Analysis of Different Models for Optimal P2P Content Distribution Network

1. Analysis of Different Models for Optimal P2P Content Distribution Network Subhamoy Ghosh sghosh@cc.hut.fi

2. Agenda • Introduction • The Next – Step Problem • Analysis of the Next – Step Problem • Chunk – based CDS • Analysis of Chunk – based CDS • Discussion – Other Models: Merits/Demerits • Conclusion • References

3. Introduction • P2P systems – • designed to share computer resources by direct exchange, w/o any central authority. • Application overlay network on top of conventional protocols. • Fault-tolerant, reliable, scalable massive content distribution system. • Only possible option to manage flash crowds. • Content Distribution – • Has been the main focus of P2P research. • Responsibility is spread amongst all downloader(s). • Clients contribute resources of the system as a function of their upload capacities.

4. Introduction • Performance perceived by user – • Time taken to fulfill request for a particular file. • Download time as the dominant factor. • Generic trend for file dissemination – • Partition the file to N equal parts. • User can download either from server or from a peer who has the requested chunk.

5. The Next-Step Problem • Source node s divides a file into k equal parts to disseminate amongst n peers. • Assumptions: • Communications are synchronous. • Ignores link latencies • File reaches the destination in the same round, as the departure. • Graph G = (V,E) with |V| = n, W:VxV--->R • File is divided into k-parts such that: • Next – Step problem calculates the actions of each node, represented by Action Matrix:

6. The Next-Step Problem • Max-Product Belief Propagation Network – • Calculates the MAP estimates of the nodes. • Provides a vector of node beliefs and selects the action with the highest probability. • Algorithm converges, when a node receives duplicate packets for two consecutive rounds from all nodes. • With the Next-Step Solution and a pre-defined Cost function, the problem reduces to:

7. Analysis of Next-Step Problem

8. Optimizing Chunk-Based CDS • Provide a network model independent lower – bound on the time taken for file dissemination in a chunk – based CDS. • Makespan: Time taken to disseminate M parts of a file to I peers in a centralized scenario. • Assumptions: • Peers upload only 1 file in each round. • Upload capacities are considered to be equal. • Lower bound on minimum number of rounds for any CDS is: • Delay Stretch: Captures the delay in download of a peer, for sharing chunks with other peers. Maximum delaystretch is calculated as:

9. Analysis of Chunk – based CDS Scatter plots of data with M = 10 and M =50 [8]. • 100 independent simulations with N = 2, 4, …215. • In each case of M = 1 – 5, 8,10, 15, 20 ,50 fits a linear model.

10. Discussion – Other Models: Merits/Demerits • Maximize peer – bandwidth utilization: • P2P is scalable since bandwidth increases with increase in participants. • Models focus on i) peer selection strategy – self-organization, ii) chunk selection strategy - duplication, iii) network degree – choose in-degree/out-degree of client based on upload/download capacity. • Uniform Workload Distribution: • Fairness in workload minimizes average download time. • Incentive – driven P2P Networks: • Minimizes download time subject to budget constraint. • Network Coding based P2P CDS: • Improves delay in transmission time, and makes network more robust and adaptive. • But almost all models suffer from the churning problem, and network coding models do not perform well, in case multiple nodes fail to reach every client.

11. Conclusion • Loopy BP algorithm - • Approximate solution in case of cycled graphs, • Currently the experiment is terminated after a user-defined threshold of operations. • The authors in [1] consider to use gradient – descent algorithm here instead, to overcome this fluctuation in local optimum. • Pre-emptive operations in belief propagation - • improve on the computational delay and the final response on the choice of nodes. • The generic file dissemination approach - • equal service capacity for all peers, and the model can be extended to consider the case of selfish peers. • However it provides a model independent performance benchmark, that can be used to compare the dissemination times of different overlay networks.

12. References • Bickson Danny, Dolev Danny, Weiss Yales, Efficient Peer-to-Peer Content Distribution Network, School of Computer Sc. & Engg, Hebrew University of Jerusalem. • Zheng Xiaoying, Cho Chunglae, Xia Ye, Optimal Peer-to-Peer Techniques for Massive Content Distribution, IEEE INFOCOMM (2008). • Felber Pascal, Biersack W. Ernst, Cooperative Content Distribution: Scalability Through Self-Organization, LNCS 3460, pp 343-357 (2005). • Li Jin, Chou A. Philip, Zhang Cha, MutualCast: An Efficient Mechanism for Content Distribution in a P2P Network, ACM SIGCOMM Asia ‘04, Beijing, China (2004). • Hamra Al Anwar, Felber A. Pascal, Design Choices for Content Distribution in P2P Networks, ACM SIGCOMM, Vol 35, pp 29-40 (2005). • Tewari Saurabh, Kleinrock Leonard, On Fairness, Optimal Download Performance and Proportional Replication in P2P Networks, LNCS 3462, pp 709 – 717, IFIP (2005). • Adler Micah, Kumar Rakesh, Ross Keith, Rubenstein Dan, Suel Torston, Yao D. David, Optimal Peer Selection for P2P Downloading and Streaming, IEEE INFOCOMM, Vol. 3, pp 1538 – 1549 (2005). • Kangasharju Jakko, Kangasharju Jussi, An Optimal basis for Efficient P2P Content Distribution Algorithms, 15th . Intl. Conf. on Computer Communications and Networks, Washington D.C. (2006).

13. References • Mudinger Jochen, Weber Richard, Weiss Gideon, Optimal Scheduling of Peer-to-Peer File Dissemination, Mathematical Performance Modeling and Analysis (MAMA) (2006). • Loginova Oksana, Lu Haibin, Wang X. Henry, Peer-to-Peer Networks: A Mechanism Design Approach, JEL Classification, Working Papers, Dept. of Economics, University of Missouri (2007). • Androutsellis – Theotokis Stephanos, Spinellis Diomedis, A Survey of Peer-to-Peer Content Distribution Technologies, ACM Computing Surveys, Vol. 36, pp 335 – 371, (2004). • Small Tara, Li Baochun, Liang Ben, On Optimal Peer-to-Peer Topology Construction with Maximum Peer Bandwidth Contributions, Biennial Symposium on Communications, Kingston, Canada (2006).

14. Thanks to all !