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Analysis of Movie Replication and Benefits of Coding in P2P VoD

Yipeng Zhou

Aug 29, 2012

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Outline

Movie Replication Introduction Problem Formulation Analysis of Scheduling Algorithm Simulation Results

Benefits of Coding for VoD Background Analysis Simulation Results

Conclusion23/4/19

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Introduction

Objective is to minimize server load by optimizing movies replicated by different peers.

2012-5-10

Practical System:

PPTV

PPStream

UUSee

Challenge:

How to organize peers share content? Scheduling

How to place right content on peers? Replication

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Related Work Scheduling strategy and Movie

Replication strategy are not analyzed separately.

Not covered Topology: Any pair of peers can talk with each other.

However, the number of simultaneously communicated peers is limited.

No Coding: Only a complete copy is replicated by a peer to simplify model complexity.

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To simplify analysis, we assume:

Homogeneous movies. Homogeneous peers. (Same upload capacity & storage) Total peers’ uplink capacity is equal to total demand. View Upload Decoupling. No start-up delay, buffer is not considered

Assumption

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Closed queuing network model N users, continuously watching movies. Select a movie, watch for a random period. After viewing a movie, select another movie based on

transition probability matrix. By solving a fixed point equation, derive stationary

popularity of movies.

User Behavior ModelN users continuously generate N viewing requests

[D. Wu et al, Infocom’09 best paper]

Relative popularity: for movie j and

K

jj

1

1

The peer population to view movie j follows Binomial Distribution.

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Movie Popularity Zipf distribution is used for movie popularity. All movies

are ranked by descending order of popularity.

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is a parameter in the range [0.271, 1].

[N. Venkatasubramanian et al, ICDCS 97]

is a key parameter.

Solution: Derive bound of server load to ignore the effect of Θ without considering long tail.

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Kong

Formulation

Qi is the set of movies replicated by peer i. L is the storage size of each peer.

Xj is the random variable to denote the bandwidth received by peers watching movie j from P2P system.

Xj is determined by request scheduling strategy and replication strategy.

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Kong

Formulation Cont.

It is still difficult to minimize the weighted variance. Fortunately, we can get the bound of average server load.

Balance BW Allocation

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Xj

Objective

Playback RatePlayback Rate

Fig. 1 timetime

Xj

Server load

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Request Scheduling Strategy

Fixed BW allocation(FBA) Fair Sharing

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FBA A virtual super server can be used to derive average

server load, as the figure shows.

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Super Server

Replication strategy: Proportional (to popularity) in homogeneous network.

It is easy to calculate the bandwidth allocated to a particular movie.

[D. Wu et al, Infocom mini 09]

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FBA Cont.

jSi

ij N

L

UCapacity

j

jNqE ]Re[#

Server load is:

K

j Capacityq

qCapacityqB1 Re#

)RePr(#*)Re(#

Binomial Distribution

Proportional to movie popularity.

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PFS and FSFD Both of perfect fair sharing (PFS) and fair

sharing with fixed degree (FSFD) are special cases of FS

PFS When a peer wants to stream movie j, it sends out sub-

requests to all peers storing movie j to fetch parts of that movie. When serving other peers, a peer treats all sub-requests the same.

FSFD When a peer wants to stream a movie j, it sends out

sub-requests to exactly y peers who store movie j.

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PFS

Received sub-requests by peer i in PFS is:

We use Poisson distribution as an approximation of Binomial distribution

We can derive the expected value and variance of Xj(i)

The distribution of Xj(i) is: )(#Pr])(Pr[ kreqk

UiX i

ij

Xj(i) is the random variable to denote the BW received by sending a sub-request to peer i for movie j.

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PFS Cont.

The variance of Xj

The correlation determines total variance.

The distribution of Xj(i) depends on the number of sub-requests received by peer i.

The number of sub-requests received by peer i depends on Qi

It is very complicated to get the distribution of Xj

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PFS Worst Case

Correlation is equal to 1 means that peers form K/L clusters. In each cluster, all peers store the same movie set. The movie set is random selected from the whole movie set.

The received requests is the same for all peers in the same clusters. The behavior of a cluster is like a super server. The server load can be derived exactly.

Cluster 1 store movie 1, 2,..L

Cluster 1 store movie L+1,L+2,..2L

Cluster L store movie K-L+1,..K

LKRRR /21 ...

KNLH /

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PFS Best Case

The upper bound is achieved when all peers have the same load λi and the bandwidth from different peers is independent.

Xj(i)s are independent identical distributed for different i. Normal distribution is used as approximation of Xj.

The required server load to support one peer is: The total serever load is:

N ...21 KNLH /

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Random Load Balancing Algorithm

Initialization

To minimize correlation

To balance bandwidth allocation

Bj = E[Xj]

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FSFD Each peer sends out exactly y sub-requests to randomly

selected peers replicating target movie. Similar to PFS, the received BW from one sub-request is:

ij iXE

1

)]([

Proportional replication strategy achieves the balanced bandwidth allocation since λi = y

1)]([][ iXEyXE jj

[J. Wu et al, Infocom mini 2009] [K. Suh et al, JSAC 2007]

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FSFD Worst Case

The received requests is perfect correlated for all peers in the same clusters. The behavior of a cluster is like a super server. The server load can be derived exactly.

Cluster 1 store movie 1, 2,..L

Cluster 1 store movie L+1,L+2,..2L

Cluster L store movie K-L+1,..K

Here, the difference from PFS is that the each peer sends only y sub-requests instead of sending sub-requests to all peers.

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FBA, PFS vs FSFD

Scheduling Strategy Optimal Replication Strategy

FBA Proportional

PFS RLB

FSFD Proportional

H = NL/K, which is the average storage resource.

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FSBDWhen a peer wants to stream a movie j, it sends out at most Y sub-requests to random selected peers who store movie j.

Balanced BW allocation, equivalent to E[Xj] = 1

Nk is the expected peer population to view movie k.

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FSBD Worst Case The worst case is similar to the worst case of PFS. But

there are two type clusters. In type I cluster: y = Y, similar to FSFD. In type II cluster: y = No. of Peers, similar to PFS.

Request

Sub- requestType I

An example with Y = 3

Type IIRequest

Sub- request

Type IIRequest

Sub- request

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FSBD Cont.

LK

ii NR

/

1

Type I Type II

Ri is the peer population of cluster i.

B is maximized whenγ = 1

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FSBD Cont.

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Performance comparison of FSBD with FSFD and PFS

The next question: design a replication strategy to work no matter what the bound of out-degree, i.e. Y

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DAR Algorithm

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N = 10000, Fix ratio of K/L= 50, Homo. movie popularity and peer uplink bandwidth

Bound Validation of PFS

COV 0

B = O(K/L)

B = O(Sqrt(NK/L))

COV 1

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Model Validation

FBA

Bound of PFS

FSFD

N=4000, K=400, L=4

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FSBD

DAR

DAR

ARLB

Proportional

N=4000, K=400, L=4

Proportional

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Outline

Movie Replication Introduction Problem Formulation Analysis of Scheduling Algorithm Simulation Results

Benefits of Coding for VoD Background Analysis Simulation Results

Conclusion23/4/19

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Background

For P2P, helper no. = peer no.

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Previous Work

[F. Liu et al, Infocom’11] adopts RS Coding.[Y. Kao et al, TPDS’11] adopts Network Coding.

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To simplify analysis, we assume:

Perfect View Upload Decoupling. Random Selected Enough Neighbors. Limited Downloading. No Encoding or Decoding Overhead. Discrete time slot.

Model & Assumption

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Model with d=1

For Greedy Strategy

For FF Strategy

Buffer map X X X X

1 2 3 4 5 6 7 8playback

FF Selection Greedy Selection N

Ip

N

i

i 1

8

)8(

Performance depends on p(n). Streaming cost is 1-p(n)

Helper

Selection

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Proposition 1: In a P2P system with perfect view-uploaddecoupling, the Greedy strategy is always the optimal strategy to maximize p(n, d).

Proposition 2: For two coding schemes using Greedy strategywith block size d1 and d2, if d1 < d2 and d2 is divisibleby d1, the streaming cost for coding scheme d2 is smaller thanthat for d1.

Main Result

It is a tradeoff between streaming cost and movie replication cost.

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Simulation

Helpers are assumed to have stored necessary encoded chunks.

Streaming cost decreases with d

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Simulation Cont.

A scenario with new movie.No helper replicates the new movie.

Two ways for new movie replication:1.Pushed from server.2.Distributed among helpers.

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We use a new approach to analyze three kinds of request scheduling strategies.

Real-world systems is likely to be in between fair sharing (with some fixed degree) and perfect fair sharing. Therefore, we propose a novel FSBD model with varying out-degree. This allows us to illustrate the effect of out-degree in request scheduling.

We use a simple mean field stochastic model to analyze the benefits by adopting coding for movie replication.

Conclusion

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The end

Thank you

Q & A