Vytautas Valancius, Cristian Lumezanu, Nick Feamster, Ramesh Johari, and
Vijay V. Vazirani

Sellers
 Large ISPs
 National or international reach

Buyers
Cogent
Traffic
Invoice
 Smaller ISPs
 Enterprises
 Content providers
Stanford
University
 Universities
Connectivity is sold at bulk using blended rates
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

Single price in $/Mbps/month
Charged each month on
aggregate throughput
 Some flows are costly
EU
Cost: $$$
Cogent
US
Cost: $
 Some are cheaper to serve
 Price is set to recover total costs +
margin

Convenient for ISPs and clients
Blended rate
Price: $$
Stanford
University
Can be inefficient!
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Uniform price yet diverse resource costs
Clients
Lack of incentives to conserve
resources to costly destinations

ISPs
Lack of incentives to invest
in resources to costly destinations
Pareto inefficient resource allocation
 A well studied concept in economics

Potential loss to ISP profit and client surplus
Alternative: Tiered Pricing
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Price the flows based on cost and demand

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
Where is tiered pricing in the Internet?
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Some ISPs already use limited tiered pricing
Regional pricing
On/Off-Net Pricing
Global, Cost: $$$
Client
Revenue: $
Peer
No revenue
Local
Cost: $
Cogent
Cogent
Price:
$$$
Stanford
University
Price:
$
Price:
$
Price:
$$$
Stanford
University
Question:
How efficient are the current ISP pricing strategies?
Can ISPs benefit from more tiers?
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How can we test the effects of
tiered pricing on ISP profits?
1.
 Demand of different flows
 Servicing costs of different flows
Modeling
Data
mapping
Number
crunching
Construct an ISP profit model that accounts for:
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!
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Profit = Revenue – Costs
(for all flows)

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?
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Traffic Demands
Current Prices
Network Topologies
Demand Models
Cost Models
Demand Functions
Relative costs
1. Finding Demand
Functions
Profit Model
2. Modeling Costs
Absolute costs
3. Reconciling cost
with demand
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Canonical commodity demand function:
Demand = F(Price, Valuation, Elasticity)
Price
Inelastic demand
Elastic demand
Valuation – how valuable flow is
Elasticity – how fast demand changes with price
Demand
How do we find the demand function parameters?
Valuation = F-1(Price, Demand, Elasticity)
Assumed range of elasticities
Current price
Current flow
demand
We mapped traffic data to
demand functions!
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Traffic Demands
Current Prices
Network Topologies
Demand Models
Cost Models
Demand Functions
Relative costs
1. Finding Demand
Functions
Profit Model
2. Modeling Costs
Absolute costs
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How can we model flow costs?
Linear:
Concave:
Region:
Dest. type:
ISP topologies and peering information alone
can only provide us with relative flow servicing costs.
real_costs = γ * relative_costs
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Traffic Demands
Current Prices
Network Topologies
Demand Models
Cost Models
Demand Functions
Relative costs
1. Finding Demand
Functions
Profit Model
2. Modeling Costs
Absolute costs
3. Reconciling cost
with demand
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Assuming ISP is rational and profit maximizing:
Profit = Revenue – Costs = F(price, valuations, elasticities, real_costs)
F’(price*, valuations, elasticities, real_costs) = 0
F’ (price*, valuations, elasticities, γ * relative_costs) = 0
γ = F’-1(price*, valuations, elasticities, relative_costs)
Data mapping is complete: we know demands and costs!
Subject to the noise that is inherent in any structural estimation.
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Select a number of pricing tiers to test
1.

Map flows into pricing tiers
2.

3.
1, 2, 3, etc.
Optimal mapping and mapping heuristics
Find profit maximizing price for each pricing tier and
compute the profit
Repeat above for:
- 2x demand models
- 4x cost models
- 3x network topologies and traffic matrices
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Constant elasticity demand with linear cost model
Tier 1: Local traffic
Tier 2: The rest of the traffic
*Elasticity – 1.1, base cost – 20%, seed price - $20
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
NetFlow records and geo-location information
 Group flows in to distance buckets
Data
Set
Traffic
(TB/day)
Local
Traffic
Bit-Weighted Distance Distance
Average (miles)
CV
CDN
1037
~30%
1988
0.59
EU ISP
400
~40%
54
0.70
Abilene
43
~40%
660
0.54
Approximate measure
of flow servicing cost spread
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Linear Cost Model
Concave Cost Model
Constant
Elasticity
Demand
Logit
Demand
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
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
Questions?
http://valas.gtnoise.net
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21

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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