo de Veciana,et al.  Service capacity of peer to peer networks , 2004, IEEE INFOCOM 2004.

[7]  Zongpeng Li,et al.  On achieving optimal throughput with network coding , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[8]  Qian Zhang,et al.  MMC03-4: On the Optimal Scheduling for Media Streaming in Data-driven Overlay Networks , 2006, IEEE Globecom 2006.

[9]  Reza Rejaie,et al.  PRIME: Peer-to-Peer Receiver-drIven MEsh-Based Streaming , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[10]  Diego Perino,et al.  PULSE: An Adaptive, Incentive-Based, Unstructured P2P Live Streaming System , 2007, IEEE Transactions on Multimedia.

[11]  Lifeng Sun,et al.  Understanding the Power of Pull-Based Streaming Protocol: Can We Do Better? , 2007, IEEE Journal on Selected Areas in Communications.

[12]  Rakesh Kumar,et al.  Stochastic Fluid Theory for P2P Streaming Systems , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[13]  Yong Liu On the minimum delay peer-to-peer video streaming: how realtime can it be? , 2007, ACM Multimedia.

[14]  Mung Chiang,et al.  Performance bounds for peer-assisted live streaming , 2008, SIGMETRICS '08.

[15]  Giuseppe Bianchi,et al.  A Theory-Driven Distribution Algorithm for Peer-to-Peer Real Time Streaming , 2008, IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference.