Cache Capacity Allocation for BitTorrent-like Systems to Minimize - - PowerPoint PPT Presentation

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Cache Capacity Allocation for BitTorrent-like Systems to Minimize - - PowerPoint PPT Presentation

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Problem Definition Bandwidth Allocation Evaluation Conclusions Cache Capacity Allocation for BitTorrent-like Systems to Minimize Inter-ISP Traffic Valentino Pacifici, Frank Lehrieder, Gy orgy D an School of Electrical Engineering

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SLIDE 1

Problem Definition Bandwidth Allocation Evaluation Conclusions

Cache Capacity Allocation for BitTorrent-like Systems to Minimize Inter-ISP Traffic

Valentino Pacifici, Frank Lehrieder, Gy¨

  • rgy D´

an

School of Electrical Engineering Institute of Computer Science KTH Royal Institute of Technology University of W¨ urzburg Stockholm, Sweden W¨ urzburg, Germany

Orlando, March 29, 2012

  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 1 / 17

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SLIDE 2

Problem Definition Bandwidth Allocation Evaluation Conclusions P2P Traffic

P2P Traffic

  • Up to 70 % of network traffic
  • Source of Inter-ISP traffic ⇒ cost for low level ISPs

Decreasing Inter-ISP traffic

1 Locality awareness 2 P2P caching

Cache ISP 1 "rest of internet"

  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 2 / 17

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SLIDE 3

Problem Definition Bandwidth Allocation Evaluation Conclusions P2P Caching

P2P Caching

Cache resource management

1 Storage capacity ⇒ cache eviction (LRU,LFU,GDS,ARC,...) 2 Bandwidth ⇒ not actively managed (e.g. Web caches)

Should bandwidth be actively managed so as to minimize the amount of Inter-ISP traffic?

Cache ISP 1 "rest of internet"

  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 3 / 17

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SLIDE 4

Problem Definition Bandwidth Allocation Evaluation Conclusions P2P Caching

P2P Caching

Cache resource management

1 Storage capacity ⇒ cache eviction (LRU,LFU,GDS,ARC,...) 2 Bandwidth ⇒ not actively managed (e.g. Web caches)

Should bandwidth be actively managed so as to minimize the amount of Inter-ISP traffic?

Cache ISP 1 "rest of internet"

  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 3 / 17

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SLIDE 5

Problem Definition Bandwidth Allocation Evaluation Conclusions P2P Caching

P2P Caching

Cache resource management

1 Storage capacity ⇒ cache eviction (LRU,LFU,GDS,ARC,...) 2 Bandwidth ⇒ not actively managed (e.g. Web caches)

Should bandwidth be actively managed so as to minimize the amount of Inter-ISP traffic?

Cache ISP 1 "rest of internet"

  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 3 / 17

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Problem Definition Bandwidth Allocation Evaluation Conclusions System Model

System Model without Cache

  • Set of ISPs I = {1, . . . , I}, Set of swarms S = {1, . . . , S}
  • Markovian model of system dynamics
  • System state Zi,s(t) = (Xi,s(t), Yi,s(t))
  • Parameters (λi,s, θ, γ, µ, η)

qi,s λi,s θXi,s γYi,s

Swarm s, ISP i

Xi,s Yi,s qi,s = Xi,s Xs µ(ηXs + Ys)

  • available upload rate
  • Incoming inter-ISP traffic rate Ii,s(Zs(t), .)
  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 4 / 17

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Problem Definition Bandwidth Allocation Evaluation Conclusions System Model

System Model without Cache

  • Set of ISPs I = {1, . . . , I}, Set of swarms S = {1, . . . , S}
  • Markovian model of system dynamics
  • System state Zi,s(t) = (Xi,s(t), Yi,s(t))
  • Parameters (λi,s, θ, γ, µ, η)

qi,s λi,s θXi,s γYi,s

Swarm s, ISP i

Xi,s Yi,s qi,s = Xi,s Xs µ(ηXs + Ys)

  • available upload rate
  • Incoming inter-ISP traffic rate Ii,s(Zs(t), .)
  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 4 / 17

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SLIDE 8

Problem Definition Bandwidth Allocation Evaluation Conclusions System Model

System Model with Cache

  • Set of ISPs I = {1, . . . , I}, Set of swarms S = {1, . . . , S}
  • Markovian model of system dynamics
  • System state Zi,s(t) = (Xi,s(t), Yi,s(t))
  • Parameters (λi,s, θ, γ, µ, η,κi,s)
  • Ki < ∞ bandwidth capacity of cache in ISP i

qi,s λi,s θXi,s γYi,s

Swarm s, ISP i

Xi,s Yi,s qi,s = Xi,s Xs µ(ηXs + Ys)+κi,s

  • available upload rate
  • Incoming inter-ISP traffic rate Ii,s(Zs(t), κi,s(t))
  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 5 / 17

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Problem Definition Bandwidth Allocation Evaluation Conclusions Optimal Allocation

Cache Bandwidth Allocation Problem

  • Cache bandwidth allocation of ISP i at time t

κi(t) = (κi,1(t), . . . , κi,S(t))

  • Defined by policy π: κi(t) = Fπ
  • Z(u)
  • u<t,
  • κi(u)
  • u<t
  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 6 / 17

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SLIDE 10

Problem Definition Bandwidth Allocation Evaluation Conclusions Optimal Allocation

Cache Bandwidth Allocation Problem

  • Cache bandwidth allocation of ISP i at time t

κi(t) = (κi,1(t), . . . , κi,S(t))

  • Defined by policy π: κi(t) = Fπ
  • Z(u)
  • u<t,
  • κi(u)
  • u<t
  • Expected incoming inter-ISP traffic under allocation policy π

Cπ

i (Z(0), T) = Eπ Z(0)

T

  • s∈S

Ii,s(Zs(t), κi,s(t))dt

  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 6 / 17

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SLIDE 11

Problem Definition Bandwidth Allocation Evaluation Conclusions Optimal Allocation

Cache Bandwidth Allocation Problem

  • Cache bandwidth allocation of ISP i at time t

κi(t) = (κi,1(t), . . . , κi,S(t))

  • Defined by policy π: κi(t) = Fπ
  • Z(u)
  • u<t,
  • κi(u)
  • u<t
  • Expected incoming inter-ISP traffic under allocation policy π

Cπ

i (Z(0), T) = Eπ Z(0)

T

  • s∈S

Ii,s(Zs(t), κi,s(t))dt

  • Find the optimal policy π∗ ∈ Π s.t.

inf

π∈Π Cπ i (Z(0)) = inf π lim sup T→∞

1 T Cπ

i (Z(0), T).

  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 6 / 17

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SLIDE 12

Problem Definition Bandwidth Allocation Evaluation Conclusions Optimal Allocation

Cache Bandwidth Allocation Problem

  • Cache bandwidth allocation of ISP i at time t

κi(t) = (κi,1(t), . . . , κi,S(t))

  • Defined by policy π: κi(t) = Fπ
  • Z(u)
  • u<t,
  • κi(u)
  • u<t
  • Expected incoming inter-ISP traffic under allocation policy π

Cπ

i (Z(0), T) = Eπ Z(0)

T

  • s∈S

Ii,s(Zs(t), κi,s(t))dt

  • Find the optimal policy π∗ ∈ Π s.t.

inf

π∈Π Cπ i (Z(0)) = inf π lim sup T→∞

1 T Cπ

i (Z(0), T).

  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 6 / 17

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Problem Definition Bandwidth Allocation Evaluation Conclusions Optimal Allocation

Existence of Optimal Stationary Policy

  • Markov Decision Process

< Z, K, Q(κ), I(z, κ) >

qi,s(κi,s) λi,s θXi,s γYi,s Xi,s Yi,s

Theorem

There exists an optimal stationary policy π∗ ∈ Π that minimizes Cπ

i (Z(0))

The optimal policy π∗

  • Stationary: κi(t) is only a function of the system state Z(t)
  • Calculation requires steady state probabilities
  • Prohibitive even for few ISPs and swarms
  • Use of simple approximations to gain insight...
  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 7 / 17

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SLIDE 14

Problem Definition Bandwidth Allocation Evaluation Conclusions Optimal Allocation

Existence of Optimal Stationary Policy

  • Markov Decision Process

< Z, K, Q(κ), I(z, κ) >

qi,s(κi,s) λi,s θXi,s γYi,s Xi,s Yi,s

Theorem

There exists an optimal stationary policy π∗ ∈ Π that minimizes Cπ

i (Z(0))

The optimal policy π∗

  • Stationary: κi(t) is only a function of the system state Z(t)
  • Calculation requires steady state probabilities
  • Prohibitive even for few ISPs and swarms
  • Use of simple approximations to gain insight...
  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 7 / 17

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SLIDE 15

Problem Definition Bandwidth Allocation Evaluation Conclusions Allocation Policies

One-Step Look Ahead (OLA)

  • Minimize the incoming inter-ISP traffic rate given the system state

κi(t) = arg min

κi∈Ki

  • s∈S

Ii,s(Zs(t), κi,s)

  • Short term approximation → disregards system dynamics
  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 8 / 17

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Problem Definition Bandwidth Allocation Evaluation Conclusions Allocation Policies

One-Step Look Ahead (OLA)

  • Minimize the incoming inter-ISP traffic rate given the system state

κi(t) = arg min

κi∈Ki

  • s∈S

Ii,s(Zs(t), κi,s)

  • Short term approximation → disregards system dynamics

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Cache bandwidth K1 of ISP 1 [Mbit/s] Inter−ISP traffic savings [Mbit/s] Swarm 1 Swarm 2 Swarm 3

Optimal κi(t) leads to equal marginal traffic saving for every swarm

κi,s > 0 ⇒ ∂Ii,s(zs, κi,s) ∂κi,s = ζ κi,s = 0 ⇒ ∂−Ii,s(zs, κi,s) ∂κi,s ≥ ζ

  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 8 / 17

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Problem Definition Bandwidth Allocation Evaluation Conclusions Allocation Policies

Steady-State Optimal (SSO)

  • Minimize the incoming inter-ISP traffic rate at steady state

π∗ = arg min

κi∈Ki

  • s∈S

Ii,s(κi,s)

  • Long term approximation → non adaptive policy
  • Ii,s(κi,s) = I
  • xπ

i,s(κi,s), yπ i,s(κi,s), κi,s

  • Based on fluid model [1] of cache impact on system state

xπ

i,s

= λi,s ν

  • 1 + θ

ν

− κi,s µη

  • 1 + θ

ν

− ∆i(x, y, κ) yπ

i,s

= λi,s γ

  • 1 + θ

ν

+ κi,sθ µηγ

  • 1 + θ

ν

+ θ γ ∆i(x, y, κ),

  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 9 / 17

[1] F. Lehrieder, G. D´

an, T. Hoßfeld, S. Oechsner and V. Singeorzan “The Impact of Caching on BitTorrent-like Peer-to-peer Systems” in Proc. IEEE Int’l Conf. Peer-to-Peer Computing (P2P), Aug. 2010

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Problem Definition Bandwidth Allocation Evaluation Conclusions Allocation Policies

Steady-State Optimal (SSO)

  • Minimize the incoming inter-ISP traffic rate at steady state

π∗ = arg min

κi∈Ki

  • s∈S

Ii,s(κi,s)

  • Long term approximation → non adaptive policy
  • Ii,s(κi,s) = I
  • xπ

i,s(κi,s), yπ i,s(κi,s), κi,s

  • Based on fluid model [1] of cache impact on system state

xπ

i,s

= λi,s ν

  • 1 + θ

ν

− κi,s µη

  • 1 + θ

ν

− ∆i(x, y, κ) yπ

i,s

= λi,s γ

  • 1 + θ

ν

+ κi,sθ µηγ

  • 1 + θ

ν

+ θ γ ∆i(x, y, κ),

  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 9 / 17

[1] F. Lehrieder, G. D´

an, T. Hoßfeld, S. Oechsner and V. Singeorzan “The Impact of Caching on BitTorrent-like Peer-to-peer Systems” in Proc. IEEE Int’l Conf. Peer-to-Peer Computing (P2P), Aug. 2010

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Problem Definition Bandwidth Allocation Evaluation Conclusions Allocation Policies

Smallest-Ratio Priority (SRP)

  • Approximation of SSO for small cache bandwidth
  • For two ISPs at steady state:

I1(κ1) ≈ x1 x1 + x2 µ(ηx2 + y2)

  • ∂I1(κ1)

∂κ1 |κ1=0

κ2=0 < 0 and decreases monotonically in r = λ2

λ1

  • Swarms with lowest ratio

λi

  • j=i λj

have highest priority

  • Practical implementation ˆ

ri,s = xi,s(t)

  • j=i zj,s(t)
  • Adaptive policy
  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 10 / 17

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SLIDE 20

Problem Definition Bandwidth Allocation Evaluation Conclusions Allocation Policies

Smallest-Ratio Priority (SRP)

  • Approximation of SSO for small cache bandwidth
  • For two ISPs at steady state:

I1(κ1) ≈ x1 x1 + x2 µ(ηx2 + y2)

  • ∂I1(κ1)

∂κ1 |κ1=0

κ2=0 < 0 and decreases monotonically in r = λ2

λ1

  • Swarms with lowest ratio

λi

  • j=i λj

have highest priority

  • Practical implementation ˆ

ri,s = xi,s(t)

  • j=i zj,s(t)
  • Adaptive policy
  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 10 / 17

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SLIDE 21

Problem Definition Bandwidth Allocation Evaluation Conclusions Evaluation Methods

Evaluation Methodology

  • Model of the incoming inter-ISP traffic for OLA and SSO policies

Simulations

  • Flow level simulation in the ProtoPeer framework
  • 6.5 hours of simulated time, up to 12.000 BitTorrent peers
  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 11 / 17

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SLIDE 22

Problem Definition Bandwidth Allocation Evaluation Conclusions Evaluation Methods

Evaluation Methodology

  • Model of the incoming inter-ISP traffic for OLA and SSO policies

Simulations

  • Flow level simulation in the ProtoPeer framework
  • 6.5 hours of simulated time, up to 12.000 BitTorrent peers

Experiments

  • 500 PlanetLab nodes running BitTorrent
  • BitTorrent Mainline client 4.4.0
  • 4 hours experiments, 1 hour of warm-up period
  • Up to 8400 peers distributed among 12 swarms
  • Dedicated Linux computer running the P2P cache
  • Bandwidth allocation policies implemented in Linux kernel TC
  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 11 / 17

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SLIDE 23

Problem Definition Bandwidth Allocation Evaluation Conclusions Evaluation Methods

Evaluation Methodology

  • Model of the incoming inter-ISP traffic for OLA and SSO policies

Simulations

  • Flow level simulation in the ProtoPeer framework
  • 6.5 hours of simulated time, up to 12.000 BitTorrent peers

Experiments

  • 500 PlanetLab nodes running BitTorrent
  • BitTorrent Mainline client 4.4.0
  • 4 hours experiments, 1 hour of warm-up period
  • Up to 8400 peers distributed among 12 swarms
  • Dedicated Linux computer running the P2P cache
  • Bandwidth allocation policies implemented in Linux kernel TC
  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 11 / 17

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SLIDE 24

Problem Definition Bandwidth Allocation Evaluation Conclusions Results

When Bandwidth Allocation Matters - Simulations

Normalized inter−ISP traffic savings unif.,1:10 zipf,1:10 unif.,1:1+1:10 het.,2:2+1:10 0.1 0.2 0.3 Scenario (swarm sizes, distribution ISP1:ISP2) 0.2 0.4 0.6 Demand−driven One−step look ahead Steady−state optimal Incoming Outgoing

  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 12 / 17

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SLIDE 25

Problem Definition Bandwidth Allocation Evaluation Conclusions Results

Bandwidth Allocation Policies Evaluation - Simulations

  • Scenario unif.,1:1+1:10:

20 40 60 80 100 0.2 0.4 0.6 0.8 1 Normalized inter−ISP traffic savings Cache bandwidth K1 of ISP 1 [Mbit/s] Demand−driven One−step look ahead Steady−state optimal Smallest−ratio priority Incoming Outgoing

  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 13 / 17

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SLIDE 26

Problem Definition Bandwidth Allocation Evaluation Conclusions Results

Validation - Experiments on PlanetLab

0.4667 0.9333 1.4 1.8667 2.3333 2.8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cache bandwidth K1 of ISP 1 [Mbit/s] Normalized inter−ISP traffic savings Demand−driven Steady−state optimal Smallest−ratio priority

Incoming Outgoing

  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 14 / 17

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SLIDE 27

Problem Definition Bandwidth Allocation Evaluation Conclusions Results

Indifference Map - Simulations

5 10 15 20 10 20 30 40

κ1,s for swarm s ∈ {1, . . . , 10} [Mbit/s] κ1,s for swarm s ∈ {11, 12} [Mbit/s]

∆I1=20Mbit/s ∆I1=32Mbit/s ∆I1=44Mbit/s K1=33Mbit/s K1=61Mbit/s K1=108Mbit/s

  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 15 / 17

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SLIDE 28

Problem Definition Bandwidth Allocation Evaluation Conclusions

Conclusions

  • Cache upload bandwidth allocation problem
  • Existence of a stationary bandwidth allocation policy
  • Various adaptive bandwidth allocation policies

Main observations

  • Cache’s impact on system dynamics is important
  • Difference in swarms symmetry is the key
  • Significant traffic savings possible
  • ∼60% improvement in incoming inter-ISP traffic saving
  • ∼250% improvement in outgoing inter-ISP traffic saving
  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 16 / 17

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SLIDE 29

Problem Definition Bandwidth Allocation Evaluation Conclusions

Conclusions

  • Cache upload bandwidth allocation problem
  • Existence of a stationary bandwidth allocation policy
  • Various adaptive bandwidth allocation policies

Main observations

  • Cache’s impact on system dynamics is important
  • Difference in swarms symmetry is the key
  • Significant traffic savings possible
  • ∼60% improvement in incoming inter-ISP traffic saving
  • ∼250% improvement in outgoing inter-ISP traffic saving
  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 16 / 17

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SLIDE 30

Problem Definition Bandwidth Allocation Evaluation Conclusions

Cache Capacity Allocation for BitTorrent-like Systems to Minimize Inter-ISP Traffic

Valentino Pacifici, Frank Lehrieder, Gy¨

  • rgy D´

an

School of Electrical Engineering Institute of Computer Science KTH Royal Institute of Technology University of W¨ urzburg Stockholm, Sweden W¨ urzburg, Germany

Orlando, March 29, 2012

  • V. Pacifici, F. Lehrieder, G. D´

an () INFOCOM 2012 March 29, 2012 17 / 17