Insights from modeling P2P content distribution

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Insights from modeling P2P content distribution

• Dah Ming Chiu, Chinese University of Hong Kong
• Summer, 2007

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What is P2P content distribution?

• BitTorrent, CoolStreaming, PPlive
• Sending a file, or video stream to a large number
  of peers, with the help of peers
• Producing the most Internet traffic today
• What IP multicast tried to support
• Application layer multicast
• Leverage on peers uplink capacity
• Leverage on peers storage
• Modeling these systems insights

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Some basic questions

• Scalability what happens when peers increases
• Capacity makespan for downloading a file, or
  rate for streaming
• Price of incentive keeping high-contribution
  peers around longer improves system performance
• The last piece problem and the time it takes to
  get each piece in file sharing
• The effect of piece selection strategy on
  continuity and delay in streaming

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Three kinds of models

• Capacity models
• Bandwidth constraint X can help Y if X has
  enough uplink capacity
• What is the maximum rate each peer gets served?
• Population models
• Content availability constraint X can help Y if
  X has the content Y needs
• What is the population of each type of peers,
  hence max rate?
• Peers content model
• Assume homogeneous peers
• What is in a peers buffer for playback?

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The uplink sharing model

• Mundingers thesis
• Assume
• only uplinks can be bottlenecks
• heterogeneous peers (with different uplink
  bandwidths)
• What is the minimum makespan?

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Uplink sharing model related work

• Previous work
• The broadcast problem (unidirectional telephone
  model)
• The broadcast problem (bidirectional telephone
  model)
• Simultaneous send/receive model
• Uplink sharing model heterogeneous peers
• Solve a finite number of mixed integer
  programming (MILP) problems (for small number of
  file parts M)
• Fluid limit solution (for large M)

J Mundinger et al, Analysis of Peer-to-peer File
Dissemination amongst Users of Different Upload
Capacities, IFIP Performance, Nov 2005.
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Uplink sharing model main result

• Maximum throughput
• R minC0, (C0?Ci)/n
• R is clearly the upper bound
• The bound can be achieved if content is fluid

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Achieving the upper bound

• Use multiple spanning trees
• 1 1-hop tree (server sends to all peers)
• n 2-hop trees (server sends to 1 peer, which
  forwards content to rest of the peers)
• Use the 2-hop trees as much as possible, till
  either
• Server used up its bandwidth
• Peers used up their uplink bandwidth
• In case 2, server uses rest of bandwidth for
  1-hop tree

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Some subsequent work

• Use the maximum capacity to show that network
  coding cannot further help throughput
• DM Chiu et al, Can Network Coding Help in
  P2P Networks, invited talk at 2nd Network Coding
  workshop, April 2006.
• For two (or more) classes of users, show the
  trade-off of fairness and performance
• B Fan, DM Chiu, JCS Lui, The delicate
  trade-off in BitTorrent-like file sharing
  protocol design, IEEE ICNP, Oct 2006.
• For streaming, show how to allocate the total
  uplink bandwidth to two classes of peers
• R Kumar, Y Liu, K Ross, Stochastic Fluid
  Theory for P2P Streaming Systems, IEEE Infocom,
  May 2007.

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A generalized queueing system

• Peers are both customers as well as servers
• Peers arrive with rate lambda, but service rate
  given by the maximum rate R formula
• For homogeneous peers, it is like a M/M/inf queue
  infinitely scalable performance depends on
  each peers contribution
• For heterogeneous peers, the situation is more
  interesting

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Stochastic uplink sharing model

• Two or more classes of peers
• Consider different ways to share uplink capacity
• Allocation that minimize avg downloading time
• Max-min allocation
• Fair allocation
• fair more contribution more allocated

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Mean value analysis

• Ui ? Di
• ui ? Ui
• di ? Di
• ?di ?ui
• Ni pi?/di
• ?uiNi ? ? ?piui/di 1
• T ? Ni/? ? pi/di
• These equations gives the feasible set of ui and
  di

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The performance vs fairness tradeoff

• Performance avg downloading time
• Fairness variance of share ratio
• Share ratio ui/di
• better downloading time ? more uneven share ratio
• Pareto trade-off curve

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What does BitTorrent do?

• Tit-for-tat equal share ratio (roughly)
• Optimistic unchoking random
• max-min sharing (roughly)
• BT peer selection is 4/5 Tit-for-tat and 1/5
  random
• Possible to use different ratio for different
  trade-off

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Three kinds of models - continued

• Capacity models
• Population models
• Peers content model

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Coupon replication model

• A collection of coupons
• Each peer arrives with one coupon initially
• Each peer collects additional coupons till
  completion
• A Markov Chain
• Can solve it for special cases
• Get coupon from peer in same layer (layered)
• Random (flat)

L Massoulie and M Vojnovic Coupon Replication
Systems, ACM Sigmetrics 2005, best paper
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Some results from coupon collection

• For scaled up system
• Get population size (of each layer)
• Get sojourn time in each layer and total time
  (via Littles Law)
• For layered, T K O(1)
• For random, 1
• T ? K O(sqrt(K))
• Note, in this model, there is no uplink bandwidth
  constraint

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Extension to the Coupon paper

• MH Lin et al, Stochastic Analysis of File
  Swarming Systems, to appear IFIP Performance
  2007
• Obtained a tighter bound T K log(K) O(1)
• Also tighter results for time in each layer,
  Ti, the last piece problem
• When peers have uplink bandwidth constraint, the
  sojourn time bound is increased by 1/(1- e-1)

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Three kinds of models - continued

• Capacity models
• Population models
• Peers content model

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Simple peer model

• M homogeneous peers
• Each has a playback buffer
• In each time slot, the server uploads one peer
  with probability 1/M
• Without P2P network
• continuity p(n)
• 1/M

server
playback
1/M
1/M
M peers
1/M
YP Zhou et al, A simple model for analyzing p2p
streaming protocols, to appear ICNP 2007
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Sliding window

• Each peers buffer is a sliding window
• In each time slot, each peer downloads from a
  random neighbor
• q(i) the probability Bufi gets filled

p(1)1/M p(n)?
timet
sliding window
t1
p(1)1/M p(i1) p(i) q(i)

• q(i) w(i)h(i)s(i)
• w(i) peer wants to fill Bufi
• h(i) the selected peer has the content for
  Bufi
• s(i) Bufi determined by chunk selection
  strategy

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Chunk selection strategies

• Greedy
• try to fill the empty buffer closest to playback
• Rarest First
• try to fill the empty buffer for the newest
  chunk
• since p(i) is an increasing function, this means
  Rarest First

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Chunk selection strategy - cont

• Greedy
• p(i1) p(i) p(i) (1- p(i)) (1- p(1) - p(n)
  p(i1))
• Rarest first
• p(i1) p(i) p(i) (1- p(i))2
• Also studied
• continuous forms for these difference equations
• simulation

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Which strategy is better?

• What do you mean by better?
• Playback continuity p(n) as large as possible
• Start-up latency ? p(i) as small as possible
• Given buffer size (n) and relatively large peer
  population (M)
• Rarest first is better in continuity!
• Greedy is better in start-up latency

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Numerical result

• M1000
• N40
• In simulation,
• neighbors60
• Uploads at most 2 in each time slot

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Mixed strategy

• Partition the buffer into 1,m and m1,n
• Use RF for 1,m first
• If no chunks available for download by RF, use
  Greedy for m1,n
• Difference equations become
• p(1) 1/M
• p(i1) p(i) p(i) (1- p(i))2
  for i 1,,m-1
• p(i1) p(i) p(i) (1- p(i))(1- p(m)- p(n)
  p(i1)) for i m, n-1

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Comparison

• For different buffer sizes
• Mixed achieves better continuity than both RF
  and Greedy
• Mixed has better start-up latency than RF

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Closer look with simulation

• Simulate 2000 time slots
• Continuity is the average of all peers
• Continuity for Mixed is more consistent, as well
  highest

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Adapting m to unknown population

• Adjust m so that p(m) achieves a target
  probability (e.g. 0.3)
• In simulation study, 100 new peers arrive every
  100 slots
• m adapts to a larger value as population increases

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Related works

• Coolstreaming
• A prototype and experiments, demonstrating
  RF-like strategy works well for large-scale P2P
  streaming
• X Zhang et al, Coolsteaming/donet A
  data-driven overlay network for efficient live
  media streaming, IEEE Infocom 2005
• BiTos
• Proposed something similar to our Mixed
  strategy, with a simulation study
• A Vlavianos, M Iliofotou, M Faloutsos, Bitos
  Enhancing bit-torrent for supporting streaming
  applications IEEE Infocom 2006

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The major contributors
Yipeng Zhou 1st year M.Phil student from USTC
Minghong Lin 1st year M.Phil student from USTC
Bin Fan also from USTC finished M.Phil won a
generous fellowship to study for
PhD at CMU