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Optimal Capacity Sharing of Networks with Multiple Overlays Zheng Ma, Jiang Chen, Yang Richard Yang and Arvind Krishnamurthy Yale University University of Washington Presented by Zheng Ma Jun 19, 2006

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Introduction Overlay networks are becoming widely deployed: P2P applications: e.g., BitTorrent, PPlive VoIP applications: e.g., Skype Testbeds: e.g., Planetlab, Emulab

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Example of Overlays The overlay O 1 is trying to find the max flow from node 1 to node 5. There is a TCP flow from node 2 to node 5, which could be viewed as an overlay with only 1 link. How to model their behavior when they share the network resource? Topology of Overlay O 1

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State of Art: Resource Allocation of Multiple Overlays No congestion control Network collapse Using UDP to probe available bandwidth is possible but the packets may be dropped by the network if you dont react to the network feedback correctly. ISP will limit the rate. Use TCP at each overlay link e.g. Skype and BitTorrent use TCP on each overlay link with the hope that it will share network resource fairly and efficiently. If the flow rate on each link is controlled by TCP without coordinating with other links of the same overlay application, we refer to such a scheme as flow-level rate control. Is this enough? NO!

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Talk Outline Introduction Problem statement Design of distributed algorithm for capacity sharing of multiple overlays Case study: overlay maximum flow problem Evaluation: simulation results Related works and conclusion

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Problem Statement Network model: Physical : G = (V,L,C), node set V, link set L, with capacity C={ C l }. Overlay: G i = (H i,E i ) : node set H i overlay link set E i Each overlay link has rate x e -- control variables. Mapping between overlay link and a physical path: A le =1 if e goes link l in physical network, otherwise 0. So the capacity constraint at physical network is Each overlay may have application constraints, e.g., flow conservation constraint F he =1 if e=(h,v), F he =-1 if e=(u,h), otherwise F he =0 Utility function: Each overlay has a utility function U i which is strictly concave. The input to U i is an aggregation function f i applied to f i is differentiable, application-specified. For overlay maximal flow problem: The overlay i is trying to maximize:

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System Problem Capacity sharing of multiple overlays If the system design objective is to maximize the sum of the utilities of all overlays, we can write down the system optimization problem as: When all overlays are single end-to-end flows, the above formulation is reduced to that of Frank Kellys framework. Reminder: we call a rate control mechanism in overlay network flow- level rate control if each control variable x e is controlled by TCP or other transport protocol without coordinating within the overlay. A rate control mechanism is overlay flows control if the overlay will coordinate the control of all x e.

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Example 1: Unfair Sharing with TCP Using Only Flow-level Rate Control The system optimal is x 1 =(1,0,1,0,1), x 2 =1,total utility 0 With only flow-level rate control: x 1 =(1,1/3,2/3,1/3,2/3), x 2 =1/3, total utility Topology of Overlay O /3 2/3 1

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Example 2: Sub-optimal Capacity Sharing Among Multiple Overlays The system optimal is x 1 =(1,1,0,1,0), x 2 =(0,1,0,1,1), total utility 2 With only flow-level rate control: x 1 =(1/3,0,1/3,0,1/3), x 2 =(1/3,1/3,1/3,1/3,2/3), total utility /3 2/3 Overlay O 1 Overlay O 2

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Our Contributions The traditional flow-level rate control is not enough for resource allocation among multiple overlays. It may reach sub-optimal equilibrium. We propose overlay flows control to coordinate the rate flow to solve the problem by controlling flows in an overlay network coordinatively. Key Idea: to solve the overlay utility maximization system problem in a distributed way. We don t require the knowledge of the underlay networks (i.e. A and C in the physical network). Instead we use a try and back off approach.

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Algorithmic Design in P is not strictly concave. We use Proximal Minimization method to make the objective function strictly concave. B={b e } is the introduced auxiliary variables. In P1, it is fixed. Iterative process: Solve P1 and obtain optimal solution X, set B=X, and solve P1 again.

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A Price Based Approach P1 can be solved by a price based approach. Lagrangian form: Path Price Link Price Maximizer Application price Node Price

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Case Study: Overlay Maximum Flow Rate adaptation and price calculation Link Price Update, we can use queuing delay as an approximation Node Price Update Overlay Flows Rate Adaptation Convergence We used Lyapunov stability theory to prove the algorithm is globally asymptotically stable.

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Evaluation: Convergence Simulation setup: BRITE topology generator. All experiments showed a similar result. Use the algorithm for overlay maximum flow. Results for example 1 and example 2. Convergence results Overlay 1 TCP flow Overlay 1 Overlay 2

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Evaluation: Dynamics Simulation setup: In example 1, add more TCP flows between node 2 and node 5 at different time. The algorithm can react to the change and converge to the fair share quickly. One could consider our algorithm as a generalization of protocol compliance requirements: e.g. TCP friendliness. TCP flow

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Related Work Coexistence of multiple overlays (focusing on cost or delay) Selfish routing effects (Qiu et al. SIGCOMM 03). Interaction of multiple overlay routing (Jiang et al. Performance 05). Can overlays inadvertently step on each other? (Keralapura et al. ICNP 05). Overlay networks Overlay networks with linear capacity constraints. (Zhu et al. IWQoS 05) Transport protocol design Fast TCP: motivation, architecture, algorithms, performance. (Wei et al. TON 07)

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Conclusion and Future Work Our contributions: Define the problem of optimal capacity sharing of multiple overlays. Show that flow-level rate control cannot achieve system-wide optimality. Develop a framework to use overlay flows rate control to solve the problem in distributed way and show its convergence and effectiveness. The protocol can be implemented by measuring end-to-end queuing delay at overlay level. This is a try-band-back-off approach similar to TCP Vegas and FAST TCP. Future work: Convergence of the algorithm in other setups. Utility function design for overlay networks, implementing different types of fairness among overlays. Consider other popular overlay applications like network coded overlay multicast.

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The End Thanks! Questions? More information: Google zheng ma

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Backup Slides Non-triviality of overlay maximum flow algorithm Overlay maximum flow problem is non-trivial even for a single overlay. i.e. we cant use traditional max flow algorithm by measuring available bandwidth on overlay level. In above topology, each link is overlay link, all underlay physical links has unit capacity. Suppose (2,4), (4,5) and (4,6) share a physical link. The max flow algorithm will try to push 1 unit traffic at each overlay link. (2,4) (4,5) and (4,6) will get 1/3 each, no more bandwidth available, no augmenting path. The max flow rate is 2/3. However, by sending 1 unit traffic on (1,3)(3,4)(4,6)(6,7), we get max flow 1.

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