1

Network Congestion Control

EL 933, Class10

Yong Liu

11/22/2005

2

Motivation

! Network bandwidth shared by all users

! Given routing, how to allocate bandwidth

" efficiency

" fairness

" stability

! Challenges

" distributed/selfish/uncooperative end systems

" remote/dumb/oblivious routers

3

Outline

! Basics on TCP/RED

! Paper 1: "Rate control in communication networks:

shadow prices, proportional fairness and stability",

Frank Kelly, A.K. Maulloo and D.K.H. Tan, , Journal of

the Operational Research Society

! Paper 2: "Fluid-based analysis of a network of AQM

routers supporting TCP flows with an application to

RED", Vishal Misra, Weibo Gong and Don Towsley,

ACM SIGCOMM 2000

4

Congestion Control

! Network is a distributed

resource sharing system

! Overload means low

throughput

! Individual user depends on

feed back from system to

regulate its load

5

Criteria for Congestion Control

! Efficiency: the closeness of

the total usage to the

optimal level

! Fairness:

Fairness index:

Max-Min Ratio:

! Convergence:

How fast does the system

converge to the desired

state.

6

Internet Congestion Control

Transport Control Protocol

(TCP) at edge

Active Queue Management

(AQM) in core

7

AIMD

! Additive Increase Multiplicative Decrease

! AI: aggressive in grabbing

available bandwidth

! MD: conservative when

network is congested

! trade-off

" efficiency & fairness

8

TCP Congestion Control

! adapt sending rate to network congestion

! window-based rate control# send out a window of W packets each round

# increase W by 1 every RTT if no packet loss

sender

receiver

W

RTT

9

TCP Congestion Control

! adapt sending rate to network congestion

! window based rate control# send out a window W of packets each round

sender

receiver

W

RTT

# decrease W by half upon packet loss

x

# increase W by 1 every RTT if no packet loss

10

More on TCP

! slow-start,

congestion avoidance,

time-out

! triple-duplicated ack

loss & time-out loss

! fast retransmit,

fast recovery

! TCP Tahoe, Reno,

New Reno, Vegas

11

Queue Management

! natural solution: DropTail-- drop new packetsif buffer full" synchronization among flows (?)

" response too late

" large buffer --> large delay

! Active Queue Management (AQM)" random drop: break synchronization

" proactively drop: earlier reaction

" new approaches: RED, BLUE, PI, AVQ, REM ……

12

Random Early Detection

RED: Marking/dropping based on average queue length x (t)

tmin tmax

pmax

1

Marking probability profile has a

discontinuity at tmax

discontinuity removed in gentle_ variant

2tmax

Mar

king

pro

bab

ilit

y p

Average queue length x

t ->

- q (t)

- x (t)

x (t): smoothed, time averaged q (t)

13

Rate Control for Communication Networks:

shadow prices, proportional fairness and stability

FP Kelly, AK Maulloo and DFH Tan

14

Outline

! optimal rate control

! decomposition

! primal/dual algorithms

! user adaptation

! extensions

15

Optimal Rate Control

! Demand v.s. supply" demand: user rate

" supply: link bandwidth

" consumption: routing matrix

! Quantification" utility function:

" link cost:

! Optimal routing" maximize aggregate utility under

resource constraint

" convex optimization solvable

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Centralized v.s. Distributed

! Centralized solution" network determines rate for all users

" require knowledge of routing and utility functions ofall users

! Distributed algorithm more realistic" user determines its own sending rate

" network uses “pricing” to regulate users

" minimum info. exchange between users and network

" right price --> selfish optimum==global optimum

" analogy from Market Economics

17

Decomposition: distributed optimization

! User Optimization

" given a price, how much

to send?

! Network Optimization

" given user payment, how

to allocate?

18

Decomposition: consistency

!

"

"

"

19

Decomposition: efficiency & fairness

! find optimal rate allocation for all users

" user optimizes his own utility independently

" links are not over-loaded, some fully-loaded, some

under-loaded

" the aggregated utility is maximized (efficiency)

" proportional fairness:

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Network Opt.: primal-dual formulation

! primal problem: optimal

rates for users

! dual problem: optimal

prices on links

duality theorem: dual solution matches primal solution

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Network Opt.: primal algorithm

! link penalty function

! unconstrained optimization

! dynamic algorithm: user rate adjustment

! convergence

"

"

22

Network Opt.: dual algorithm

! dynamic algorithm: link price adjustment

! convergence"

"

23

User Adaptation

! network optimization:

" approximation:

" user scheme:

! system optimization:

" approximation:

" user scheme:

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Other Properties

! speed of convergence to the optimum

! robustness against

" information accuracy

" information delay

! Utility function of TCP

" reno:

" vegas:

25

Extensions! One user employ multiple paths

"

"

! Joint rate control and routing

! System converges to optimum" user only uses paths with minimum price

" traffic rates on selected paths equal26

Summary

! Network optimal rate allocation decomposed intodistributed optimization" users maximize net gain

" links minimize cost

" dynamically approach optimum

• right link price

• optimal rate allocation

• maximized aggregate utility

! TCP Works!!" maximize efficiency

" maintain some sort of fairness

" stable and robust

27

Fluid-based Analysis of a Network of AQM Routers

Supporting TCP Flows with an Application to RED

Vishal Misra Wei-Bo Gong Don Towsley

University of Massachusetts, Amherst

MA 01003, USA

(slides borrowed from Vishal)

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Overview

!motivation

!key idea

!modeling details

!validation with ns

!analysis sheds insights into RED

!conclusions

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Motivation

! current simulation technology, e.g. ns

" appropriate for small networks

10s - 100s of network nodes 100s -

1000s IP flows

" inflexible packet-level granularity

! current analysis techniques

" UDP flows over small networks

" TCP flows over single link

...

......30

ChallengeExplore large scale systems

" 100s - 1000s network elements

" 10,000s - 100,000s of flows (TCP, UDP, NG)

Our BeliefFluid-based techniques that abstract out protocol details

are key to scalable network simulation/understanding

Contribution of PaperFirst differential equation based fluid model to

enable transient analysis of TCP/AQM networks

developed

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Key Idea

! model traffic as fluid

! describe behavior of flows and queues using

Stochastic Differential Equations

! obtain Ordinary Differential Equations by taking

expectations of SDEs

! solve resultant coupled ODEs numerically

Differential equation abstraction:

computationally highly efficient32

Loss Model

Sender

AQM Router

Receiver

Loss Rate as seen by Sender: !(t) = B(t-")#p(t-")

Round Trip Delay (")

B(t)p(t)Packet Drop/Mark

!(t) = B(t)#p(t)

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Start Simple: A Single Congested Router

TCP flow i,prop. delay Ai

AQMrouter

C, p

! One bottlenecked AQM router

" capacity {C (packets/sec) }

" queue length q(t)

" drop prob. p(t)

! N TCP flows

" window sizes Wi (t)

" round trip time

Ri (t) = Ai+q (t)/C" throughputs

Bi (t) = Wi (t)/Ri (t)

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System of Differential Equations

Window Size: dWi

dt

^= 1

^R̂i(q(t))

Additive

increase

Wi

2

^-

Mult.

decrease

Wi(t-")^

Ri (q(t-"))p̂(t-")

Loss arrival

rate

^^

-1[q(t) > 0]C^

Outgoing

traffic

Queue length: dq

dt=^

All quantities are average values. Timeouts and slow start ignored

+ $Ri(q(t))^

Wi(t)^

Incoming

traffic

^

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System of Differential Equations (cont.)

Average queue length: q(t)^dx

dt=

ln (1-%)

&

ln (1-%)

&-x(t)^

Where

% = averaging parameter of RED(wq)

& = sampling interval ~ 1/C

^

Loss probability:dp

dt= dp

dx

dx

dt

^^

Where dp is obtained from the marking profile

dx

p

x 36

Stepping back: Where are we?

dWi

dt= f1(p,Ri) i = 1..N

dp

dt= f3(q) dq

dt= f2(Wi)

N+2 coupled equations solved numerically using MATLAB

W=Window size, R = RTT, q = queue length, p = marking probability

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Extension to Network

Networked case: V AQM routers

Other extensions to the model

Timeouts: Leveraged work done in [PFTK Sigcomm98] to model timeouts

Aggregation of flows: Represent flows sharing the same route by a

single equation

queuing delay = aggregate delay

q(t) = $V qV(t)

loss probability = cumulative loss probability

p(t) = 1-'V(1-pV(t))

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Validation Scenario

! DE system programmed with

RED AQM policy

! equivalent system simulated in

ns

! transient queuing performance

obtained

! one way, ftp flows used as

traffic sources

Flow set 1

Flow set 2

Flow set 3

Flow set 4

Flow set 5

RED router 1RED router 2

Topology

5 sets of flows

2 RED routers

Set 2 flows through both routers

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Performance of SDE method

! queue capacities 5 Mb/s

! load variation at t=75 and

t=150 seconds

! 200 flows simulated

! DE solver captures

transient performance

! time taken for DE solver ~

5 seconds on P450

DE method

ns simulation

Inst

. qu

eue

leng

th

Time

Inst. queue length for router 2

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Observations on RED

! “Tuning” of RED is difficult

- sensitive to packet sizes, load levels, round trip

delay, etc.

! discontinuity of drop function contributes to, but is not the

only reason for oscillations.

! RED uses variable sampling interval &. This could cause

oscillations.

Further Work

Detailed Control Theoretic Analysis of TCP/RED available

at http://gaia.cs.umass.edu/papers/papers.html

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Conclusions

! differential equation based model for evaluatingTCP/AQM

networks

! computation cost of DE method a fraction of the discrete

event simulation cost

! formal representation and analysis yields better

understanding of RED/AQM

42

Future Directions

! model short lived and non-responsive flows"Unresponsive Flows and AQM Performance”, (INFOCOM 2003)

! demonstrate applicability to large networks“Fluid Models and Solutions for Large-Scale IP Networks”,(Sigmetrics 2003)

! analyze theoretical model to rectify RED shortcomings“On Designing Improved Controllers for AQM RoutersSupporting TCP Flows”, (INFOCOM 2001)

! apply techniques to

- other protocols, e.g. TCP-friendly

protocols

- other AQM mechanisms like Diffserv"Providing Throughput Differentiation for TCP Flows UsingAdaptive TwoColor Marking and Multi-Level AQM”,(INFOCOM 2002)

43

New Directions…

! high speed networks" linear increase not efficient enough: HTCP, FAST

" more feedback from routers: XCP

! wireless networks" corruption loss: Explicit Congestion Notification

" link coupling: cross layer design

! overlay/p2p networks" application layer control: parallel/relay

" revisit: efficiency/fairness/stability