Vytautas Valancius, Cristian Lumezanu, Nick Feamster, Ramesh Johari, and Vijay V. Vazirani.

Vytautas Valancius, Cristian Lumezanu, Nick Feamster, Ramesh Johari, and Vijay V. Vazirani

Sellers Large ISPs National or international

reach

Buyers Smaller ISPs Enterprises Content providers Universities

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CogentCogent

Stanford Universit

y

Stanford Universit

y

Connectivity is sold at bulk using blended rates

InvoiceTraffic

Single price in $/Mbps/month

Charged each month on aggregate throughput Some flows are costly Some are cheaper to serve Price is set to recover total

costs + margin

Convenient for ISPs and clients

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CogentCogent

EUCost: $$$

USCost: $

Blended rate Price: $$

Stanford Universit

y

Stanford Universit

y

Can be inefficient!

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Uniform price yet diverse resource costs

Lack of incentives to conserveresources to costly destinations

Lack of incentives to investin resources to costly destinations

Pareto inefficient resource allocation A well studied concept in economics

Potential loss to ISP profit and client surplus

Clients ISPs

Alternative: Tiered Pricing

Some industries use tiered pricing extensively Parcel services, airlines, train companies Pricing on distance, weight, quality of service

Other industries offer limited tiered pricing USPS mail, London’s Tube, Atlanta’s MARTA Limited number of pricing tiers

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Price the flows based on cost and demand

Where is tiered pricing in the Internet?

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CogentCogent

Global, Cost: $$$

LocalCost: $

Stanford Universit

y

Stanford Universit

y

Regional pricing

Price:$$$

Price:$

Some ISPs already use limited tiered pricing On/Off-Net Pricing

CogentCogent

Stanford Universit

y

Stanford Universit

y

ClientRevenue: $

PeerNo revenue

Price:$$$

Price:$

Question:How efficient are the current ISP pricing strategies?

Can ISPs benefit from more tiers?

1. Construct an ISP profit model that accounts for:

Demand of different flows Servicing costs of different flows

2. Drive the model with real data Demand functions from real traffic data Servicing costs from real topology data

3. Test the effects of tiered pricing!7

How can we test the effects oftiered pricing on ISP profits?

Modeling

Datamapping

Numbercrunching

Flow revenue Price * Traffic Demand Traffic Demand is a function of price How do we model and discover demand

functions?

Flow cost Servicing Cost * Traffic Demand Servicing Cost is a function of distance How do we model and discover servicing

costs? 8

Profit = Revenue – Costs(for all flows)

1. Finding Demand Functions

1. Finding Demand Functions

3. Reconciling cost with demand

3. Reconciling cost with demand

2. Modeling Costs2. Modeling Costs

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Traffic Demands Network TopologiesCurrent Prices

Demand Models

Demand Functions

Cost Models

Relative costs

Profit Model

Absolute costs

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Demand = F(Price, Valuation, Elasticity)

Valuation = F-1(Price, Demand, Elasticity)

Canonical commodity demand function:Price

Demand

Elastic demand

Inelastic demand

Valuation – how valuable flow isElasticity – how fast demand changes with price

Current price

Current flowdemand

Assumed range of elasticities

We mapped traffic data to demand functions!

How do we find the demand function parameters?

1. Finding Demand Functions

1. Finding Demand Functions 2. Modeling Costs2. Modeling Costs

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Traffic Demands Network TopologiesCurrent Prices

Demand Models

Demand Functions

Cost Models

Relative costs

Profit Model

Absolute costs

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Linear: Concave:

Region: Dest. type:

How can we model flow costs?

ISP topologies and peering information alone can only provide us with relative flow servicing costs.

real_costs = γ * relative_costs

1. Finding Demand Functions

1. Finding Demand Functions

3. Reconciling cost with demand

3. Reconciling cost with demand

2. Modeling Costs2. Modeling Costs

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Traffic Demands Network TopologiesCurrent Prices

Demand Models

Demand Functions

Cost Models

Relative costs

Profit Model

Absolute costs

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Data mapping is complete: we know demands and costs!

Subject to the noise that is inherent in any structural estimation.

Profit = Revenue – Costs = F(price, valuations, elasticities, real_costs)

F’(price*, valuations, elasticities, real_costs)

F’ (price*, valuations, elasticities, γ * relative_costs) = 0

γ = F’-1(price*, valuations, elasticities, relative_costs)

Assuming ISP is rational and profit maximizing:

= 0

1. Select a number of pricing tiers to test 1, 2, 3, etc.

2. Map flows into pricing tiers Optimal mapping and mapping heuristics

3. Find profit maximizing price for each pricing tier and compute the profit

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Repeat above for:-2x demand models -4x cost models-3x network topologies and traffic matrices

16*Elasticity – 1.1, base cost – 20%, seed price - $20

Constant elasticity demand with linear cost model

Tier 1: Local trafficTier 2: The rest of the traffic

Data Set

Traffic (TB/day

)

Local Traffi

c

Bit-Weighted Distance Average

(miles)

Distance CV

CDN 1037 ~30% 1988 0.59

EU ISP 400 ~40% 54 0.70

Abilene

43 ~40% 660 0.54

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Approximate measureof flow servicing cost spread

NetFlow records and geo-location information Group flows in to distance buckets

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Linear Cost Model Concave Cost Model

ConstantElasticityDemand

LogitDemand

Refine demand and cost modeling Hybrid demand and cost models are likely more

realistic

Establish better metrics that predict the benefit of tiered pricing

Establish formal conditions under which demand and cost normalization framework works E.g., can we normalize cost and demand if cost is a

product of the unit cost and the log of the demand?

Test the framework on other industries

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ISPs today predominantly use blended rate pricing

Some ISPs started using limited tiered pricing

Our study shows that having more than 2-3 pricing tiers adds only marginal benefit to the ISP

The results hold for wide range of scenarios Different demand and cost models Different network topologies and demands Large range of input parameters

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Questions?http://valas.gtnoise.net

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Very hard to model!

Perhaps requires game-theoretic approach and more data (such as where the topologies overlap, etc.)

It is possible to model some effects of competition by treating demand functions as representing residual instead of inherent demand. See Perloff’s “Microeconomics” pages 243-246 for discussion about residual demand.

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We don’t know elasticities, so we test large range of them.

The data might be biased already for the traffic because of congestion signalling (maybe real demand is more than we can see).

We can’t model competition effects in long term (in fact, no one can.)

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