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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work Optimal Internal Congestion Control in A Cluster-based Router Qinghua Ye Nov.17,

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

Optimal Internal Congestion Control in A Cluster-based Router

Qinghua Ye Nov.17, 2009

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

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

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Outline 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

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

Figure: IP Forwarding Path

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

Optimal Utility-based Control

◮ An optimization approach to congestion control problems

◮ Objective: maximize the aggregate source utility ◮ Constraints: network link capacities.

◮ The network links and traffic sources are viewed as a

distributed system that acts to solve the optimization problem

◮ Traffic sources adjust their transmission rates in order to

maximize their own benefit

◮ The network links adjust bandwidth prices to coordinate the

sources decisions on the evolution of their transmission rates

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

Classification of Optimal Utility-based Control

According to the controlled objects:

◮ Primal algorithms (TCP) ◮ Dual algorithms (Active Queue Management) ◮ Primal-dual algorithms (Combination of TCP and AQM)

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

Internal Congestion Control As An Optimization Problem

◮ Consider a network with unidirectional links. There is a finite

forwarding capacity C associated with the egress. The egress is shared by a set S of sources, where source s ∈ S is characterized by a utility function Us(xs) that is concave increasing in its transmission rate xs to the egress.

◮ Model:

P :

s∈S

Us(xs) (1) subject to

s∈S

xs ≤ C (2)

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

Decentralized Approach

◮ The dual theory of optimization leads us to a distributed and

decentralized solution which results in the coordination of all sources implicitly

◮ 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)

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

Decentralized Approach

◮ The objective function of the dual problem:

D(p) = max

xs L(x, p)

=

s∈S

max(Us(xs) − xs ∗ p) + p ∗ C (4)

◮ The dual problem:

D : min

p≥0 D(p)

(5)

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

Decentralized Approach

◮ The congestion control problem can be generalized to tasks of

finding distributed algorithms that can make sources adapt transmission rates with respect to the egress price and make egress adapt prices with respect to loads

◮ The optimal solution to the distributed congestion control

problem satisfies: {

∂D(p) ∂xs

= ∂Us(xs)

∂xs

= U′

s(xs) − p = 0 ∂D(p) ∂p

=

s∈S (−xs) + C = 0

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

Discrete Optimal Utility-based Control

◮ To reduce the overhead of transferring the link price, we only

send the price from the egress to the sources at the beginning

f each control interval, which results in a discrete-time

control 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 > 0 max(g(x), 0), y = 0 and K and 1/R are step sizes.

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

Queue Status as an Indicator of Congestion

◮ In real system, the transmission capacity of the egress in the

model vary for different situations or times

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

◮ 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)

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

Queue Status as an Indicator of Congestion

◮ The system may be stable at large queue length ◮ 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)

◮ Let f (q) = (q − qo) ∗ u, where qo is the objective of egress

queue length and u is the degree that the queue length would be taken into the price calculation.

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

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 Simulation

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

500000 1e+06 1.5e+06 2e+06 2.5e+06 100 200 300 400 500

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

Transmission Rate Reception Rate Reception Rate from Ingress 1 Reception Rate from Ingress Reception Rate from Ingress 3

Figure: Optimization utility-based scheme transmission rate behavior

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

500000 1e+06 1.5e+06 2e+06 2.5e+06 50 100 150 200

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

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

Figure: AIMD scheme transmission rate behavior

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500

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

Queue Length

Figure: Optimization utility-based scheme queue behavior

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

200 400 600 800 1000 50 100 150 200

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

Queue Length

Figure: AIMD scheme queue behavior

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

200000 400000 600000 800000 1e+06 1.2e+06 100 200 300 400 500

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

Transmission Rate Reception Rate Reception Rate from Ingress 1 Reception Rate from Ingress Reception Rate from Ingress 3

Figure: Fairness - Optimization utility-based scheme transmission rate behavior

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

1000 2000 3000 4000 5000 10 20 30 40 50 60 70 80 90 100

Packet Rate - K Packet Per Second Input Rate at Ingress Nodes(Percentage of Wire Rate) Optimal Utility-based VS. AIMD VS. Original

Reception Rates at Ingress Nodes - original Injection Rates at Ingress Nodes - original Transmission Rate at Egress Node - original Reception Rates at Ingress Nodes - AIMD Injection Rates at Ingress Nodes - AIMD Transmission Rate at Egress Node - AIMD Reception Rates at Ingress Nodes - optimal Injection Rates at Ingress Nodes - optimal Transmission Rate at Egress Node - optimal

Figure: Transmission rate comparison

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

200 400 600 800 1000 1200 20 40 60 80 100

Output Queue Length Input Rate at Ingress Nodes (Percentage of Wire Rate) Queue Length With Increasing Offered Traffic

utput queue length - original
utput queue length - AIMD
utput queue length - optimal

Figure: Queue variance comparison

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

200 400 600 800 1000

298 298 298 AIMD 298 298 298 Optimal 298 298 224 AIMD 298 298 224 Optimal 298 298 149 AIMD 298 298 149 Optimal 298 298 75 AIMD 298 298 75 Optimal

Packet Rate - K Packets Per Second Offered Rate at Ingress Nodes(K Packets Per Second) Fairness Among Different Ingress Nodes

Reception Rate at Ingress Node 1 Reception Rate at Ingress Node 2 Reception Rate at Ingress Node 3 Injection Rate at Ingress Node 1 Injection Rate at Ingress Node 2 Injection Rate at Ingress Node 3 Transmission Rate at Egress Node

Figure: Fairness comparison

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

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Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work

◮ Optimal Utility-based Congestion Control

◮ Fair to different flows ◮ Efficient to reduce the injection rates of traffic to the internal

network to avoid congestion

◮ Related Work

◮ Analyze and improve the Internet congestion control schemes

such as TCP and AQM

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

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

◮ WeiQiang Xu, etc., ”Dual decomposition method for optimal

and fair congestion control in Ad Hoc networks: Algorithm, implementation and evaluation”

◮ Matthew Andrews, ”Joint Optimization of Scheduling and

Congestion Control in Communication Networks”

◮ Danhua Zhang, Chao Zhang and Jianhua Lu, ”Joint

congestion control, contention control and resource allocation in wireless networks”

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