Presentation on theme: "Giochi non cooperativi per l’instradamento di pacchetti IP nella rete Internet Stefano Secci a, in collaborazione con J.-L. Rougier a, A. Pattavina b,"— Presentation transcript:
Giochi non cooperativi per l’instradamento di pacchetti IP nella rete Internet Stefano Secci a, in collaborazione con J.-L. Rougier a, A. Pattavina b, F. Patrone c, G. Maier b a Telecom ParisTech, France b Politecnico di Milano, Italy c Università di Genova, Italy Corso di Teoria dei Giochi, Applicazioni Collegio Borromeo, Università di Pavia, Marzo 2010, Pavia
Stefano Secci DEI 2 Internet dissected Sources: the CIDR report The Autonomous Systems (ASs) number increases very fast!
Stefano Secci DEI 3 Internet as an interconnection of ASs AS u AS w AS x AS z AS y ISP 1 ISP 2 ISP 3 Multi-homed AS Border Gateway ISP 4... ISP 4... Internet Exchange point Stub AS Carrier AS Source: The CIDR report AS number detected on a backbone BGP router routing table
Stefano Secci DEI 4 Intra- and Inter- Autonomous System (AS) Routing An EGP protocol, i.e., the Border Gateway Protocol (BGP) for inter-AS routing Many IGP protocols, e.g., OSPF, ISIS, RIP, for intra-AS routing BGP and IGP routing is coupled AS 13 Address Range: /8 EGP AS 1712 Address Range: /16 AS 1972 Address Range: /24IGP
Stefano Secci DEI 5 Inter-AS business relationships: transit agreement Client Provider ISP regional ISP regional ISP regional ISP regional ISP regional ISP regional ISP national ISP national ISP national ISP national ISP international ISP international A provider announces to its clients all the routes customers have full access to its network € Can you give me more bw? IGP MED I’d prefer you use link A, then C, B MED=10 MED=100 MED=50 SURE! ($$$ ) SURE! announce me your preferences via the MED Transit agreements directly imply infrastructure upgrades Upgrade of inter-AS link capacity, routers (the customer pays for)
Stefano Secci DEI 6 Inter-AS business relationships: peering agreement ISP regional ISP regional ISP regional ISP regional ISP regional ISP regional ISP national ISP national ISP national ISP national ISP international ISP international A provider announces to its peer its network and all the routes by its clients Peer provider For free! Can you give me more bw? Well. only if you do the same OK Peering agreements do not imply upgrades and coordination Peering links are becoming the real bottleneck of the Internet Peering agreements are not binding on the routing strategy IGP MED mapping : I’d prefer you use link G, then H, I Uhm.. why should I?
Stefano Secci DEI 7 Hot potato and least MED BGP rules – BGPv4 Hot potato routing If same AS hop count, If least MED does not apply, Choose the closer egress point. Least MED routing If same AS hop count If many ingress points to a same upstream AS, Choose the least MED-icated route.
Stefano Secci DEI 8 Rationales Technical (BGP) BGP routing is selfish and inefficient on peering links Hot-potato and tie-breaking rules exclude collaborations High bottleneck risk on peering links Classical load sharing on peering links? Would be inefficient too The Multi-Exit Discriminator (MED) has a collaboration nature, but is often disabled on peering links none is customer each other’s MED-icated preferences shall be equivalent MED usage on peering links shall be coordinated Game theoretic The BGP bilateral routing solution is far from the social optimum The MED allows exchanging routing cost information The peering link capacity is a scarce resource Carriers shall coordinate to avoid unstable routes and peering link congestions –while preserving their independence
Stefano Secci DEI 9 A simple 2-link peering game example AS I and AS II exchange their internal routing cost via the MED for NET A and NET B (resp.) Game strategy set = possible egress links Table I: BGP+MED seen with a game theoretic standpoint dummy game (unilateral choices l 1,l 2 are equivalent): 4 Nash equilibria Table II: considering both peers’ IGP path costs (=MEDs) NET A and NET B shall be equivalent (e.g. w.r.t. the bandwidth) ClubMED (Coordinated MED) game: 1 Nash equilibrium
Stefano Secci DEI 10 Simple 3-link ClubMED game examples 10 The Pareto-superior Nash equilibrium is not Pareto-efficient any longer! The Nash equilibrium is unique and Pareto-efficient REMINDER: A strategy profile s is Pareto-superior to another strategy profile s’ if a player’s cost can be decreased from s to s’ without increasing the other player’s cost. And s’ is Pareto-inferior to s. A strategy profile is Pareto-efficient if it is not Pareto-inferior to any other strategy profile. 4
Stefano Secci DEI 11 The ClubMED game The resulting ClubMED game can be described as G = G s + G d + G c G s, a selfish game (endogenous) G d, a dummy game, of pure externality G c, a congestion game (endogenous) For m pairs and n links: permutation of m single-pair n-link ClubMED games |X m |=|Y m |=n m Generalization Mono-directional costs Many peering links Multiple pairs of destination communities Congestion costs on peering links
Stefano Secci DEI 12 The ClubMED game: properties It is a potential game The incentive to change expressed in one global potential function; The difference in individual costs by an individual strategy move has the same value as the potential difference Nash equilibrium Potential minimum And a Nash equilibrium always exists Frequent occurrence of multiple equilibria A ClubMED Nash equilibrium is not necessarily a Pareto-efficient profile The Pareto-frontier may not contain Nash equilibria G d guides the Pareto-efficiency, G s + G c guides the Nash equilibrium
Stefano Secci DEI 13 Dealing with IGP Weight Optimizations (IGP-WO) In practice, ASs may implement IGP-WO operations within their domain the IGP path cost can change after the route change ClubMED G s adaptation. Each peer: Computes δ cost variations for each path w.r.t. each possible ClubMED decisions Computes optimistic directional cost errors (ingress and egress) Codes in the MED its two errors. For example, egress error cost for AS I: Broadening of the Nash set and of the Pareto-frontier A potential threshold is arisen above the minimum Many candidate Nash equilibria Coordination strategies are still more necessary TpTp
Stefano Secci DEI 14 ClubMED-based peering link congestion controls With multiple pairs, inter-peer links congestion can be controlled with G c The more egress flows routed on a peering link, the more congested the link, and the higher the routing cost. Objective: weighting the inter-carrier links when congestion may arise A congestion cost function H: set of inter-peer flow pairs ρ i h the outgoing bit-rate of the flow pair h on link i C i the egress capacity of l i G c practically not considered when
Stefano Secci DEI 15 Nash Equilibrium MultiPath (NEMP) routing 1.Collect the MEDs and flows’ bandwidth information 2.Compute the potential minimum 3.Compute the delta IGP path cost variations and the potential treshold 4.Compute the Nash set 5.Restrain the Nash set to the Pareto-superior equilibria When more than one, we have a multipath solution 6.The corresponding routes are the coordinated routing solution
Stefano Secci DEI 16 Three peering links Traffic matrix datasets: 360 rounds (delayed of 8 hours) By courtesy of S. Uhlig, Y. Zhang IGP-WO run with the TOTEM toolbox (developed by UCL,ULG) xc Results for a Internet2 – Geant2 peering emulation
Stefano Secci DEI 17 Results: IGP routing cost
Stefano Secci DEI 18 Results: maximum link utilization
Stefano Secci DEI 19 Results: Nash equilibria dynamic
Stefano Secci DEI 20 Results: route stability
Stefano Secci DEI 21 Peering Equilibrium MultiPath (PEMP) routing policies (cont.) 1.Nash Equilibrium MultiPath (NEMP) coordination (one-shot) Play the Pareto-superior equilibria of the Nash set Fine-selected multipath routing on peering link 2.Repeated coordination: (repeated, high trust) Play the profiles of the Pareto-frontier Needs a very high level of trust between peers for the long-run 3.Repeated Jump coordination: (repeated, low trust) Unself-jump: After shrinking the Nash set w.r.t. the Pareto-efficiency, the ASs agree to make both a further step toward a choice (x j,y j ) s.t.(1): ψ (x j,y j ) - ψ (x 0,y 0 ) + φ (x j,y j ) – φ (x 0,y 0 ) < 0 (1) The unselfish loss that one may have is compensated by the improvement upon the other Pareto-Jump: toward Pareto-superior profiles without unselfish unilateral loss, i.e. such that (1) and (2): ψ (x j,y j ) - ψ (x 0,y 0 ) ≤ 0ANDφ (x j,y j ) – φ (x 0,y 0 ) ≤ 0 (2)
Stefano Secci DEI 22 Results: route stability under intra-AS congestion (PEMP) With decimated link capacities The route stability performance depends on the IGP-WO cost function
Stefano Secci DEI 23 Results: PEMP policy trade-offs (IGP routing cost) (with decimated link capacities)
Stefano Secci DEI 24 Results: PEMP policy trade-offs (link utilization) With decimated link capacities
Stefano Secci DEI But is route stability a real issue? 25 Dataset source: « A Radar for the Internet », M. Latapy et al.
Stefano Secci DEI 26 But is route stability a real issue?
Stefano Secci DEI 27 But is route stability a real issue? (2) Dataset source: « A Radar for the Internet », M. Latapy et al.
Stefano Secci DEI 28 Very promising results. ClubMED-based NEMP strategy can: Avoid peering link congestion Improve significantly the peering routing stability Significantly decrease the bilateral routing cost Implementation aspects Coding of multiple attributes in the MED Refinement of the BGP decision process (at the MED step) Ongoing work: Extended peering coordination routing game Resilient extension of the PEMP framework Summary
Stefano Secci DEI 29 1.S. Secci, J.-L. Rougier, A. Pattavina, F. Patrone, G. Maier, " Peering Games for Critical Internet Flows",submitted to Euro-NF 5 th Int. Workshop on Traffic Management and Traffic Engineering for the Future Internet, 7-8 Dec. 2009, Paris, France. 2.S. Secci, J.-L. Rougier, A. Pattavina, F. Patrone, G. Maier, "PEMP: Peering Equilibrium MultiPath routing", in Proc. of 2009 IEEE Global Communications Conference (GLOBECOM 2009), 30 Nov. - 4 Dec. 2009, Honolulu, USA. 3.S. Secci, J.-L. Rougier, A. Pattavina, F. Patrone, G. Maier, "ClubMED: Coordinated Multi-Exit Discriminator Strategies for Peering Carriers", in Proc. of th Euro-NGI Conference on Next Generation Internet Networks (NGI 2009), Aveiro, Portugal, 1- 3 July Best Paper Award. Related publications
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