optimal internal congestion control in a cluster-based routernetworks/gswnr2009/qinghua... ·...

OutlineCongestion in the Cluster-based Router

Optimal Utility-based ControlSimulation With NS-3

Evaluations In the Real SystemConclusions and Related Work

Optimal Internal Congestion Control in ACluster-based Router

Qinghua Ye

Nov.17, 2009

Qinghua Ye Optimal Internal Congestion Control in A Cluster-based Router




Congestion in the Cluster-based Router

Optimal Utility-based Control

Simulation With NS-3

Evaluations In the Real System

Conclusions and Related Work





Figure: Cluster-based Router Architecture





Figure: IP Forwarding Path





Optimal Utility-based Control

I An optimization approach to congestion control problemsI Objective: maximize the aggregate source utilityI Constraints: network link capacities.

I The network links and traffic sources are viewed as adistributed system that acts to solve the optimization problem

I Traffic sources adjust their transmission rates in order tomaximize their own benefit

I The network links adjust bandwidth prices to coordinate thesources decisions on the evolution of their transmission rates





Classification of Optimal Utility-based Control

According to the controlled objects:

I Primal algorithms (TCP)

I Dual algorithms (Active Queue Management)

I Primal-dual algorithms (Combination of TCP and AQM)





Internal Congestion Control As An Optimization Problem

I Consider a network with unidirectional links. There is a finiteforwarding capacity C associated with the egress. The egressis shared by a set S of sources, where source s ∈ S ischaracterized by a utility function Us(xs) that is concaveincreasing in its transmission rate xs to the egress.

I Model:P :

∑s∈S

Us(xs) (1)

subject to ∑s∈S

xs ≤ C (2)





Decentralized Approach

I The dual theory of optimization leads us to a distributed anddecentralized solution which results in the coordination of allsources implicitly

I Lagrangian function:

L(x , p) =∑s∈S

Us(xs)− p(∑s∈S

xs − C )

=∑s∈S

Us(xs)−∑s∈S

xs ∗ p + p ∗ C(3)






I The objective function of the dual problem:

D(p) = maxxs

L(x , p)

=∑s∈S

max(Us(xs)− xs ∗ p) + p ∗ C (4)

I The dual problem:D : min

p≥0D(p) (5)






I The congestion control problem can be generalized to tasks offinding distributed algorithms that can make sources adapttransmission rates with respect to the egress price and makeegress adapt prices with respect to loads

I The optimal solution to the distributed congestion controlproblem satisfies:

{∂D(p)∂xs

= ∂Us(xs)∂xs

= U ′s(xs)− p = 0∂D(p)∂p =

∑s∈S (−xs) + C = 0





Discrete Optimal Utility-based Control

I To reduce the overhead of transferring the link price, we onlysend the price from the egress to the sources at the beginningof each control interval, which results in a discrete-timecontrol model:

{xs(k + 1) = [xs(k) + K ∗ xs(k) ∗ (U ′s(xs(k))− p(k))]+xs [k]

= [xs(k) + K ∗ (W − xs(k) ∗ p(k))]+xs [k]p(k + 1) = [p(k) + (

∑s∈S xs(k)− C )/R]+p(k)

(6)Here

[g(x)]+y = { g(x), y > 0max(g(x), 0), y = 0

and K and 1/R are step sizes.





Queue Status as an Indicator of Congestion

I In real system, the transmission capacity of the egress in themodel vary for different situations or times

I More than one port may share the same busI Sharing of a single egress port by multiple egress queues

I Queue-based approach:

{xs(k + 1) = [xs(k) + K ∗ (W − xs(k) ∗ p(k))]+xs [k]p(k + 1) = [p(k) + (delta(q))/R]+p(k)

(7)





Queue Status as an Indicator of Congestion

I The system may be stable at large queue length

I To reduce the stable queue length:

{xs(k + 1) = [xs(k) + K ∗ (W − xs(k) ∗ p(k))]+xs [k]p(k + 1) = [p(k) + (delta(q) + f (q))/R]+p(k)

(8)

I Let f (q) = (q − qo) ∗ u, where qo is the objective of egressqueue length and u is the degree that the queue length wouldbe taken into the price calculation.





IP Packet BECN

Adjust Scheduler Parameters

Receive

IP Header Check

Internal Transmit

External

IP Lookup

Check Queue Status

and Generate BECN

Get MAC of Internal Network Device

Packet Classifier

...

Packet Scheduler

Get Mac of External Network Device

Internal

Packet Classifier

To External

To Internal

Local

Forward To Up Layer

External Transmit

External Transmit

Figure: IP Forwarding Path in SimulationQinghua Ye Optimal Internal Congestion Control in A Cluster-based Router




0

500000

1e+06

1.5e+06

2e+06

2.5e+06

0 100 200 300 400 500

Tra

nsm

issi

on R

ate

Time

Transmission Rate Behavior - (K:100000, R:500000000000)

Transmission RateReception Rate

Reception Rate from Ingress 1Reception Rate from Ingress

Reception Rate from Ingress 3

Figure: Optimization utility-based scheme transmission rate behavior





0

500000

1e+06

1.5e+06

2e+06

2.5e+06

0 50 100 150 200

Tra

nsm

issi

on R

ate

Time

Transmission Rate Behavior - (W:50000, Q:100)


Reception Rate from Ingress 1Reception Rate from Ingress 2Reception Rate from Ingress 3

Figure: AIMD scheme transmission rate behavior





0

100

200

300

400

500

600

700

800

900

1000

0 100 200 300 400 500

Que

ue L

engt

h

Time

Queue Length - (K:100000, R:500000000000)

Queue Length

Figure: Optimization utility-based scheme queue behavior





0

200

400

600

800

1000

0 50 100 150 200

Que

ue L

engt

h

Time

Queue Length - (W:50000, Q:100)

Queue Length

Figure: AIMD scheme queue behavior





0

200000

400000

600000

800000

1e+06

1.2e+06

0 100 200 300 400 500

Tra

nsm

issi

on R

ate

Time

Transmission Rate Behavior - (K:100000, R:500000000000)


Reception Rate from Ingress 1Reception Rate from Ingress

Reception Rate from Ingress 3

Figure: Fairness - Optimization utility-based scheme transmission ratebehavior





0

1000

2000

3000

4000

5000

10 20 30 40 50 60 70 80 90 100

Pack

et R

ate

- K

Pac

ket P

er S

econ

d

Input Rate at Ingress Nodes(Percentage of Wire Rate)

Optimal Utility-based VS. AIMD VS. Original

Reception Rates at Ingress Nodes - originalInjection Rates at Ingress Nodes - original

Transmission Rate at Egress Node - originalReception Rates at Ingress Nodes - AIMD

Injection Rates at Ingress Nodes - AIMDTransmission Rate at Egress Node - AIMD

Reception Rates at Ingress Nodes - optimalInjection Rates at Ingress Nodes - optimal

Transmission Rate at Egress Node - optimal

Figure: Transmission rate comparison





-200

0

200

400

600

800

1000

1200

0 20 40 60 80 100

Out

put Q

ueue

Len

gth

Input Rate at Ingress Nodes (Percentage of Wire Rate)

Queue Length With Increasing Offered Traffic

output queue length - originaloutput queue length - AIMD

output queue length - optimal

Figure: Queue variance comparison





0

200

400

600

800

1000

298298298

AIMD

298298298

Optimal

298298224

AIMD

298298224

Optimal

298298149

AIMD

298298149

Optimal

29829875

AIMD

29829875

Optimal

Pack

et R

ate

- K

Pac

kets

Per

Sec

ond

Offered Rate at Ingress Nodes(K Packets Per Second)

Fairness Among Different Ingress Nodes

Reception Rate at Ingress Node 1Reception Rate at Ingress Node 2Reception Rate at Ingress Node 3

Injection Rate at Ingress Node 1Injection Rate at Ingress Node 2Injection Rate at Ingress Node 3

Transmission Rate at Egress Node

Figure: Fairness comparison





I Optimal Utility-based Congestion ControlI Fair to different flowsI Efficient to reduce the injection rates of traffic to the internal

network to avoid congestionI Related Work

I Analyze and improve the Internet congestion control schemessuch as TCP and AQM

I In wireless cross-layer congestion control:I Lijun Chen , Stevenh. Low , Mung Chiang , John C. Doyle,

”Optimal cross-layer congestion control, routing andscheduling design in ad hoc wireless networks”

I WeiQiang Xu, etc., ”Dual decomposition method for optimaland fair congestion control in Ad Hoc networks: Algorithm,implementation and evaluation”

I Matthew Andrews, ”Joint Optimization of Scheduling andCongestion Control in Communication Networks”

I Danhua Zhang, Chao Zhang and Jianhua Lu, ”Jointcongestion control, contention control and resource allocationin wireless networks”


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