BALANCING THROUGHPUT,
ROBUSTNESS, AND IN-ORDER
DELIVERY IN P2P VOD
Bin 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
Slope: playback
rate
Out of
buffer
Buffer time
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
chk 1
3
2
4
4
5
bandwidth
7
8
8
10
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

num of chunk
i’s copies
Proof:
peers go
peers come
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.
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

Total number
of chunks

R’s upper bound:
SEQUENTIALITY
useful chunks
Denote 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
#num of peers
having x chunks
#pro of having chunk i

Thus,

Upper bound! Perfect robustness.
Sequentiality
 Completely no sequentiality.

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.

grey: x
xs
higher s improves
sequentiality but may
reduce the system
throughput.

x(1-s)
HYBRID STRATEGY
Discussion: bandwidth division
1. 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.
chunk
segment
Segments in order
 Chunks random

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
7.33, robust
awful seq
high
throughput
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.