Unidad II -Sesion 4 - Aplication to Pricing Comm

Pricing for Communication Networks�-Introduction

Roberto Battiti

Slides based on: Courcoubetis and Weber, Pricing Communication Networks, Wiley 2003 – chap1

Pricing in computer networks, Roberto Battiti

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Motivation

• Deregulation, Internet: from large monopolies (prices based on potential competition) to a highly competitive environment

• Technology not sufficient for success: pricing, competition (regulation), ...economics– Customer value depends on pricing and congestion– Pricing as incentive for performance and stability of flexible

services– Possible exchange of economic signals on fast time scales– Pricing is an art (e.g., flat or usage-based?)– Open competition and regulation (e.g., access)

New graduates should be competent in both technology and economics


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Current trends: the market

• A revolution (TCP/IP,optical nets, WWW)• Network externality: user value increases with network

size (size gives a competitive advantage, decrease price to increase demand,... simple versions for free!)

• Topology and capacity: a factory to produce various combinations of network services

• Large fixed infrastructure costs, very small marginal costs

Metcalf’s law: network value � n^2

Lowering price increases demandPricing can be used to control congestionCompetition can drive prices to marginal cost


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Current trends: the market (2)

• Communication services and information goods (CD, software)– Costly to produce, cheap to reproduce– Public goods like highways?– Very small marginal cost, ...but capacity limits (congestion)– Network management / accounting and billing can have large costs

(single technology – IP – is cheaper)– Commodities (web news, bit transport) or goods with committed

customers (so that price can reflect the value...Autocad)?– Externality effects (e.g., Word)

Transporting data bits at diferent quality levels (loss, delay, jitter)Substitutability, arbitrage (buy, repackage and resell) and splitting

Many parameters and many contractsStatistical multiplexing (bursty traffic � overbooking, economy of scale)


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Recent developments• Optical networks, IP, late 90’s Internet bubble, new low cost technology

threatening traditional telephone operators• Market for transport services commoditized: companies may not be able to

recover cost. Network is “stupid”, end-to-end principle: complexity and differentiation at the edges.

• The best network is the hardest one to make money running: very difficult to recover sunk costs

• Data services may drive voice networks out of business• Bandwidth glut (5% lit fibers, demand growing only 50% per year,

complementary services like access slow to develop)• Fierce competition in the long-haul (local operators have loyal base of tel.

customers)

Scenarios:1. regulator acquires and controls fibre onfrastructure2. industry self-regulates: horizontal integration, outsourcing of

the management, service-centered economy


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Role of economics• Decentralized/distributed control

large decentralized systems governed by incentives – like price and congestion levels (in Internet but also for public road usage, electricity, ...)

• Holistic viewEconomic performance is more than just engineering performance (not only

delay and blocking but also flexibility, customization, simplicity for the customer...)

Customers and networks are not separate entities but interacting ones

Agents decide with limited information, where it is available (no full information / centralized control)

Distributed control moves system to an equilibrium point where resources are used efficiently and performance is maximized


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Overprovision or control?

• Hard to estimate bandwidth– Downloading of complete web sites, streaming, peer-to-peer, storage area networks...– Most of the future traffic will be generated by computers (can grow extremaly rapidly)

• A freeway example: over-design or implement priority services/pricing?

• Overprovisioning may be reasonable in the backbone, probably not in the metropolitan access (huge costs)

• Controlled access and differentiation: spend less on capacity but more on control

• On the borderline of being overprovisioned? Congestion signals the need for expansion (pricing used in the transient phase to reduce quality fluctuations)

Social value fo a system increasede when users have incentives to choose the most appropriate service


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Pricing for control and signalling• TCP: congestion signals are generated by

the user’s packet losses � TCP reduces the sending rate

• What if a user cheats? He will be better off!• No cheating if signals impose a monetary

charge Pricing as flexible policingFeedback loop to stabilize the networkTariff is incentive-compatible if it inducescustomers to choose depending on real needs,increasing the aggregate utility of all users


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All-you-can-eat? Who pays the bill?

• Flat-rate charging is popular but not efficient (consider a restaurant, a-la-carte better for health )

• Complex dynamic pricing schemes increase efficiency but may be difficult to implement for the end user– Intelligent agents to hide complexity– Charging structures for many stakeholders but

with simple tariffs for the end user


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Charge, Price, Tariff

• Charge: amount that is billed for a service• Price: amount of money for a unit of

service• Tariff: general structure of prices

– Ex. a + p T

Taxi: a + b Time + c Distance ....behavior


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Dynamic pricing in an Internet cafeeasyInternetCafe

• Price varies dynamically to reflect demand– Ticket 5 Euros– Off period 150 minutesOtherwise depends on number of free terminals

n 0-15, 16-30, 30-45– Peak period minutes 150, 120, 90– Normal period 90, 60, 30

Dynamic pricing with feedback from the systemCan better control demand for resources


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Pricing a single link

• Sharing policies:– Equal share: xi = C/N– Fair shares

• C/N or request• Repeat until all C allocated:

Remaining bandwidthshared amongnot satisefied requests

C (capacity)

X1

X2

..XN


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Pricing a single link (2)

• Take allocation value into account – Utility function ui (xi)

– If ui( ) concave increasing, P can be solved by setting a price p and allowing each user to solve

– p is the Lagrangian multiplier to solve the constrained optimization

P: maximize �i ui (xi) , subject to �i xi � Cx1,...,xN

Maximize ( ui (xi) – p xi )xi


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xi( p) – maximizing value, is the demand functiondecreasing with price

As p increases, the total demand �i xi (p) decreases to reach �i xi (p) = C

By setting this price, demand equals supply and the total benefit is maximized

Properties:•No need for network to know ui( xi )•Decisions decentralized•No network sharing policy: users decide the sharing, with price as aflow control


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Operator gets revenue: p CCustomers get user surplus ui( xi(p) ) – p xi(p)

Can the operator get a larger revenue?- take-it-or-leave-it offer ui( xi ) minus epsilon- pi : higher prices to less price-sensitive customers- nonlinear prices (quantity discounts)- different prices to different groups (home vs business)

- different versions of the service

Need to know ui


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J service types 1, ..., J

Must make choice of number of connections for the different services (nj) so that:

�i nj �j � C�j depends on burstiness of the source and amount of

statistical multiplexing

How to charge for the J different services?


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Lagrangian methods for constrained optimization

P: maximize f(x), subject to g(x) = bx in X

Regional constraint Functional constraint

The solution can often be found by the Lagrangian method

Optimal point x(�), ...by “turning” � can I get g(x(�*) ) = b ?

maximize L(x, � ) = f(x) + � ( b - g(x) )x in X

g(x) > b reduces L if � > 0


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Lagrangian methods for constrained optimization (2)• Lagrangian Sufficiency Theorem

– Suppose there exist x* in X and �* s.t.x maximizes L(x, �*) over all Xg(x*) = b

Then x* solves P

Proofmax f(x) = max f(x) + �* ( b – g(x) ) �

x in X x in Xg(x) = b g(x) = b

max f(x) + �* ( b – g(x) ) = f(x*) + �* ( b – g(x*) ) = f(x*)x in X


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Lagrangian methods for constrained optimization (3)

Example: NETWORK1: max �i wi log xi, subject to �i xi = bx � 0

L1(x,�) = �i wi log xi + � ( b - �i xi )

� L1/ �xi = wi/xi – � = 0 ..... xi(�) = wi / �

Does a �* exist s.t. ( b - �i wi / �* ) =0 ?

�* = �i wi / b ... xi = ( wi / �i wi ) b


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�(x)=0max f(x)

Constrained maximum


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• If x0 is a constrained relative extremum on a manifold �(x)=0

grad f(x0) = � grad �(x0)(grad f must be normal to the manifold, but grad �

forms a basis of the normal space)• In other words, x0 is a critical point of

f(x) + � �(x)


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�(x)=b – g(x)max f(x)

grad f(x) = grad g(x)

if one changes constraint b + dbhow does optimum change?db �

df � grad f . dx = �* grad g . dx

... df � �* db

�* is called a shadow price


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what happens if the “bandwidth” b changes by a small amount? Let Bestf(b) be the optimal value

Bestf(b) = f(x*(b)) + �* ( b – g(x*(b) )

� Bestf(b)/ �b = �i � /�xi (�xi/�b) + � /� � (� �/�b) + � /�b

= 0 (stationary) + ( b – g(x*(b) ) (� �/�b) + �* = �*

�* is the rate at which the maximized value increases with bcalled a shadow price (for an increase dBestf we shouldbe prepared to pay �* db)

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Unidad II -Sesion 4 - Aplication to Pricing Comm

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