Optimal Capacity Sharing of Networks with Multiple Overlays

1. Optimal Capacity Sharing of Networks with Multiple Overlays Zheng Ma, Jiang Chen, Yang Richard Yang and Arvind Krishnamurthy Yale University University of Washington {zhengma,criver,yry}@cs.yale.edu {arvind}@cs.washington.edu Presented by Zheng Ma Jun 19, 2006

2. Introduction • Overlay networks are becoming widely deployed: • P2P applications: e.g., BitTorrent, PPlive • VoIP applications: e.g., Skype • Testbeds: e.g., Planetlab, Emulab http://www.cachelogic.com

3. Example of Overlays The overlay O1 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 O1

4. 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 don’t 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-levelrate control. • Is this enough? NO!

5. 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

6. Problem Statement • Network model: • Physical : G = (V,L,C), node set V,link set L, with capacity C={ Cl }. • Overlay: Gi = (Hi ,Ei): node set Hi overlay link set Ei • Each overlay link has rate xe -- control variables. • Mapping between overlay link and a physical path: Ale=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 • Fhe=1 if e=(h,v), Fhe=-1 if e=(u,h), otherwise Fhe=0 • Utility function: • Each overlay has a utility function Ui which is strictly concave. • The input to Ui is an aggregation function fi applied to fi is differentiable, application-specified. For overlay maximal flow problem: • The overlay i is trying to maximize:

7. 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 Kelly’s framework. • Reminder: we call a rate control mechanism in overlay network flow-level rate controlif each control variable xe is controlled by TCP or other transport protocol without coordinating within the overlay. • A rate control mechanism is overlay flowscontrol if the overlay will coordinate the control of all xe.

8. 1/3 1 1/3 1 2/3 1 1 2/3 Topology of Overlay O1 Example 1: Unfair Sharing with TCP Using Only Flow-level Rate Control The system optimal is x1=(1,0,1,0,1), x2=1,total utility 0 With only flow-level rate control: x1=(1,1/3,2/3,1/3,2/3), x2=1/3, total utility -0.48

9. 1 1 1 1/3 1/3 1/3 1/3 1/3 1 1/3 1 1/3 2/3 1 Example 2: Sub-optimal Capacity Sharing Among Multiple Overlays Overlay O1 The system optimal is x1=(1,1,0,1,0), x2=(0,1,0,1,1), total utility 2 With only flow-level rate control: x1=(1/3,0,1/3,0,1/3), x2=(1/3,1/3,1/3,1/3,2/3), total utility 1 Overlay O2

10. 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.

11. Algorithmic Design • in P is not strictly concave. • We use Proximal Minimization method to make the objective function strictly concave. • B={be} 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.

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

13. 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.

14. Overlay 1 TCP flow 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. Overlay 1 Overlay 2 Convergence results

15. TCP flow 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.

16. 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)

17. 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.

18. The End • Thanks! Questions? • More information: • Google “zheng ma”

19. 2 5 1 4 7 3 6 Non-triviality of overlay maximum flow algorithm Backup Slides • Overlay maximum flow problem is non-trivial even for a single overlay. i.e. we can’t 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.