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Analysis of price competitionunder peering and transitagreements in ISP to P2P users

CCNC 2011

Las Vegas, 11 January

Luis Guijarro

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Agenda

Objective Models

Method

Results and analysis

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Internet (IBP)

ISP1 ISP2

N

n2n1

11

Bp1

Bp2

Bd2Bd

1

Objective To model ISP service

provision to P2P users

To model peering

agreements between

ISPs

To analyze equilibrium

under competition

between ISPs in localmarkets

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M/G/1-PS ISPj

Bpiaborted

M/G/1-PS IBP

Bdiaborted

ISPi

vi

(1-

vi

) vji

=ni

qi

i

solved

at Internet

Service model Basic service model

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Service model

Basic service modelAssumptions

Internal downloads always complete

successfullyLink dimensioning is such that links are

100% utilized

Users are impatient and no bandwidth iswasted

Performance metrics

( )pidiiiiii BBnN ,,,,

==

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ISPj

M/G/1-PS IBP

Bdiaborted

ISPi

vi

(1-

vi

) vji

=ni

qi

i

solved

at Internet

Service model Unlimited peering

service model

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Service model

Unlimited peering service modelAssumption relaxed

Link dimensioning is such that

Transit links are 100% utilized

Peering links are not

Peering capacity is large enough so that

downloads are always completed successfully

More realistic and a limiting case

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Demand and supply model Demand

Utility

Supply

Income Flat-rate

Costs Fixed peering costs

Transit costsproportional tobandwidth

Profits

( ) ),(1log iiiiii pUpU =+

p

i

d

i

d

iiii

CBCnp =

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Method Game theory

Multi-leader-follower game

The 2 ISPs fix their pricespiin order tomaximize profits

Each user subscribe to the ISPi which offershigher utility Ui

Solved by backward induction

First, solve subscription game

Then, solve competition game anticipatingthe reaction by users.

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Method

Game theory Multi-leader-follower game

Subscription game

Wardrop equilibrium

Assume n

is high enough

Equilibrium is reached when there is no

incentive to change subscription decision

Assume that every user subscribe to service

)1,(),( 122111 = pUpU

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Method

Game theory Multi-leader-follower game

Competition game

Nash equilibrium

The operator does not know the strategy

chosen by the competitor, but space of

available strategies are common knowledge

),(maxarg

),(maxarg

2

*

12

*

2

*211

*1

2

1

ppp

ppp

p

p

=

=

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Results and analysis Constant parameters

# of users, Nand n

Transit capacity Bd1 Costs

Variable parameters

Peering capacities Bpi

Transit capacity B

d

2

Internet (IBP)

ISP1 ISP2

N=5e7

n11

1

Bp1

Bp2

Bd2Bd1

=1000

n2

n=1e4

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Results and analysis Results

Market shares i Quality of service i Pricespi User utilities Ui Profits i Price of Anarchy PoA

Social welfare

the sum of the utilities of all agents in the system (n1

U1

+n2

U2

+1

+2)

PoA

the quotient between the maximum value of the social welfare and

the

social welfare obtained at the Nash equilibrium

i.e., PoA

>=1

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Results and analysis Transit link

provisioning

Objective

Competitive

advantage

Experiment

Bd2varies from 100

to 2000 objects perday

Internet (IBP)

ISP1 ISP2

N=5e7

n11

1

Bp1

=10

Bp2

=10

Bd2Bd1

=1000

n2

n=1e4

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Results and analysis Transit link

provisioning

Results

ISP2 gains market

share and improvesQoS

ISP1 looses market

share although

improves QoS

Free riding

Users are better off

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Results and analysis Transit link

provisioning Results

ISP2 can raise

prices and increasesprofits

ISP1 should lowerprices and reducesprofits

Conclusion

The provisioning iseffective

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Results and analysis Transit link

provisioning

Objective

Social welfare

Experiment

Bd2varies from 100

to 2000 objects per

day Bpi takes different

values: 10, 50 and

Internet (IBP)

ISP1 ISP2

N=5e7

n11

1

Bp1

Bp2

Bd2

Bd1

=1000

n2

n=1e4

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Results & analysis Transit link provisioning

Results

PoA increases quasi-

linearly with the

absolute value of

(Bd2+Bp

2)-(Bd1+B

p1)

PoA decreases as the

peering capacities

increase

Conclusion

The provisioning

causes welfare loss

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Results and analysis Increasing competition

Objective

User utility

Experiment

Increasing the # of

ISPs (M)

Restrictions

Bd

and n are keptconstant

Bdi

=Bd/M

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Results and analysis Increasing competition

Results

User utility

increases

Profits decrease

Conclusion

Users are better off

and ISPs are worseoff

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Conclusions

Analysis based on an explicit model of theISP service that is provided to users that

run P2P applications

Study of transit link provisioning It is effective, but causes welfare loss

Study of increasing competition

Benefits users, but hurts competitors