balancing throughput, robustness, and in- order delivery in p2p vod bin fan, david g. andersen,...
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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.
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