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Peter Key, Laurent Massoulie, Don Towsley

Infocom 07

presented by Park HoSung

Path selection and multipath congestion

control

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Motivation• multipath data transfer – efficiency : performance gain– robustness : overcome node failure

• already a large fraction of internet traf -fic

• we need multipath congestion con-trol

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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)

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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)

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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

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Solution Approach• set the modeling framework• make assumptions– coordinated or uncoordinated– RTT biased or unbiased– route resampling or not

• derive results mathematically• No Experiments!

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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

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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 con-

gestion control mechanism (e.g. TCP)– criterion for optimality is achieved rate

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(cont’d)• constraint

• outcome of congestion control is de-fined to the solution of the welfare maximization problem

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(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

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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

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(cont’d)• constraint

• optimal rates Λr actually solves the following

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Static, Random Route Selec-tions

• N resources with unit capacity• penalty step function

• a*N users• each user selects b resources at

random• measure worst case rate alloca-

tion

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(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 infin-

ity

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(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 balanc-ing load among available resoureces

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(cont’d)

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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

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(cont’d)• Nash equilibrium

– If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged

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(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

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(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

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(cont’d)• C.coordinated congestion control– Nash equilibirum if

is satisfied

– path allocation solve the welfare maxi-mization problem

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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

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(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

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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

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Comment• How can it work with existing con-

trollers– Is it possible to deploy gradually?

• How can we implement?• No experimental data– there will be many other variables

• Good guideline for a design