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

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

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

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

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

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

7. 7 Internet Clouds Normal traffic Overlay traffic

8. 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. 9 Overlay Network: an Example Physical nodes Overlay nodes Physical link Logical link (Overlay link) Physical Network Overlay Network A C A C B D E F F G H I J G J

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

11. 11 Taxonomy CategoryFunctionality & Purpose Example Peer-to-peer (P2P)File sharing & distribution BitTorrent, Gnutella Routing OverlayEnhance IP-routing, reduce routing delay, improve resilience, etc Resilient Overlay Network (RON) Content Delivery Network (CDN) Distributed content caching Akamai, Chord, Pastry, CAN Multicast OverlayMulticastEnd System Multicast, Mbone OthersVarious PurposeSecurity: VPN, SOS; Experimental: PlanetLab, I3; VoIP: Skype.

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

13. 13 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 ? Adaptive routing controls on multiple layers (overlays, underlay TE -- traffic engineering) over one common physical network Simultaneous feedback controls over one system Stability ? Performance ?

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

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

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

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

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

19. 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. 20 Navigation  Overlay Networks Preliminary  Motivation  Mathematical Modeling  Overlay Routing Game  Implications of Interaction  Pricing  Conclusion

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

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

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

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

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

26. 26 Overlay Routing Game  Nash Routing Game  Player -- N all overlays  Strategy -- Γ s feasible routing policy: feasible region of OVERLAY (s)  Preference relation -- ≥ s low delay: player ’ s utility function is -delay (s) Strategic Game: G overlay

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

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

29. 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. 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. 31 Fluid Simulation Six overlays One flow per overlay Congested network Asynchronous routing update

32. 32 Overlay performance Transient period Quick convergence

33. 33 Overlay routing decisions

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

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

36. 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. 37 Selfish Routing  Also a Nash equilibrium of a mixed strategic game  Player: flow { f }  Strategy: p ∈ P f  Preference: low delay  System Optimization Problem

38. 38 Performance Comparison Overlay One Overlay Two Average Delay Centralized Global Optimal Routing 2.502.382.46 NE of Overlay Optimal Routing 2.462.532.50 NE of Selfish Routing2.632.752.68

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

40. 40 Example Network 1 unit y1y1 1-y 1 y2y2 1-y 2

41. 41 Sub-Optimality physical linkdelay function d e (l e ) 1-51+l 3-4l 2-62.5+l Routing (y 1, y 2 ) Average Delay (overlay1, overlay2 ) NE (0.5, 1.0)(1.5, 1.5) Pareto Curve (0.4, 0.9)(1.4, 1.4) y1y1 y2y2 Non Pareto-optimal !

42. 42 Fairness Paradox physical linkdelay function d e (l e ) 1-5a+l 3-4bl α 2-6c+lc+l y1y1 y2y2  a, b, c, α are non-negative parameters  Everything is symmetric except two private links – a & c

43. 43 Fairness Paradox physical linkdelay function d e (l e ) 1-5a+l 3-4bl α 2-6c+lc+l y1y1 y2y2 a < c

44. 44 Fairness Paradox physical linkdelay function d e (l e ) 1-5a+l 3-4bl α 2-6c+lc+l y1y1 y2y2 a delay 2

45. 45 Fairness Paradox y1y1 y2y2 a < c → delay 1 < delay 2 Unbounded Unfairness

46. 46 War of Resource Competition 1 unit y1y1 1-y 1 y2y2 1-y 2 p oil (y 1 +y 2 ) p usa (1-y 1 ) p chn (1-y 2 ) p usa < p chn USAChina Min Cost usa (y 1 ; y 2 ) = y 1 p oil (y 1 +y 2 )+(1-y 1 )p usa (1-y 1 )

47. 47 War of Resource Competition 1 unit y1y1 1-y 1 y2y2 1-y 2 p oil (y 1 +y 2 ) p usa (1-y 1 ) p chn (1-y 2 ) p usa < p chn USAChina Min Cost chn (y 2 ; y 1 ) = y 2 p oil (y 1 +y 2 )+(1-y 2 )p chn (1-y 2 )

48. 48 War of Resource Competition 1 unit p oil (y 1 +y 2 ) p usa (1-y 1 ) p chn (1-y 2 ) p usa < p chn → Cost usa > Cost chn USA China

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

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

51. 51 Pricing I – Improve Delay  Objective: to achieve global optimality  NE of overlay routing game  Global optimal l e (s) : traffic of overlay s l e (-s) : traffic other than overlay s

52. 52 Pricing I – Improve Delay  Objective: to achieve global optimality  New NE of overlay routing game  Global optimal

53. 53 Pricing I – Improve Delay  New NE of overlay routing game  Global optimal KKT condition: p e (s) =l e (-s) d e ’ (l e )

54. 54 Pricing II – improve fairness  Cause of unfairness:  Over-utilize good common resources  Unfair resource (bandwidth) allocation  Pricing Scheme ISP maximize profit Improve performance & Reduce cost Overlay price p routing decision

55. 55 Incentive Resource Allocation  For overlays: : sensitivity factor new Nash equilibrium → {l e }

56. 56 Revenue Distribution  For ISPs (links): : profit of link e : revenue : operating cost --

57. 57 Interpretation of Price

58. 58 Effectiveness of Pricing

59. 59 Conclusion  Study the interaction between multiple co- existing overlays.  Non-cooperative Nash routing game.  Prove the existence of NEP.  Show the anomalies and implications of the NEP.  Present two pricing schemes to address the anomalies.

60. 60 Thanks for your attention! Comments Q & A

61. 61 Backup Slides