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
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
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
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
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
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
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 U s ( x s ) that is concave increasing in its transmission rate x s to the egress. ◮ Model: � P : U s ( x s ) (1) s ∈ S subject to � x s ≤ C (2) s ∈ S Qinghua Ye Optimal Internal Congestion Control in A Cluster-based Router
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 ) = U s ( x s ) − p ( x s − C ) s ∈ S s ∈ S (3) � � = U s ( x s ) − x s ∗ p + p ∗ C s ∈ S s ∈ S Qinghua Ye Optimal Internal Congestion Control in A Cluster-based Router
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 x s L ( x , p ) (4) � = max( U s ( x s ) − x s ∗ p ) + p ∗ C s ∈ S ◮ The dual problem: D : min p ≥ 0 D ( p ) (5) Qinghua Ye Optimal Internal Congestion Control in A Cluster-based Router
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 ) = ∂ U s ( x s ) = U ′ s ( x s ) − p = 0 ∂ x s ∂ x s { ∂ D ( p ) = � s ∈ S ( − x s ) + C = 0 ∂ p Qinghua Ye Optimal Internal Congestion Control in A Cluster-based Router
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 of each control interval, which results in a discrete-time control model: s ( x s ( k )) − p ( k ))] + x s ( k + 1) = [ x s ( k ) + K ∗ x s ( k ) ∗ ( U ′ x s [ k ] = [ x s ( k ) + K ∗ ( W − x s ( k ) ∗ p ( k ))] + { x s [ k ] s ∈ S x s ( k ) − C ) / R ] + p ( k + 1) = [ p ( k ) + ( � p ( k ) (6) Here y = { g ( x ) , y > 0 [ g ( x )] + 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
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: { x s ( k + 1) = [ x s ( k ) + K ∗ ( W − x s ( k ) ∗ p ( k ))] + x s [ k ] (7) p ( k + 1) = [ p ( k ) + ( delta ( q )) / R ] + p ( k ) Qinghua Ye Optimal Internal Congestion Control in A Cluster-based Router
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: { x s ( k + 1) = [ x s ( k ) + K ∗ ( W − x s ( k ) ∗ p ( k ))] + x s [ k ] (8) p ( k + 1) = [ p ( k ) + ( delta ( q ) + f ( q )) / R ] + p ( k ) ◮ Let f ( q ) = ( q − q o ) ∗ u , where q o 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
Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work Receive BECN IP Packet IP Header Check Adjust External Internal Scheduler Parameters IP Lookup Packet To To Classifier Internal External Local Packet Get Mac of External Classifier Network Device Forward To Up Layer ... Packet Scheduler Check Queue Status Get MAC of Internal and Network Device Generate BECN Internal External External Transmit Transmit Transmit Figure: IP Forwarding Path in Simulation Qinghua Ye Optimal Internal Congestion Control in A Cluster-based Router
Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work Transmission Rate Behavior - (K:100000, R:500000000000) 2.5e+06 Transmission Rate Reception Rate Reception Rate from Ingress 1 Reception Rate from Ingress Reception Rate from Ingress 3 2e+06 Transmission Rate 1.5e+06 1e+06 500000 0 0 100 200 300 400 500 Time Figure: Optimization utility-based scheme transmission rate behavior Qinghua Ye Optimal Internal Congestion Control in A Cluster-based Router
Outline Congestion in the Cluster-based Router Optimal Utility-based Control Simulation With NS-3 Evaluations In the Real System Conclusions and Related Work Transmission Rate Behavior - (W:50000, Q:100) 2.5e+06 Transmission Rate Reception Rate Reception Rate from Ingress 1 Reception Rate from Ingress 2 Reception Rate from Ingress 3 2e+06 Transmission Rate 1.5e+06 1e+06 500000 0 0 50 100 150 200 Time Figure: AIMD scheme transmission rate behavior Qinghua Ye Optimal Internal Congestion Control in A Cluster-based Router
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 Length - (K:100000, R:500000000000) 1000 Queue Length 900 800 700 Queue Length 600 500 400 300 200 100 0 0 100 200 300 400 500 Time Figure: Optimization utility-based scheme queue behavior Qinghua Ye Optimal Internal Congestion Control in A Cluster-based Router
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