Optimal Internal Congestion Control in A Cluster-based Router

Transcription

1 Optimal Internal Congestion Control in A Cluster-based Router Nov.17, 2009

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3 Figure: Cluster-based Router Architecture

4 Figure: IP Forwarding Path

5 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

6 Classification of According to the controlled objects: Primal algorithms (TCP) Dual algorithms (Active Queue Management) Primal-dual algorithms (Combination of TCP and AQM)

7 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 : s S U s (x s ) (1) subject to x s C (2) s S

8 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 = U s (x s ) x s p + p C s S s S (3)

9 Decentralized Approach The objective function of the dual problem: D(p) = max x s L(x, p) = s S max(u s (x s ) x s p) + p C (4) The dual problem: D : min D(p) (5) p 0

10 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) x s = Us(xs) x s = U s(x s ) p = 0 D(p) p = s S ( x s) + C = 0

11 Discrete 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: { x s (k + 1) = [x s (k) + K x s (k) (U s(x s (k)) p(k))] + x s[k] = [x s (k) + K (W x s (k) p(k))] + x s[k] Here p(k + 1) = [p(k) + ( s S x s(k) C)/R] + p(k) [g(x)] + y = { g(x), y > 0 max(g(x), 0), y = 0 and K and 1/R are step sizes. (6)

12 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] p(k + 1) = [p(k) + (delta(q))/r] + p(k) (7)

13 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] p(k + 1) = [p(k) + (delta(q) + f (q))/r] + p(k) (8) 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.

14 BECN Receive IP Packet Adjust Scheduler Parameters To Internal Packet Classifier External IP Lookup Local Forward To Up Layer IP Header Check To External Internal Packet Classifier Get Mac of External Network Device... Packet Scheduler Get MAC of Internal Network Device Check Queue Status and Generate BECN Internal Transmit External Transmit External Transmit Figure: IP Forwarding Path in Simulation

15 2.5e+06 2e+06 Transmission Rate Behavior - (K:100000, R: ) Transmission Rate Reception Rate Reception Rate from Ingress 1 Reception Rate from Ingress Reception Rate from Ingress 3 Transmission Rate 1.5e+06 1e Time Figure: Optimization utility-based scheme transmission rate behavior

16 2.5e+06 2e+06 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 Transmission Rate 1.5e+06 1e Time Figure: AIMD scheme transmission rate behavior

17 Queue Length - (K:100000, R: ) 1000 Queue Length Queue Length Time Figure: Optimization utility-based scheme queue behavior

18 1000 Queue Length Queue Length - (W:50000, Q:100) 800 Queue Length Time Figure: AIMD scheme queue behavior

19 1.2e+06 1e+06 Transmission Rate Behavior - (K:100000, R: ) Transmission Rate Reception Rate Reception Rate from Ingress 1 Reception Rate from Ingress Reception Rate from Ingress 3 Transmission Rate Time Figure: Fairness - Optimization utility-based scheme transmission rate behavior

20 Packet Rate - K Packet Per Second 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 Input Rate at Ingress Nodes(Percentage of Wire Rate) Figure: Transmission rate comparison

21 Queue Length With Increasing Offered Traffic 1200 output queue length - original output queue length - AIMD output queue length - optimal 1000 Output Queue Length Input Rate at Ingress Nodes (Percentage of Wire Rate) Figure: Queue variance comparison

22 Packet Rate - 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 0 75 Optimal 75 AIMD 149 Optimal 149 AIMD 224 Optimal 224 AIMD Optimal Offered Rate at Ingress Nodes(K Packets Per Second) AIMD Figure: Fairness comparison

23 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