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 A Disruptive Technology “Because, sometimes, the Internet doesn’t quite work…” -- MIT RON (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 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 Internet Clouds Normal traffic Overlay traffic

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

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

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

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 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 -- 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 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 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 Fluid Simulation Six overlays One flow per overlay Congested network Asynchronous routing update

32 Overlay performance Transient period Quick convergence

33 Overlay routing decisions

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

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 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 ∈ P f  Preference: low delay  System Optimization Problem

38 Performance Comparison Overlay One Overlay Two Average Delay Centralized Global Optimal Routing NE of Overlay Optimal Routing NE of Selfish Routing

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

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

41 Sub-Optimality physical linkdelay function d e (l e ) 1-51+l 3-4l 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 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 Fairness Paradox physical linkdelay function d e (l e ) 1-5a+l 3-4bl α 2-6c+lc+l y1y1 y2y2 a < c

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

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

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

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

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

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

57 Interpretation of Price

58 Effectiveness of Pricing

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 Thanks for your attention! Comments Q & A

61 Backup Slides