Analysis of Different Models Analysis of Different Models for Optimal P2P Content for Optimal P2P Content

Distribution NetworkDistribution Network

Subhamoy GhoshSubhamoy Ghoshsghosh@cc.hut.fisghosh@cc.hut.fi

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

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.

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.

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:

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:

Analysis of Next-Step Problem

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:

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.

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.

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.

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Thanks to all !