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2011, 1(4): 611-626. doi: 10.3934/naco.2011.1.611

## A stochastic fluid model for on-demand peer-to-peer streaming services

 1 Graduate School of Informatics, Kyoto University, Yoshida Honmachi, Sakyo-ku, Kyoto 606-8501, Japan 2 Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501

Received  May 2011 Revised  August 2011 Published  November 2011

On-demand video streaming services have become popular in recent years. In current streaming services, however, the growth of user population leads to the lack of the upload rate of the video server. This mainly causes starvation in the playout buffer at a client, resulting in the degradation of user-level quality of service (QoS). In this paper, we consider an on-demand streaming service based on a peer-to-peer (P2P) technology. Focusing on the stochastic behavior of streaming data contents in the playout buffer at a client peer, we consider an analytical stochastic fluid model, which takes into account the heterogeneity among peer nodes and the peer churn. We derive the starvation probability that the playout buffer is empty. Numerical examples show that the starvation probability increases when the population of peer nodes grows. It is also shown that even when the population of peer nodes is extremely large, a small increase in the upload rate at ordinary-peer nodes significantly improves the QoS of P2P streaming services.
Citation: Shuichiro Senda, Hiroyuki Masuyama, Shoji Kasahara. A stochastic fluid model for on-demand peer-to-peer streaming services. Numerical Algebra, Control & Optimization, 2011, 1 (4) : 611-626. doi: 10.3934/naco.2011.1.611
##### References:
 [1] B. Cohen, Incentives build robustness in BitTorrent,, 2003. Available from: , (). [2] F. Clevenot-Perronnin, P. Nain and K. W. Ross, Multiclass P2P networks: Static resource allocation for bandwidth for service differentiation and bandwidth diversity,, Performance Evaluation, 62 (2005), 32. [3] , eDonkey., Available from: , (). [4] R. Gaeta, M. Gribaudo, D. Manini and M. Sereno, Analysis of resource transfers in peer-to-peer file sharing applications using fluid models,, Performance Evaluation, 63 (2006), 149. [5] , Gnutella., Available from: , (). [6] S. Guha, N. Daswani and R. Jain, An experimental study of the Skype peer-to-peer VoIP system,, Proceedings of IPTPS'06, (2006). [7] X. Hei, C. Liang, J. Liang, Y. Liu and K. W. Ross, A measurement study of a large-scale P2P IPTV system,, IEEE Transactions on Multimedia, 9 (2007), 1672. doi: 10.1109/TMM.2007.907451. [8] D. Jurca, J. Chakareski, J. P. Wagner and P. Frossard, Enabling adaptive video streaming in P2P systems,, IEEE Communications Magazine, 45 (2007), 108. doi: 10.1109/MCOM.2007.374427. [9] V. G. Kulkarni, Fluid models for single buffer systems,, in, (1997), 321. [10] R. Kumar, Y. Liu and K. Ross, Stochastic fluid theory for P2P streaming systems,, Proceedings of IEEE INFOCOM, (2007), 919. [11] G. Latouche and V. Ramaswami, A logarithmic reduction algorithm for Quasi-Birth-Death processes,, Journal of Applied Probability, 30 (1993), 650. doi: 10.2307/3214773. [12] G. Latouche and V. Ramaswami, "Introduction to Matrix Analytic Methods in Stochastic Modeling,", ASA-SIAM Series on Statistics and Applied Probability, (1999). doi: 10.1137/1.9780898719734. [13] G. Latouche and T. Takine, Markov-renewal fluid queues,, Journal of Applied Probability, 41 (2004), 746. doi: 10.1239/jap/1091543423. [14] R. M. Loynes, The stability of a queue with non-independent inter-arrival and service times,, Proc. of the Cambridge Philosophical Society: Mathematical and physical sciences, 58 (1962), 497. [15] J. Lu, Signal processing for Internet video streaming: A review,, Proc. SPIE Image and Video Communications and Processing, 3974 (2000), 246. [16] , Nielsen // Netratings Adds 'Total Minutes' Metric to Syndicated Service as Best Measure of Online Engagement., Available from: , (). [17] , PPLive., Available from: , (). [18] D. Qiu and S. Srikant, Modeling and performance analysis of BitTorrent-like peer-to-peer networks,, Proc. ACM SIGCOMM 2004, (2004), 367. [19] V. Ramaswami, Matrix analytic methods for stochastic fluid flows,, Proc. the 16th International Teletraffic Congress, (1999), 1019. [20] A. da Silva Soares, "Fluid Queues Building upon the Analogy with QBD Processes,", Doctoral Dissertation, (2005). [21] , SopCast., Available from , (). [22] T. Takine, Single-server queues with Markov-modulated arrivals and service speed,, Queueing Systems, 4 (2005), 7. doi: 10.1007/s11134-004-5553-9. [23] , YouTube., Available from , (). [24] X. Zhang, J. Liu, B. Li and T. S. P. Yum, CoolStreaming/DONet: A data-driven overlay network for peer-to-peer live media streaming,, Proc. IEEE INFOCOM 2005, 3 (2005), 2102.

show all references

##### References:
 [1] B. Cohen, Incentives build robustness in BitTorrent,, 2003. Available from: , (). [2] F. Clevenot-Perronnin, P. Nain and K. W. Ross, Multiclass P2P networks: Static resource allocation for bandwidth for service differentiation and bandwidth diversity,, Performance Evaluation, 62 (2005), 32. [3] , eDonkey., Available from: , (). [4] R. Gaeta, M. Gribaudo, D. Manini and M. Sereno, Analysis of resource transfers in peer-to-peer file sharing applications using fluid models,, Performance Evaluation, 63 (2006), 149. [5] , Gnutella., Available from: , (). [6] S. Guha, N. Daswani and R. Jain, An experimental study of the Skype peer-to-peer VoIP system,, Proceedings of IPTPS'06, (2006). [7] X. Hei, C. Liang, J. Liang, Y. Liu and K. W. Ross, A measurement study of a large-scale P2P IPTV system,, IEEE Transactions on Multimedia, 9 (2007), 1672. doi: 10.1109/TMM.2007.907451. [8] D. Jurca, J. Chakareski, J. P. Wagner and P. Frossard, Enabling adaptive video streaming in P2P systems,, IEEE Communications Magazine, 45 (2007), 108. doi: 10.1109/MCOM.2007.374427. [9] V. G. Kulkarni, Fluid models for single buffer systems,, in, (1997), 321. [10] R. Kumar, Y. Liu and K. Ross, Stochastic fluid theory for P2P streaming systems,, Proceedings of IEEE INFOCOM, (2007), 919. [11] G. Latouche and V. Ramaswami, A logarithmic reduction algorithm for Quasi-Birth-Death processes,, Journal of Applied Probability, 30 (1993), 650. doi: 10.2307/3214773. [12] G. Latouche and V. Ramaswami, "Introduction to Matrix Analytic Methods in Stochastic Modeling,", ASA-SIAM Series on Statistics and Applied Probability, (1999). doi: 10.1137/1.9780898719734. [13] G. Latouche and T. Takine, Markov-renewal fluid queues,, Journal of Applied Probability, 41 (2004), 746. doi: 10.1239/jap/1091543423. [14] R. M. Loynes, The stability of a queue with non-independent inter-arrival and service times,, Proc. of the Cambridge Philosophical Society: Mathematical and physical sciences, 58 (1962), 497. [15] J. Lu, Signal processing for Internet video streaming: A review,, Proc. SPIE Image and Video Communications and Processing, 3974 (2000), 246. [16] , Nielsen // Netratings Adds 'Total Minutes' Metric to Syndicated Service as Best Measure of Online Engagement., Available from: , (). [17] , PPLive., Available from: , (). [18] D. Qiu and S. Srikant, Modeling and performance analysis of BitTorrent-like peer-to-peer networks,, Proc. ACM SIGCOMM 2004, (2004), 367. [19] V. Ramaswami, Matrix analytic methods for stochastic fluid flows,, Proc. the 16th International Teletraffic Congress, (1999), 1019. [20] A. da Silva Soares, "Fluid Queues Building upon the Analogy with QBD Processes,", Doctoral Dissertation, (2005). [21] , SopCast., Available from , (). [22] T. Takine, Single-server queues with Markov-modulated arrivals and service speed,, Queueing Systems, 4 (2005), 7. doi: 10.1007/s11134-004-5553-9. [23] , YouTube., Available from , (). [24] X. Zhang, J. Liu, B. Li and T. S. P. Yum, CoolStreaming/DONet: A data-driven overlay network for peer-to-peer live media streaming,, Proc. IEEE INFOCOM 2005, 3 (2005), 2102.
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