1. FAIR CHARGES FOR INTERNET CONGESTION Damon Wischik Statistical Laboratory, Cambridge Electrical Engineering, Stanford www.stanford.edu/~wischik

2. 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. A B

3. 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) ENTITYDOES WHAT?KNOWS WHAT?WANTS WHAT? userchooses rate at which to send packets how many of its packets are dropped send lots of packets quickly routerforwards packets; drops some queue size; net incoming packet rate ?

4. PRICE AS AN INCENTIVE  Give users an incentive to control congestion  let each user send what it wills; charge accordingly  (Gibbens+Kelly 1999) (Gibbens+Kelly 1999) ENTITYDOES WHAT?KNOWS WHAT?WANTS WHAT? userchooses rate at which to send packets its bill; how many of its packets are dropped low bill; send lots of packets quickly routerforwards packets; drops some; charges users queue size; net incoming packet rate control congestion

5. OBJECTIVE  The network aims to distribute resources  efficiently  fairly  simply  We seek mechanisms that are feasible  technologically  economically

6. EFFICIENT. FAIR. SIMPLE.  Economists  efficient but impractical pricing schemes (MacKie-Mason+Varian 1994) (MacKie-Mason+Varian 1994)  regulators are interested in fairness  Engineers  simple working idea of fairness, efficiency  simple algorithms such as RED (Floyd+Jacobson 1993) (Floyd+Jacobson 1993)  Queueing theorists  analyze how congestion occurs

7. EFFICIENT. FAIR. SIMPLE.  Economists  efficient but impractical pricing schemes (MacKie-Mason+Varian 1994) (MacKie-Mason+Varian 1994)  regulators are interested in fairness  Engineers  simple working idea of fairness, efficiency  simple algorithms such as RED (Floyd+Jacobson 1993) (Floyd+Jacobson 1993)  Queueing theorists  analyze how congestion occurs (Wischik 1999) (Wischik 1999)

8. OUTLINE OF TALK  Define what it means for prices to be  efficient  fair  Analyse and devise  simple charging algorithms

9. EFFICIENCY

10. 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 

11. 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 

12. 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 

13. 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.

14. THREE PRICING SCHEMES CHARGESEFFICIENT, WHENFAIR? SPSP X a fluid quantity LL X a random process EB X belongs to some fixed traffic class

15. FAIRNESS

16. 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”

17. 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!

18. 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

19. 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 queued serviced dropped

20. FAIRNESS 4/4  A price is anonymously equitable if  no user, no collection of users, and no part of a user benefits from cross-subsidization;  that is, any collection of packets Z is charged at least  P(Z) >= C(Z) = L(Y)-L(Y-Z)  To be fair  charge every packet that contributes to congestion

21. SAMPLE PATH SHADOW PRICING  Charge every packet whose removal would lead to one less drop (Gibbens+Kelly 1999) (Gibbens+Kelly 1999)  This is anonymously equitable queued (charged) serviced dropped

22. THREE SORTS OF FAIRNESS CHARGES A USER EFFICIENT, WHEN FAIR? SPSPthe extra cost of each individual packet X a fluid quantityanonymously equitable LL the net extra cost of its packets X a probability distribution satisfies the burden test EBthe effective bandwidth of its distribution X a predefined traffic type achieves a total allocation of costs

23. 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

24. A FAIRNESS ANALOGY  Andrew, Betty and Charles share a cake. Each takes one third.  The cost is split equally.

25. 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.

26. SIMPLE CHARGING ALGORITHMS

27. MARKING AND CHARGING  Let routers mark packets to indicate congestion — but how? (Ramakrishnan+Floyd 1999)(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) (Gibbens+Kelly 1999)

28. 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

29. ANALYSIS OF ALGORITHMS  Theorem: (Wischik 1999) sample path large deviations(Wischik 1999)  Let X i = random amount of work that a user generates at time i, X =( X 1,X 2,…)  The most likely path to lead to marking is given by   can be calculated  Proof: large deviations

30. 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)Floyd+Jacobson 1993Cisco 1998  Fair? Not close to SPSP marked packets bursty flow smooth flow incoming work time REDSPSP Paths most likely to lead to marking

31. 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?

32. 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 $3 network service provider +3 marks +2 marks +1 mark nsp

33. USER BEHAVIOUR  Is the system stable?  Kelly, Maulloo, Tan (1998) Rate control in communication networks Rate control in communication networks  How might users behave?  Gibbens, Kelly (1999) The evolution of congestion control The evolution of congestion control  Microsoft Research Cambridge A distributed network game A distributed network game