Content-peering Dynamics of Autonomous Caches in a Content-centric - - PowerPoint PPT Presentation

Introduction Model Perfect Information Imperfect Information Conclusions

Content-peering Dynamics of Autonomous Caches in a Content-centric Network

Valentino Pacifici, Gy¨

• rgy D´

an

Laboratory for Communication Networks School of Electrical Engineering KTH, Royal Institute of Technology Stockholm - Sweden

Stockholm, December 13, 2012

• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 1 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Content-centric Networks

• Caches part of the protocol stack
• Existing research optimizes global performance
• Cache dimensioning
• Efficient routing
• Efficient cache eviction policies
• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 2 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Content-centric Networks

ISP 1 ISP 2 ISP 3

• Caches part of the protocol stack
• Existing research optimizes global performance
• Cache dimensioning
• Efficient routing
• Efficient cache eviction policies
• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 2 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Content-centric Networks

ISP 1 ISP 2 ISP 3

• Caches part of the protocol stack
• Existing research optimizes global performance
• Cache dimensioning
• Efficient routing
• Efficient cache eviction policies
• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 2 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Content-centric Networks

ISP 1 ISP 2 ISP 3

• Networks of caches optimized for local performance
• Decrease transit traffic costs through content-level peering
• New challenges:
• Stability of cache content
• Coordination among ASes
• Effect of eviction
• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 2 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Modeling the Interaction among ASes

ISP 1 ISP 2 ISP 3

C2 C3 C1½O

• ∈ O
• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 3 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Modeling the Interaction among ASes

ISP 1 ISP 2 ISP 3

C2 C3 C1½O

• ∈ O
• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 3 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Modeling the Interaction among ASes

ISP 1 ISP 2 ISP 3

C2 C3 C1½O

• ∈ O
• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 3 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Modeling the Interaction among ASes

ISP 1 ISP 2 ISP 3

C2 C3 C1½O

• ∈ O
• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 3 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Modeling the Interaction among ASes

ISP 1 ISP 2 ISP 3

C2 C3 C1½O

• ∈ O
• Each ISP optimizes its internal network through
• Routing of content and interest messages
• Cache dimensioning and eviction policies
• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 3 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Modeling the Interaction among ASes

ISP 1 ISP 2 ISP 3

C2 C3 C1½O

• ∈ O
• Each ISP optimizes its internal network through
• Routing of content and interest messages
• Cache dimensioning and eviction policies

⇓

• Li = Hi ∪ Ci → content available at ISP i
• Ri =

j∈N(i) Lj → content available from the peering ISPs

• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 3 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Modeling the Interaction among ASes

• Interest messages (i.m.) for item o at ISP i
• wo

i ∈ R+ → average arrival intensity

• Independent Reference Model (IRM):
• inter arrival times ∼ F o

i (x) = 1 − e−wo

i x

• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 4 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Modeling the Interaction among ASes

• Interest messages (i.m.) for item o at ISP i
• wo

i ∈ R+ → average arrival intensity

• Independent Reference Model (IRM):
• inter arrival times ∼ F o

i (x) = 1 − e−wo

i x

• Unit cost of serving item o at ISP i
• αi if o available locally or at peering ISP (o ∈ Li ∪ Ri)
• γi if o retrieved from a transit link (o /

∈ Li ∪ Ri)

• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 4 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Modeling the Interaction among ASes

• Interest messages (i.m.) for item o at ISP i
• wo

i ∈ R+ → average arrival intensity

• Independent Reference Model (IRM):
• inter arrival times ∼ F o

i (x) = 1 − e−wo

i x

• Unit cost of serving item o at ISP i
• αi if o available locally or at peering ISP (o ∈ Li ∪ Ri)
• γi if o retrieved from a transit link (o /

∈ Li ∪ Ri)

Total cost for ISP i:

Ci(Ci, C−i) = αi

• Li∪Ri

wo

i + γi

• O{Li∪Ri}

wo

i ,

• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 4 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Coordinated Content-peering

• Peering ISPs periodically exchange Summary cache Li
• Upon interest message for item o at ISP i:
• if o ∈ Li → the item is served
• if o ∈ Ri → i.m. forwarded to a peer
• if o /

∈ Ri → i.m. forwarded to transit provider

• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 5 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Coordinated Content-peering

• Peering ISPs periodically exchange Summary cache Li
• Upon interest message for item o at ISP i:
• if o ∈ Li → the item is served
• if o ∈ Ri → i.m. forwarded to a peer
• if o /

∈ Ri → i.m. forwarded to transit provider

1 2 a a

Figure: No content-peering

• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 5 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Coordinated Content-peering

• Peering ISPs periodically exchange Summary cache Li
• Upon interest message for item o at ISP i:
• if o ∈ Li → the item is served
• if o ∈ Ri → i.m. forwarded to a peer
• if o /

∈ Ri → i.m. forwarded to transit provider

1 2 a a

Figure: No content-peering

1 2 a a

Figure: Content-peering

• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 5 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Coordinated Content-peering

• Peering ISPs periodically exchange Summary cache Li
• Upon interest message for item o at ISP i:
• if o ∈ Li → the item is served
• if o ∈ Ri → i.m. forwarded to a peer
• if o /

∈ Ri → i.m. forwarded to transit provider

1 2 a a

Figure: No content-peering

1 2 b b

Figure: Content-peering

• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 5 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Coordinated Content-peering

• Peering ISPs periodically exchange Summary cache Li
• Upon interest message for item o at ISP i:
• if o ∈ Li → the item is served
• if o ∈ Ri → i.m. forwarded to a peer
• if o /

∈ Ri → i.m. forwarded to transit provider

1 2 a a

Figure: No content-peering

1 2 a a

Figure: Content-peering

• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 5 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Coordinated Content-peering

• Peering ISPs periodically exchange Summary cache Li
• Upon interest message for item o at ISP i:
• if o ∈ Li → the item is served
• if o ∈ Ri → i.m. forwarded to a peer
• if o /

∈ Ri → i.m. forwarded to transit provider

1 2 a a

Figure: No content-peering

1 2 a a

Figure: Content-peering

• Need for algorithms to reach stable allocation
• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 5 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Coordinated Content-peering

• Peering ISPs periodically exchange Summary cache Li
• Upon interest message for item o at ISP i:
• if o ∈ Li → the item is served
• if o ∈ Ri → i.m. forwarded to a peer
• if o /

∈ Ri → i.m. forwarded to transit provider

1 2 a a

Figure: No content-peering

1 2 a a

Figure: Content-peering

• Need for algorithms to reach stable allocation

perfect information: Perfect estimation of wo

i

• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 5 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Cache-or-Wait (CoW) Algorithm

• Independent set I ⊆ N: it does not contain peering ISPs
• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 6 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Cache-or-Wait (CoW) Algorithm

• Independent set I ⊆ N: it does not contain peering ISPs

At every time slot t:

• Pick It.
• ISPs i ∈ It allowed to change their cached items Ci(t−1)→Ci(t)
• For all j /

∈ It, Cj(t) = Cj(t − 1).

• Inform peering ISPs about Ci(t)
• Transitions as a Markov Process P 0
• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 6 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Cache-or-Wait (CoW) Algorithm

• Independent set I ⊆ N: it does not contain peering ISPs

At every time slot t:

• Pick It.
• ISPs i ∈ It allowed to change their cached items Ci(t−1)→Ci(t)
• For all j /

∈ It, Cj(t) = Cj(t − 1).

• Inform peering ISPs about Ci(t)
• Transitions as a Markov Process P 0

CoW terminates in an equilibrium allocation after a finite number of efficient updates

• At slot t no ISP j /

∈ It can perform an update

• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 6 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Cache-no-Wait (CnW) Algorithm

At every time slot t

• ∀ ISP i ∈N allowed to perform efficient updates Ci(t−1)→Ci(t)
• ∀ ISP i informs the ISPs j ∈ N(i) about Ci(t).
• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 7 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Cache-no-Wait (CnW) Algorithm

At every time slot t

• ∀ ISP i ∈N allowed to perform efficient updates Ci(t−1)→Ci(t)
• ∀ ISP i informs the ISPs j ∈ N(i) about Ci(t).

CnW terminates in an equilibrium allocation with probability one. At every time slot:

• Prob. e−wo

i ∆ item o not requested

• Prob. ǫ(Ci(t − 1)) > 0 no “useful” item requested
• Prob. k(C(t − 1)) that updating ISPs belong to an independent set

k(C(t − 1)) >

• i∈It

[1 − ǫi(Ci(t − 1))] ·

• i∈NIt

ǫi(Ci(t − 1)) > 0

• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 7 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Numerical Results - CoW vs CnW

• CAIDA graph: largest connected component in CAIDA dataset
• 616 ISPs, average node degree 9.66
• Erd˝
• s-R´

enyi (ER) and Barab´ asi-Albert (BA) random graphs

• Arrival intensities ∼ Zipf’s law with exponent 1
• Cache size 10 at every ISP
• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 8 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Numerical Results - CoW vs CnW

• CAIDA graph: largest connected component in CAIDA dataset
• 616 ISPs, average node degree 9.66
• Erd˝
• s-R´

enyi (ER) and Barab´ asi-Albert (BA) random graphs

• Arrival intensities ∼ Zipf’s law with exponent 1
• Cache size 10 at every ISP

2 4 6 8 10 12 14 16 1000 2000 3000 4000 5000 6000 7000 8000

Time slot duration ∆ [s] Number of iterations to terminate CoW CnW Erdos−Renyi graph CAIDA graph Barabasi−Albert graph

2 4 6 8 10 12 14 16 1 2 3 4 5

CoW − Inefficiency of updates

2 4 6 8 10 12 14 16 100 200 300 400 500 600 700

Time slot duration ∆ [s] CnW − Inefficiency of updates

CoW CnW Erdos−Renyi graph CAIDA graph Barabasi−Albert graph

• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 8 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Content-peering under Imperfect Information

• Avg. arrival intensities wo

i are estimated

• Probability of misestimation:

If wo

i > wp i

⇒ P(wo

i < wp i ) ∝ ǫe− 1

β (wo i −wp i )

• System leaves equilibrium allocations
• P β regular perturbed Markov process of P 0
• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 9 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Content-peering under Imperfect Information

• Avg. arrival intensities wo

i are estimated

• Probability of misestimation:

If wo

i > wp i

⇒ P(wo

i < wp i ) ∝ ǫe− 1

β (wo i −wp i )

• System leaves equilibrium allocations
• P β regular perturbed Markov process of P 0

When β → 0, the stationary distribution of P β is a stationary distribution of P 0 ⇒ equilibrium allocation under perfect information.

• Some cache allocations more likely than others..
• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 9 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Imperfect Information - Disjoint Interests

• Disjoint interests case:

the Ki items with highest arrival intensity of the ISPs form disjoint sets. The stationary distribution of P β is the stable allocation C∗ in which every ISP caches its most popular items.

• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 10 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Imperfect Information - Disjoint Interests

• Disjoint interests case:

the Ki items with highest arrival intensity of the ISPs form disjoint sets. The stationary distribution of P β is the stable allocation C∗ in which every ISP caches its most popular items.

• ,p

p,o X,p

• ,Y

p,Y X,o X,Y

2 2 1 1 2 1 2 2 1 1

• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 10 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Imperfect Information - Numerical Results

• 105 time slots
• 50 ISPs, Ki = 1 for every i ∈ N
• τ estimation interval in seconds for a LFU cache

50 100 150 200 10

−5

10

−4

10

−3

10

−2

10

−1

10

Estimation period τ [s] Relative permanence ER node degree=3 BA node degree=3 BA node degree=12

3rd ranked item 2nd ranked item 1st ranked item

• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 11 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Conclusions

• Model of interaction between ISPs in CCNs
• Content-level peering reaches a stable allocation
• Fast convergence if no simultaneous updates by peering ISPs
• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 12 / 12

Introduction Model Perfect Information Imperfect Information Conclusions

Conclusions

• Model of interaction between ISPs in CCNs
• Content-level peering reaches a stable allocation
• Fast convergence if no simultaneous updates by peering ISPs
• Incorrect estimate of content popularity
• No stable state
• Still cost-efficient cache allocations
• Insights about most likely cache allocations
• V. Pacifici, G. D´

an (EE,KTH) LCN Seminar 2012 December 13, 2012 12 / 12