BALANCING THROUGHPUT, ROBUSTNESS, AND IN-ORDER DELIVERY IN P2P VODBin Fan, David G. Andersen, Michael Kaminsky†, Konstantina Papagiannaki †Carnegie Mellon University, †Intel Labs Pittsburgh

Presented by Haoming Fu

INDEX

INTRODUCTION TRS TRADEOFF BALANCING THE TRADEOFF EVALUATION CONCLUSION

1, INTRODUCTION

P2P Background Important Metrics VOD Goals

P2P BACKGROUND

P2P file transfer: Bit Torrent, Emule VoD(Video on Demand): PPLive Live Streaming: 中大网络电视 (no terminal

software, centralized solution?)

Features of VoD: Demand sequentiality for playback while

downloading chunks. Desire short buffering time but not low downloading time.

Less synchrony, permit longer buffering time(though not desired), jump & skip.

IMPORTANT METRICS

(T)hroughtput: the number of bytes downloaded per second

(R)obustness: the ability to maintain high throughput in face of network conditions such as node failure, arrival/departure and heterogeneity of users’ bandwidth.

(S)equentiality: the order of chunk arrival.

What we actually want is: high sequential throughput with tolerable robustness.

VOD GOALS

Useful chunks: a subset of chunks in a contiguous sequence from the start of the file.

Useful chunks

VOD GOALS

Buffer time

Out of buffer

Slope: playback rate

2, TRS TRADEOFF

Model Assumptions and Metrics Definitions & Assumptions Throughput Robustness Sequentiality

Three Basic Schemes Tradeoff Theorem

DEFINITIONS & ASSUMPTIONS

Downlink capacity is not bottleneck. Leave once a node has all chunks. Steady state: #the rate of departures =

#the rate of new arrivals, thus the population size of the swarm is stable.

Bandwidth allocation: Seed and peers allocate their uplink bandwidth capacity uniformly among the chunks that they are serving.chunk 1 3 4 8

chk 1 2 4 5 7 8 10

bandwidth

DEFINITIONS & ASSUMPTIONS

Ci: the sum of the share of the uplink bandwidth allocated for chunk i from the seed and all other peers.

THROUGHPUT

It’s safe to assume there is only one seed in the swarm since seeds are homogeneous(同质的 ).

gi: the seed allocates a fraction gi of its uplink bandwidth to chunk i.

fi: on average a peer allocates fi.

THROUGHPUT

Theorem 1: for a system in steady state,

b: chunk size : maximal arrival rate

Proof:

Steady state: Qi(T)/T is the rate of replicating chunk i, which

is bounded by the per-chunk capacity Ci/b. Therefore < <=Ci/b, for all i.

num of chunk i’s copies

peers go

peers come

THROUGHPUT

By eq.(1) and eq.(2), we have

Chunk k is the bottleneck chunk. Apply a little law: to eq.(3), we have

T is the average downloading time.

THROUGHPUT

Applying Theorem 1, N= T, We get the lower bound for T,

ROBUSTNESS

denotes the probability of a peer being “bad”(e.g. slow; failing)

ri be the number of available sources that each peer can download chunk i from

Intuitively, it is the probability of having at least one good source to download from.

ROBUSTNESS

In steady state, the probability for a randomly selected peer to have x chunks is 1/M, for x = 0;1;…; M-1.

the expected number of chunks that a random peer has downloaded is

R’s upper bound:

Total number of chunks

SEQUENTIALITY

useful chunksDenote U(x) as the fraction of useful chunks given x downloaded chunks.

0 <= S <= 1

e.g U(400) = 300/400

2, TRS TRADEOFF

Model Assumptions and Metrics Three Basic Schemes

Rarest Random Naive(幼稚的 ) Sequential Cascading(瀑布 )

Tradeoff Theorem

RAREST RANDOM

The probability for a peer that has downloaded x chunks to have any particular chunk i is x/M.

BT

Throughput

Apply theorem 1, we have

Lower bound! Perfect throughput.

RAREST RANDOM

Robustness

Thus,

Upper bound! Perfect robustness.

Sequentiality Completely no sequentiality.

#num of peers having x chunks

#pro of having chunk i

NAIVE SEQUENTIAL

Note, only peers with i, i+1, …, M chunks have chunk i.

In steady state, the number of peers with 0, 1, …, M-1 chunks is N/M.

Throughput CM is contributed only by

seeds.

CM is bottleneck, & Naive Sequential is unstable.

NAIVE SEQUENTIAL

Robustness

Sequentiality

CASCADING

Highest throughput, if the seed is not the bottleneck, the downloading time is

Lowest robustness, intuitively, when one link breaks down, the whole

chain collapses.

Fully sequentiality.

2, TRS TRADEOFF

Model Assumptions and Metrics Three Basic Schemes Tradeoff Theorem

TRADEOFF THEOREM

Theorem 2. A P2P VoD system can not simultaneously maximize throughput, robustness and sequentiality.

Proof Assume otherwise. Maximized T:

Maximized S: a seed has i, then has i-1, …, 1 Maximized R: serve all the chunks it has i < j, then Ci < Cj, contradiction!

3, BALANCING THE TRADEOFF

Hybrid Strategy Segment Random Many More in the Space

HYBRID STRATEGY

Combine rarest first and naive sequential. download a chunk according to naive

sequential with pro , according to random with 1-s.

higher s improves sequentiality but may reduce the system throughput.

grey: x

xsx(1-s)

HYBRID STRATEGY

Discussion: bandwidth division1. Downlink capacity d, playback rate q. d > q.Download sequentially at rate q, while

randomly at d-q?When q/d 1, it degenerate to NS.

2. Dynamic scheme. With enough useful chunks buffered, s is low?

Useful chunks buffered not enough s increase low throughput further not enough s increase …

SEGMENT RANDOM

The Segment random strategy groups all M chunks of the file into K segments, each of which consists of W chunks.

Segments in order Chunks random

chunk

segment

SEGMENT RANDOM

peers downloading chunks in the last segment can help upload this last segment.

W large, RF K large, NS

4, EVALUATION

Experiment Setup TRS Tradeoff in Emulation Buffering Time

EXPERIMENT SETUP

1 seed, 50 peers 10 Mbps up, 20 Mbps down, 10 ms latency For robustness measurement, “bad” nodes:

heterogeneous nodes (one third are significantly slower: 2 Mbps up and 5 Mbps down)

TRS TRADEOFF IN EMULATION

high throughput

7.33, robust

awful seq

BUFFERING TIME

Only when sequential throughput is high, can the buffering time become low.

beautiful aweful

5, CONCLUSION

TRS Tradeoff Theorem.

THANK YOU!

Any questions, remarks or objections?

RAREST RANDOM

The chunks are uniformly distributed among peers, thus the probability for a peer that has downloaded x chunks to have any particular chunk i is x/M. (BT)

chunk i obtains 1/x of the uplink bandwidth if it has been downloaded already (with probability x/M) 0 with pro 1-x/M

RAREST RANDOM

Throughput

, we have

Apply theorem 1, we have

Lower bound! Perfect throughput.

RAREST RANDOM

Robustness

In steady state, peers are downloading equally rapidly so the number of peers having x chunks (x = 0;1;…;M-1) is N/M, we have

Thus,

Upper bound! Perfect robustness.

RAREST RANDOM

Sequentiality

We have,

Completely no sequentiality.