1. Peter Key, Laurent Massoulie, Don Towsley Infocom 07 presented by Park HoSung 1 Path selection and multipath congestion control

2. Motivation multipath data transfer –efficiency : performance gain –robustness : overcome node failure already a large fraction of internet traffic we need multipath congestion control 2

3. Recent P2P strategies Kazaa –choose multiple paths manually Skype –select paths automatically Bittorrent –maintain 4 active paths –periodically select 1 random path –retain best paths (by throughput) 3

4. Questions 1. several paths vs all paths –we want to keep overhead small –using several paths is okay? 2. effect of RTT bias –loss of efficiency with RTT bias 3. uncoordinated vs coordinated –uncoordinated : using parallel connections (TCP) –coordinated : balancing load across paths (revised protocol or application) 4

5. Answers 1. several paths vs all paths –using a small number of paths does as well as using all the paths 2. effect of RTT bias –loss of efficiency with RTT bias 3. uncoordinated vs coordinated –static case : coordinated controller is better –path reselection, no RTT bias case : uncoordinated controller does as well as coordinated controller 5

6. Solution Approach set the modeling framework make assumptions –coordinated or uncoordinated –RTT biased or unbiased –route resampling or not derive results mathematically No Experiments! 6

7. Outline 1. With Static random path –fixed randomly selected routes 2. Allow users to change set of routes –users seek to selfishly maximize their own net utilities 3. With simple path selection policy –random path resampling with moving to paths with higher benefit 7

8. Modeling Framework Uncoordinated Congestion Control –assume that each user try to maximize their throughput –uses have to same # of connections –rate is achieved by some default congestion control mechanism (e.g. TCP) –criterion for optimality is achieved rate 8

9. (cont’d) constraint outcome of congestion control is defined to the solution of the welfare maximization problem 9

10. (cont’d) Ns’ : # of s-user Ns : # of connection of s-user Ns = b*Ns’ Nr = total # of connection of s-user, through route r Ur(λr) : utility function of λr rate Λ = {Λr} vector of aggregate rate Γ : penalty function 10

11. Modeling Framework Coordinated Congestion Control –assume that s-user can user concurrentyl paths from collection c ( c is subse of R(s) ) –C(s) is path collections allowed subset of R(s) of size b –Nc : # of users using c paths –Ns : # of s-users –Use single utility function Us with s-user 11

12. (cont’d) constraint optimal rates Λr actually solves the following 12

13. Static, Random Route Selections N resources with unit capacity penalty step function a*N users each user selects b resources at random measure worst case rate allocation 13

14. (cont’d) A. uncoorinated congestion control –λi : total rate of user i from all its connection –worst case allocation decreases like log(log(N))/log(N) B. coordinated congestion control –λi* : optimal allocation, there exists x > 0 –worst case allocation is bounded away from 0 as N tends to infinity 14

15. (cont’d) In static random path case –coordinated is better than uncoordinated –coordinated is better than greedy least-loaded resource selection [ 1/log(log(N)) ] –better use of resources by actively balancing load among available resoureces 15

16. (cont’d) 16

17. Nash Equilibria for Throughput- Maximizing Users users can choose the set of routes users greedily search for throughput optimal routes coordinated, uncoordinated without RTT bias –these equilibria achieve welfare maximization uncoordinated with RTT bias –yields inefficient equilibria 17

18. (cont’d) Nash equilibrium –If each player has chosen a strategy and no pl ayer can benefit by changing his or her strate gy while the other players keep theirs unchan ged 18

19. (cont’d) A. uncoordinated, unbiased congestion control –s-user would maintain a connection along route r only if it cannot find a better route r' (better route allocates a larger rate) –this case achieves a Nash equilibrium, solving coordinated optimization problem 19

20. (cont’d) B. uncoordinated, biased congestion control –TCP utility function regarding RTT –bad example short(s), long(l) connection –s : RTT t, capacity c –l : RTT T, capacity C –a->a’, b->b’, c->c’ s-l-s is Nash equilibrium but throughput of s-l-s is smaller than l-s-l’s 20

21. (cont’d) C.coordinated congestion control –Nash equilibirum if is satisfied –path allocation solve the welfare maximization problem 21

22. Dynamic Route Selection User with route set c proposes a new route set c’ at fixed rate Acc’ New route set is accepted if net benefit is higher than that of the current set both coordinated, uncoordinated case lead to welfare maximizing equilibrium 22

23. (cont’d) simple path selection policy –random path resampling with moving to paths with higher benefit –can lead welfare maximizing equilibria do as well as if the entire path choice was available to each user 23

24. Conclusion Without path reselection –uncoordinated control can perform poorly Small # of routes choice does as well as whole set With no RTT bias –both coordinated and uncoordinated control leasd to a system optimal Good design for multipath rate controller –coordinated controller –uncoordinated controller with no RTT bias 24

25. Comment How can it work with existing controllers –Is it possible to deploy gradually? How can we implement? No experimental data –there will be many other variables Good guideline for a design 25