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Interaction of Overlay Networks: Properties and Control

Interaction of Overlay Networks: Properties and Control. Professor John C.S. Lui. A Disruptive Technology. “Because, sometimes, the Internet doesn’t quite work…”. -- MIT RON (Resilient Overlay Networks) Project. A Disruptive Technology.

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Interaction of Overlay Networks: Properties and Control

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  1. Interaction of Overlay Networks: Properties and Control Professor John C.S. Lui Dept. of Computer Science & EngineeringThe Chinese University of Hong Kong

  2. A Disruptive Technology “Because, sometimes, the Internet doesn’t quite work…” -- MITRON (Resilient Overlay Networks) Project

  3. A Disruptive Technology • Growing trend of setting up overlay or peer-to-peer networks • BitTorrent • Resilient Overlay Network • Akamai • PlanetLab • Skype

  4. Roadmap • How do overlay networks co-exist with each other? • What is the implication of interactions? • How to regulate selfish overlay networks?

  5. Outline • Overlay Networks Preliminary • Motivation • Mathematical Modeling • Overlay Routing Game • Implications of Interaction • Pricing • Conclusion

  6. Network Edges (end nodes) • applications • Network Cores (routers) • packet forwarding Internet as an Overlay • Internet: an overlay on telephone networks • Success of the Internet • IP protocol • End-to-end design philosophy

  7. Normal traffic Overlay traffic Internet Clouds

  8. What is an overlay network? • Definition An overlay network is a set of nodes (servers) that • uses the existing Internet paths between end hosts as virtual links • Creates a virtual topology • Forwards and handles application data • Provides infrastructure to applications on top of it.

  9. Physical nodes Overlay nodes Physical link Logical link (Overlay link) Overlay Network Physical Network Overlay Network: an Example C J A F G C B I A H D J F E G

  10. conflicts Service providers (policy maker) Customers Benefits of Overlay Networks • Path diversity • Support of specific application (QoS) requirements • Quick deployment of new protocols

  11. Taxonomy

  12. Navigation • Overlay Networks Preliminary • Motivation • Mathematical Modeling • Overlay Routing Game • Implications of Interaction • Pricing • Conclusion

  13. Adaptive routing controls on multiple layers (overlays, underlay TE --traffic engineering) over one common physical network Simultaneous feedback controls over one system Stability ? Performance ? Motivation • Overlays provide a feasibility for people to control their own routing. • Routing becomes an optimization problem. • Interaction occurs. • Interaction between one overlay and underlay traffic engineering, Zhang et al, Infocom’05. • Interaction between co-existing overlays ?

  14. de(le) le– aggregate traffic traversing link e Average delay (f : flow) Performance Characteristics • Objective: minimize end-to-end delay • Delay of a physical link e: • Performance Characteristics (Underlay)

  15. de(le) le– aggregate traffic traversing link e Average delay (multipath routing) Performance Characteristics • Objective: minimize end-to-end delay • Delay of a physical link e: • Performance Characteristics (Underlay)

  16. de(le) le– aggregate traffic traversing link e Average delay (multipath routing) Performance Characteristics • Objective: minimize end-to-end delay • Delay of a physical link e: • Performance Characteristics (Underlay)

  17. System Objectives • Network Operators • Min average delay in the whole underlay network • Overlay Users • Min average delay experienced by the overlay

  18. How do Overlays Interact? • Overlapping physical links. • Performance dependent on each other. • Selfish routing optimization. • Overlays are transparent to each other.

  19. Contribution • What is the form of interaction? • Is there routing instability (oscillation)? • Is the routing equilibrium efficient? • What is the price of anarchy? • Fairness issues • Mechanism design: can we lead the selfish behaviors to an efficient equilibrium?

  20. Navigation • Overlay Networks Preliminary • Motivation • Mathematical Modeling • Overlay Routing Game • Implications of Interaction • Pricing • Conclusion

  21. Mathematical Modeling • Overlay routing: An optimization problem • Decision variable: routing policy s:overlay f:flow r:path

  22. Mathematical Modeling • Overlay routing: An optimization problem • Objective: average weighted delay

  23. Capacity Constraint • Demand constraint • (fixed transmission demand) • Non-negative Flow Constraint Overlay Routing Optimization • Convex programming

  24. Algorithmic Solution • Unique optimizer • Convex programming • feasible region: convex • delay function: continuous, non-decreasing, strictlyconvex • Solution • Apply any convex programming techniques. • Marginal cost network flow (probabilistic routing ICNP’04).

  25. Navigation • Overlay Networks Preliminary • Motivation • Mathematical Modeling • Overlay Routing Game • Implications of Interaction • Pricing • Conclusion

  26. Overlay Routing Game • Nash Routing Game • Player -- N all overlays • Strategy -- Γs feasible routing policy: feasible region of OVERLAY(s) • Preference relation -- ≥s low delay: player’s utility function is -delay(s) Strategic Game: Goverlay<N, (Γs), (≥s)>

  27. Illustration of Interaction Aggregate traffic on physical links Delay of logical paths in overlay 1 Routing decision on logical paths in overlay 1 Overlay 1 Delay of logical paths in overlay 2 Routing decision on logical paths in overlay 2 Overlay 2 Overlay probing Aggregate overlay traffic … ∑ Routing Underlay Underlay (non-overlay) traffic … Overlay n Delay of logical paths in overlay n Routing decision on logical paths in overlay n

  28. Why Nash Routing Game? • Strategic game (not repeated game) • Multiplayer Game • Asynchronous routing update • Limited information • Strategic game Nash Equilibrium

  29. Existence of Nash Equilibrium • Definition – Nash equilibrium point (NE) • A feasible strategy profile y=(y(1),…, y(s),…, y(n))T • is a Nash equilibrium in the overlay routing game if for every overlay s∈N, delay(s)(y(1),…y(s),…y(n))≤ delay(s)(y(1),…y’(s),…y(n))for any other feasible strategy profile y’(s).

  30. Existence of Nash Equilibrium • Theorem In the overlay routing game, there exists a Nash equilibrium if the delay function delay(s)(y(s) ; y(-s)) is continuous, non-decreasing and convex.

  31. Six overlays • One flow per overlay • Congested network • Asynchronous routing update Fluid Simulation

  32. Transient period Quick convergence Overlay performance

  33. Overlay routing decisions

  34. Navigation • Overlay Networks Preliminary • Motivation • Mathematical Modeling • Overlay Routing Game • Implications of Interaction • Pricing • Conclusion

  35. NSR GOR NOR The Price of Anarchy Global Performance (average delay for all flows) Efficiency Loss ? • GOR: Global Optimal Routing • NOR: Nash equilibrium for Overlay Routing Game • NSR: Nash equilibrium for Selfish Routing

  36. Selfish Routing • (User) selfish routing: a single packet’s selfishness • Every single packet chooses to route via a shortest (delay) path. • A flow is at Nash equilibrium if no packet can improve its delay by changing its route.

  37. Selfish Routing • Also a Nash equilibrium of a mixed strategic game • Player: flow { f } • Strategy: p ∈Pf • Preference: low delay • System Optimization Problem

  38. Performance Comparison

  39. Inspiration • Is the equilibrium point efficient (at least Pareto optimal) ? • Fairness issues of resource competition between overlays.

  40. 1 unit 1 unit Example Network y1 1-y1 y2 1-y2

  41. Sub-Optimality y1 y2 Non Pareto-optimal !

  42. Fairness Paradox y1 y2 • a, b, c, αare non-negative parameters • Everything is symmetric except two private links – a & c

  43. Fairness Paradox y1 y2 a <c

  44. Fairness Paradox y1 y2 a <c →delay1 > delay2

  45. Fairness Paradox y1 y2 Unbounded Unfairness a <c →delay1 < delay2

  46. y2 y1 Min Costusa(y1 ; y2) = y1poil(y1+y2)+(1-y1)pusa(1-y1) 1-y1 1-y2 War of Resource Competition 1 unit 1 unit USA China poil(y1+y2) pusa(1-y1) pchn(1-y2) pusa< pchn

  47. y2 1-y1 1-y2 War of Resource Competition 1 unit 1 unit y1 USA China poil(y1+y2) Min Costchn(y2 ; y1) = y2poil(y1+y2)+(1-y2)pchn(1-y2) pusa(1-y1) pchn(1-y2) pusa< pchn

  48. War of Resource Competition 1 unit 1 unit USA poil(y1+y2) China pusa<pchn →Costusa>Costchn pusa(1-y1) pchn(1-y2)

  49. Navigation • Overlay Networks Preliminary • Motivation • Mathematical Modeling • Overlay Routing Game • Implications of Interaction • Pricing • Conclusion

  50. Performance degradation (sub-optimal) • Fairness paradox • Global optimality • Improve fairness Pricing Mechanism Design Inefficient Nash equilibrium Desired equilibrium payment new Nash equilibrium

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