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### Comparison of MaxNet and XCP: Network Congestion Control using explicit signallingSpeaker: Bartek Wydrowski

Compiled from work by: Lachlan Andrew (2), Steven Low (1),

Iven Mareels (2), Bartek Wydrowski (1), Moshe Zukerman (2).

(2)

(1)

Talk Overview

- MaxNet & XCP Overview.
- Steady state: Rate allocation properties.
- Summary of Maxnet and XCP.
- Maxnet: A little more details
- Stability.
- Convergence Speed.

Network Congestion Control

L1

S1

D1

L2

S2

D2

L3

S3

D3

Sources transmit at a rate

controlled by a “congestion signal”

Links generate the congestion signal

based on level of congestion at link

Congestion level of end-to-end

path is fed back to source

Network Congestion Control

Congestion signal on the Internet is implicit, and can be modelled as the sum of the end-to-end link congestion levels – this is where XCP, MaxNet differs.

S

p

p

p

i

1

2

N

Link 1

Link 2

Link N

Source

Destination

Link l drops packets at rate pl:

Link l ECN marks packets at rate pl:

Link l delays packets for time pl:

Link 1

Link 2

Link 1

Link 2

Link 1

Link 2

T1

T2

- MaxNet is:
- A Fully distributed flow control architecture for large networks.
- Max-Min fair in principle.
- Stable for networks of arbitrary topology, number of users, capacity and delay.
- Fast convergence properties.
- Addresses short-flow control.
- Philosophy:
- Simple Architecture.
- Ability to scale.
- Simplicity ability to design/predict.

MaxNet: Source Algorithm

x– Transmission Rate

p - Price

Source Algorithm – Demand Function.

Each source can have a different demand function which determines the source’s relative need for capacity.

Xi = D(price_k)

Congestion Feedback from ACK k

Source rate

Source demand function

Source 1

Packet Signal = max(PacketSignal,p1(t))

Source 2

Packet Signal = max(PacketSignal ,p2(t))

Packet Signal = max(PacketSignal ,p3(t))

Signal =max(p2,p3)

Signal =max(p1,p2,p3)

MaxNet: Link Algorithm

Router Algorithm: Packet marking according to

Price_k = max ( Price_k , pl(t) )

Link price

updated at each control

interval, say every 10ms.

(single price for all flows on link)

Congestion signal

in pkt k

pl(t+1) = pl(t) + b(y(t)-aC)

Constant: convergence speed

Link capacity

Aggregate

input rate

Constant to control

Link utilization

MaxNet: Steady State Properties

S0

2 Mbps

D0

L1

3 Mbps

S1

D1

L2

2 Mbps

S2

D2

L3

S3

D3

q0 = p1 = max(p1)

q1 = p1 = max(p1,p2)

q2 =p1= max(p1,p2,p3)

q3 = p3= max(p2, p3)

p1

p2

p3

Mbps

S3

1.33

S0,S1,S2

0.66

q3

q0, q1, q2

Price

XCP Architecture

XCP Packet Header

H_cwnd

H_rtt

H_feedback

Receiver

Sender

router

router

1. Initializes pkt k:

H_throughput_k

H_rtt_k

H_feedback_k

2. Each Router Computes Feedback:

H_feedback_k = min(H_feedback_k,H_lk)

Where H_lk = link l’s feedback for pkt k.

Thus, feedback from router with minimum ‘feedback signal’ is obtained from source to destination path.

3. Send header

back to sender

in ACK.

XCP Architecture

Source Algorithm:

- Rate is governed by window
- Source sends packet containing XCP header
- Source receives feedback in ACK and adjusts window

Feedback from ACK

Change in source window

Source transmission rate

XCP Architecture

Router Algorithm: Feedback computed for each packet

H_feedback_k = min (H_feedback_k,H_feedback_i)

Round trip time of source i in packet

Feedback in Pkt

k header

Window of source i in packet

Mean of all RTTs

Packet size

Sum over control interval

Aggregate input rate

Link capacity

Queue

MaxNet: Steady State Properties

MaxNet is Max-Min fair for homogenous sources.

If all sources have the same demand function (homogenous),then MaxNet results in a max-min rate allocation.Max-min fairness maximises the minimum rate allocation,and maximizes each subsequently larger rate without reducingthe smaller rates.

MaxNet: Steady State Properties

For general demand functions, MaxNet is weighted min-max fair. (Min-Max price fair)

Sources can prioritizetheir rate allocation bychanging their demandfunctions. Roughly speaking,their rate allocation will be in proportion to the magnitude

of the demand function.

Transmission rate

x1

x2

Link price

XCP: Steady State Properties

- Analysis to compute XCP equilibrium rates for arbitrary topology: Steven H. Low, Lachlan L. H. Andrew, Bartek P. Wydrowski, “Understanding XCP: Equilibrium and Fairness”.

Rate allocation is a solution to a max-min problem with additional constraints

- Effects of additional constraint:
- Utilization can be below 100%.
- Rates can be arbitrarily small fraction of max-min fair rates
- In some topologies, residual terms are redundant.

XCP: Steady State Properties

- Given a topology, our analysis can predict rate allocation.
- Matches NS2 results very precisely
- Predicts interesting pathological cases

XCP: Steady State Properties

- Utilization of a link varies with number of sources bottlenecked at other links.
- Lower and upper bound are:
- ρl = fraction of flows at link l not bottlenecked at link l
- l= fraction of traffic at link l not bottlenecked at link l
- = shuffling parameter , = XCP parameters (conv speed,buffer)
- With standard alpha and gamma parameters, utilization is at least 80%.

XCP Scenario 1

Rate allocation can be arbitrarily smaller than max-minfair rates.

Eg: C1=155 Mbps C2=C1(n-1)/n

i=n^2-1 j=1

Alpha = 0.4 Beta = 0.226 Gamma = 0.1

XCP- Stability counter-example

Sources

0..9

Sink

Source

10

200Mbps

1x = 50ms

5x = 250ms

10x = 500ms

100Mbps

50ms

MaxNet is stable (local proven) over arbitrary network dimensions of:

Number of sources, links,hops, delay, capacity

Same properties as were shown for SumNet in:

F. Paganini, J.C. Doyle and S.H. Low, “Scalable laws for stable network congestion control,” in Proc. IEEE Conf. Decision Contr. (CDC), (Orlando, FL), 2001, pp. 185-90.

Network Control Model

L1

S1

D1

L2

S2

D2

L3

S3

D3

Physical Network

Control Model Network

Model quantities are small signal variations about equilibrium.

S1

Source Rate

x

Aggregate price

q

S2

S3

0

0

0

0

L1

0

L2

0

0

L3

0

Aggregate Rate

y

Link price

d

Network Control Model

MaxNet open-loop transfer function.

S1

S2

S3

0

0

0

0

L1

0

L2

0

0

L3

0

Source Gain

Link Gain

Link Integrator

Action

Backward Routing Matrix

Forward Routing Matrix

x– Transmission Rate

p - Price

Source Gain

Constrains slope

Of source demand

function

Link Gain

Constrains speedof link control law

pl(t+1) = pl(t) + b(y(t)-aC)

MaxNet: Convergence Speed

MaxNet has faster asymptotic convergence than the SumNet architecture.

(MaxNet is able to place the dominant pole further to the left than SumNet.)

Conclusion

- MaxNet steady state, stability and speed properties have been investigated.
- XCP steady state properties were recently analyzed.
- MaxNet offers (at least) steady state and implementation simplicity, advantages over XCP.

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