FAIR CHARGES FOR INTERNET CONGESTION Damon Wischik Statistical Laboratory, Cambridge Electrical Engineering, Stanford wischik.

FAIR CHARGES FOR INTERNET CONGESTION

Damon WischikStatistical Laboratory, CambridgeElectrical Engineering, Stanfordwww.stanford.edu/~wischik

INTERNET CONGESTION

Users send packets. When a router’s buffer fills:

it drops further incoming packets. When a user detects a dropped packet, typically:

it reduces its transmission rate; it resends the dropped packet.

Thus congestion slows down file transfers.

AB

WHO DOES WHAT

Users have no incentive to reduce rates If they cooperate, the system works

(Jacobson 1988) If they are greedy, they will cause congestion collapse

(Floyd+Fall 1999)

ENTITY DOES WHAT? KNOWS WHAT? WANTS WHAT?

user chooses rate at which to send packets

how many of its packets are dropped

send lots of packets quickly

router forwards packets; drops some

queue size; net incoming packet rate

?

PRICE AS AN INCENTIVE

Give users an incentive to control congestion let each user send what it wills;

charge accordingly (Gibbens+Kelly 1999)

ENTITY DOES WHAT? KNOWS WHAT? WANTS WHAT?

user chooses rate at which to send packets

its bill; how many of its packets are dropped

low bill; send lots of packets quickly

router forwards packets; drops some; charges users

queue size; net incoming packet rate

control congestion

OBJECTIVE

The network aims to distribute resources efficiently fairly simply

We seek mechanisms that are feasible technologically economically

EFFICIENT. FAIR. SIMPLE.

Economists efficient but impractical pricing schemes

(MacKie-Mason+Varian 1994) regulators are interested in fairness

Engineers simple working idea of fairness, efficiency simple algorithms such as RED

(Floyd+Jacobson 1993) Queueing theorists

analyze how congestion occurs

EFFICIENT. FAIR. SIMPLE.

Economists efficient but impractical pricing schemes

(MacKie-Mason+Varian 1994) regulators are interested in fairness

Engineers simple working idea of fairness, efficiency simple algorithms such as RED

(Floyd+Jacobson 1993) Queueing theorists

analyze how congestion occurs(Wischik 1999)

OUTLINE OF TALK

Define what it means for prices to be efficient fair

Analyse and devise simple charging algorithms

EFFICIENCY

ECONOMIC EFFICIENCY Let there be one router, for simplicity. Let each user

send amount , where experience average drop rate have net utility

Seek to maximize net welfare where and

Charge price Assume user acts to

Vu uX VuuXX )(

)(XLu

)()( XLXU uuu

)()(max?

YLXUu uu

u uXY

)(XPu

)()(max?

XPXU uuu

u u XLYL )()(

ECONOMIC EFFICIENCY Let there be one router, for simplicity. Let each user

send amount , where experience average drop rate have net utility

Seek to maximize net welfare where and

Charge price Assume user acts to

Vu uX VuuXX )(

)(XLu

)()( XLXU uuu

)()(max?

YLXUu uu

u uXY

)(XPu

)()(max?

XPXU uuu

u u XLYL )()(

ECONOMIC EFFICIENCY Let there be one router, for simplicity. Let each user

send amount , where experience average drop rate have net utility

Seek to maximize net welfare where and

Charge price Assume user acts to

Vu uX VuuXX )(

)(XLu

)()( XLXU uuu

)()(max?

YLXUu uu

u uXY

)(XPu

)()(max?

XPXU uuu

u u XLYL )()(

THREE SORTS OF EFFICIENCY

Three different user models: Let be a fluid amount

Let be a random process

Let belong to some fixed traffic

class (Courcoubetis+Kelly+Weber 1997)

Three different optimal prices.

uXYLXP uu /

uX)()( uu XYELYELP

uX)( Bandwidth, Effective uu XP

THREE PRICING SCHEMES

CHARGES EFFICIENT, WHEN FAIR?

SPSP X a fluid quantity

L X a random process

EB X belongs to some fixed traffic class

YLX /

)(

)(

XYL

YL

)(X

FAIRNESS

FAIRNESS 1/4

Effective bandwidth theory says

The EB scheme charge is

This yields a total allocation of costs accounting definition of fairness “crudest but most direct approach”

u ut

tXtCtBE )()(supinf)loss(log ,

]),0[exp(log)(, tXEX uut

)(ˆˆ,ˆ ut

Xt

FAIRNESS 2/4

Let each customer have bundle , and utility

u envies v if

We call an allocation no-envy fair if no one envies anyone else. well-developed mathematical theory

(Thomson+Varian 1985, Baumol 1986) avoids interpersonal comparison of utility; but of no use to us!

u)( uu bUub

)()( vuuu bUbU

FAIRNESS 3/4

The Burden Test for Fairness let C = extra cost of serving customer

X let P = revenue from X if C>P,

the firm makes a loss on X; it must make up the difference by overcharging others

X benefits from cross-subsidization The L scheme charges:

P(X) = C(X) = L(Y) – L(Y-X) precisely the cost of serving a user

SOCIAL INSTABILITY OF L

L charges a user its burden cost C( )=2; C( )=2; C( )=2

Users have an incentive to form coalitions L is socially unstable

queuedserviced

dropped

FAIRNESS 4/4

A price is anonymously equitable if no user, no collection of users,

and no part of a userbenefits from cross-subsidization;

that is, any collection of packets Z is charged at leastP(Z) >= C(Z) = L(Y)-L(Y-Z)

To be fair charge every packet

that contributes to congestion

SAMPLE PATH SHADOW PRICING

Charge every packet whose removal would lead to one less drop(Gibbens+Kelly 1999)

This is anonymously equitable

queued(charged

)serviced

dropped

THREE SORTS OF FAIRNESS

CHARGES A USER

EFFICIENT, WHEN

FAIR?

SPSP the extra cost of each individual packet

X a fluid quantity anonymously equitable

L the net extra cost of its packets

X a probability distribution

satisfies the burden test

EB the effective bandwidth of its distribution

X a predefined traffic type

achieves a total allocation of costs

WHICH FAIRNESS IS BEST?

The three definitions measure different things SPSP = “consumption” L = SPSP – discount EB = SPSP - discount discounts take account of how users

respond Technological considerations:

routers cannot model user behaviour SPSP is the right definition of fairness

A FAIRNESS ANALOGY

Andrew, Betty and Charles share a cake. Each takes one third.

The cost is split equally.

A FAIRNESS ANALOGY

Andrew, Betty and Charles share a cake. Each takes one third.

They each want different amounts: Andrew and Betty demand

exactly one third each; Charles only wants one quarter,

but is happy to eat the rest. Instead of splitting the cost equally,

Charles is given a discount.

SIMPLE CHARGING ALGORITHMS

MARKING AND CHARGING

Let routers mark packets to indicate congestion — but how? (Ramakrishnan+Floyd 1999)

Users should respond by reducing their rate but have no incentive to do so

Let us charge the user for each marked packet,and mark according to SPSP(Gibbens+Kelly 1999)

GOOD MARKING ALGORITHMS

Want to mark according to SPSP SPSP requires foreknowledge:

whether or not a packet should be marked depends on future overflows.

So seek approximations to SPSP: use theory to analyze RED, to see how close it is; to suggest new algorithms—ROSE.

queued(charged

)serviced

dropped

ANALYSIS OF ALGORITHMS

Theorem: (Wischik 1999)sample path large deviations

Let Xi = random amount of work that a user generates at time i, X=(X1,X2,…)

The most likely path to lead to marking is given by can be calculated

Proof: large deviations

)ˆexp(logˆ Xx E

THE RED ALGORITHM

Keep a moving average of queue size

When exceeds a threshold mark each incoming packet, with probability

(Floyd+Jacobson 1993, Cisco 1998) Fair? Not close to SPSP

-5 0 5 10 15

A

-5 0 5 10 15

B

marked packets

bursty flow

smooth flow

inco

min

g w

ork

timeREDSPSP

ttt qqq )1(11

tq tq

tq)( tqP

Paths most likely to lead to marking

SUMMARY

Users need incentives to cooperate, such as congestion charges.

Efficiency? No clear definition Fairness? SPSP

Marks can convey prices, so design simple marking algorithms analyse their behaviour

Other questions market structure? user behaviour?

MARKET STRUCTURE

Marks indicate how much networks should pay each other, where capacity should be expanded.

Who should pay for congestion? only the receiver knows the price but maybe the sender should pay

$6$5$3network service provider

+3 marks +2 marks +1 mark

nspnsp

USER BEHAVIOUR

Is the system stable? Kelly, Maulloo, Tan (1998)

Rate control in communication networks

How might users behave? Gibbens, Kelly (1999)

The evolution of congestion control Microsoft Research Cambridge

A distributed network game