Performance Comparison of Scheduling Algorithms for PeertoPeer Collaborative File Distribution

1
Performance Comparison of Scheduling Algorithms
for Peer-to-Peer Collaborative File Distribution

• Presented by Chan Siu Kei, Jonathan
• Supervisors Prof. VOK Li, Dr. KS Lui

2
Overview

• Introduction
• Communication Model
• Analysis
• Scheduling Algorithms
• - Rarest Piece First
• - Most Demanding Node First
• - Maximum-Flow Algorithms
• Simulation Results
• Future Work
• Conclusion

3
Introduction

• P2P file sharing applications are highly popular
  in the Internet, e.g. BitTorrent, Gnutella,
  Kazaa, Napster, etc.
• More scalable (faster) compared with traditional
  client/server approach (e.g. FTP)
• Former research focuses on topics like overlay
  topology formation, peer discovery, content
  search, fairness and incentive issues, etc. But
  seldom look into the data distribution scheduling
  problem
• We present the first effort and propose a novel
  Maximum-Flow algorithm to better solve the problem

4
Communication Model

• Synchronous Scheduling
• - same transmission time for every pair of nodes
• Asymmetric Bandwidth
• - send p pieces out, receive q pieces in for
  each cycle

5
Notations and Definitions

• N no. of peers, M no. of file pieces
• F F1, F2, , FM
• P NxM possession matrix,
• Pij 1 iff node i possesses file piece Fj,
  otherwise Pij 0
• Pt possession matrix at time t
• p p1,p2,,pN (upload limit vector),
• q q1,q2,,qN (download limit vector)

p 1,1,2,2,2, q 2,3,2,3,3
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Schedule (1)

• Specifies which file pieces each peer has to send
  out and to whom
• A possible schedule for P0 with p1,1,2,2,2,
  q2,3,2,3,3
• - Node 1 send piece 3 to node 2
• - Node 2 send piece 4 to node 1
• - Node 3 send piece 5 to node 1
• send piece 5 to node 2
• - Node 4 send piece 6 to node 2
• send piece 6 to node 3
• - Node 5 send piece 2 to node 4
• send piece 7 to node 4
• Formally, we use NxM matrix Sk to represent the
  schedule at cycle k. From Sk, we can derive
  transmission matrix Tk (NxM)

e.g. Node 1 receives piece 4 from Node 2, piece 5
from Node 3 gt and
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Schedule (2)

• Given Pk-1 and the schedule Sk-1, Tk-1, the
  possession matrix at next cycle k is Pk Pk-1
  Tk-1 (k gt 0)
• The distribution terminates after certain, say k0
  cycles, until
• Our goal is to minimize k0, which is the time
  needed for complete distribution

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Analysis on Lower Bound (1)

• Let p p1,p2,,pN, q q1,q2,,qN be the
  upload and download limit vectors.
  , ,
• Let ri be the total no. of 0s across row i, i.e.
  , the min. value of k0 is given by
• Let cj be the total no. of 1s along column j,
  i.e. , we can find the minimum no. of
  1s along all columns, , the
  min. value of k0 is given by
• Let z be the total no. of 0s in P, i.e.
  , the min. value of k0 is given by

(1)
(2)
(3)
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Analysis on Lower Bound (2)

• Combining (1),(2),(3), the lower bound k0 is
  given by

(4)
From (1),
From (2),
From (3),
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Rarest Piece First (RPF)

• Borrowed from the Rarest Element First algorithm
  employed in BitTorrent
• Rarity cj of piece j is the no. of peers who have
  piece j, i.e.

RPF Node-Oriented (p1,1,2,2,2,
q2,3,2,3,3)

RPF Piece-Oriented (p1,1,2,2,2,
q2,3,2,3,3)

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Most Demanding Node First (MDNF)

• Demand di of node i is the no. of un-received
  pieces for node i, i.e.
• When choosing recipients, prefer sending to the
  node with largest di

MDNF Node-Oriented (p1,1,2,2,2,
q2,3,2,3,3)
6
6

4
4
5
MDNF Piece-Oriented (p1,1,2,2,2,
q2,3,2,3,3)
6
6

4
4
5
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Problem with RPF and MDNF

• The max. no. of transmissions for each cycle
  cannot be achieved

Using MDNF Piece-Oriented (p2,2,2,1,
q2,1,2,2) only 6 transmissions can be
scheduled (but the max. is 7)
MDNF (only 6 transmissions)
Maximum is 7 transmissions
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Maximum-Flow (MaxFlow)
Let G (V,E) to be the flow network graph
L L1, L2, , LN
R R1, R2, , RN
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Maximum-Flow (MaxFlow)

• Edmonds-Karp Algorithm
• Find augmenting paths using BFS
• Guarantee to find maximum of transmissions in
  each cycle
• Complexity

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MaxFlow Counter Example

• Pure MaxFlow performance is unsatisfactory, as it
  does not consider whether we can match more in
  subsequent cycles

Using MaxFlow, total 3 cycles are needed
(p2,2,2,2,2, q3,3,3,3,3)

Using RPF Node-Oriented, only 2 cycles are
needed (p2,2,2,2,2, q3,3,3,3,3)
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MaxFlow - Weighted

• Put weights on both sides to give priorities to
  some nodes during searching
• Weights on Li (sum of the no. of 0s in
  other peers for those pieces that peer i has)
• Weights on Bij dij (sum of the no. of 0s across
  row i and column j)
• E.g.
• d42 7

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MaxFlow WeightedCounter Example
For p2,2,2,2,2, q3,3,3,3,3
Using MaxFlow Weighted, total 3 cycles are
needed
P3 1
Using MDNF Piece-Oriented, only 2 cycles are
needed
P2 1
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MaxFlow Dynamically-Weighted

• Allows the weights to be dynamically varied
  within each scheduling cycle

? 15,14,25,13,15,10,16,16 and d43 9 which
is the greatest value among all dij
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Simulation Results (1)
Fig. 1 Performance comparison of various
scheduling algorithms (All) with varying peer
sizes (file size 100, pi 2, qi 3, equal
probability for 1s and 0s)
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Simulation Results (2)
Fig. 2 Performance comparison of various
scheduling algorithms (Representative) with
varying peer sizes (file size 100, pi 2, qi
3, equal probability for 1s and 0s)
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Simulation Results (3)
Fig. 3 Performance comparison of various
scheduling algorithms (Representative) with
varying file sizes (peer size 10, pi 2, qi
3, equal probability for 1s and 0s)
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Future Work

• Study the case of asynchronous scheduling, where
  the transmission time is different for different
  pairs of nodes
• Study the case when the network is dynamic in
  nature, where peers can come and go at any
  instant and they may shift to communicate with
  different sets of peers during the distribution
  process

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Conclusion

• The data distribution problem in P2P networks is
  not well studied in previous research
• We formally define the collaborative file
  distribution problem with the possession and
  transmission matrix formulations
• We also deduce a theoretical bound for the
  minimum distribution time required
• We develop several types of algorithms (RPF,
  MDNF, MaxFlow) for solving the problem
• Our novel dynamically-weighted max-flow algorithm
  outperforms all other algorithms by simulations

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Thank You!

• QA