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Giochi non cooperativi per l’instradamento di pacchetti IP nella rete Internet

Giochi non cooperativi per l’instradamento di pacchetti IP nella rete Internet.

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Giochi non cooperativi per l’instradamento di pacchetti IP nella rete Internet

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  1. Giochi non cooperativi per l’instradamento di pacchetti IP nella rete Internet Stefano Seccia, in collaborazione con J.-L. Rougiera, A. Pattavinab, F. Patronec, G. Maierba Telecom ParisTech, France b Politecnico di Milano, Italyc Università di Genova, ItalyCorso di Teoria dei Giochi, ApplicazioniCollegio Borromeo, Università di Pavia, 29-30 Marzo 2010, Pavia

  2. Internet dissected The Autonomous Systems (ASs) number increases very fast! Sources: www.caida.org; the CIDR report

  3. Internet as an interconnection of ASs Carrier AS Internet Exchange point ISP 4 ISP 3 ISP 1 AS x ... ISP 4 ... AS z Multi-homed AS ISP 2 AS w AS y AS u Border Gateway Stub AS Source: The CIDR report AS number detected on a backbone BGP router routing table

  4. IGP 137.194.50.0 137.194.40.0 137.194.10.0 137.194.30.0 137.194.20.0 Intra- and Inter- Autonomous System (AS) Routing EGP AS 1972 Address Range: 192.65.10.0/24 AS 1712 Address Range: 137.194.0.0/16 AS 13 Address Range: 27.0.0.0/8 • 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

  5. Inter-AS business relationships: transit agreement Provider A provider announces to its clients all the routes  customers have full access to its network € ISP international ISP international SURE! announce me yourpreferences via the MED SURE! ($$$ ) Client ISP national ISP national ISP national ISP national Transit agreements directly imply infrastructure upgrades • Upgrade of inter-AS link capacity, routers (the customer pays for) Can you give me more bw? IGPMED I’dpreferyou use link A, then C, B MED=10 MED=100 MED=50 ISP regional ISP regional ISP regional ISP regional ISP regional ISP regional

  6. Inter-AS business relationships: peering agreement A provider announces to its peer its network and all the routes by its clients Peer provider Peer provider IGPMED mapping :I’d prefer you use link G, then H, I Can you give me more bw? For free! Well . only if you do the same Uhm.. why should I? OK OK ISP international ISP international • 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 ISP national ISP national ISP national ISP national ISP regional ISP regional ISP regional ISP regional ISP regional ISP regional

  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.

  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

  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 l1,l2 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

  10. Simple 3-link ClubMED game examples The Nash equilibrium is unique and Pareto-efficient 13 13 13 14 15 10 4 The Pareto-superior Nash equilibrium is not Pareto-efficient any longer! • 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.

  11. The ClubMED game • Generalization • Mono-directional costs • Many peering links • Multiple pairs of destination communities • Congestion costs on peering links • The resulting ClubMED game can be described as G = Gs + Gd + Gc • Gs, a selfish game (endogenous) • Gd , a dummy game, of pure externality • Gc, a congestion game (endogenous) • For m pairs and n links: permutation of m single-pair n-link ClubMED games |Xm|=|Ym|=nm

  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 • Gd guides the Pareto-efficiency, Gs + Gcguides the Nash equilibrium

  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 Gs 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 Tp

  14. ClubMED-based peering link congestion controls • With multiple pairs, inter-peer links congestion can be controlled with Gc • 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 functionH: set of inter-peer flow pairsρih the outgoing bit-rate of the flow pair h on link i Ci the egress capacity of li • Gc practically not considered when

  15. Nash Equilibrium MultiPath (NEMP) routing • Collect the MEDs and flows’ bandwidth information • Compute the potential minimum • Compute the delta IGP path cost variations and the potential treshold • Compute the Nash set • Restrain the Nash set to the Pareto-superior equilibria • When more than one, we have a multipath solution • The corresponding routes are the coordinated routing solution

  16. Results for a Internet2 – Geant2 peering emulation 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

  17. Results: IGP routing cost 17

  18. Results: maximum link utilization 18

  19. Results: Nash equilibria dynamic 19

  20. Results: route stability 20

  21. Peering Equilibrium MultiPath (PEMP) routing policies (cont.) • Nash Equilibrium MultiPath (NEMP) coordination(one-shot) • Play the Pareto-superior equilibria of the Nash set • Fine-selected multipath routing on peering link • 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 • 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 (xj,yj) s.t.(1):ψ (xj,yj) - ψ (x0,y0) + φ (xj,yj) – φ (x0,y0)< 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 (xj,yj) - ψ (x0,y0) ≤ 0 AND φ (xj,yj) – φ (x0,y0) ≤ 0 (2)

  22. Results: route stability under intra-AS congestion (PEMP) 22 With decimated link capacities The route stability performance depends on the IGP-WO cost function

  23. Results: PEMP policy trade-offs (IGP routing cost) 23 (with decimated link capacities)

  24. Results: PEMP policy trade-offs (link utilization) 24 With decimated link capacities

  25. But is route stability a real issue? Dataset source: « A Radar for the Internet », M. Latapy et al.

  26. But is route stability a real issue? 26

  27. But is route stability a real issue? (2) 27 Dataset source: « A Radar for the Internet », M. Latapy et al.

  28. Summary 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

  29. Related publications 29 S. Secci, J.-L. Rougier, A. Pattavina, F. Patrone, G. Maier, " Peering Games for Critical Internet Flows",submitted to Euro-NF 5th Int. Workshop on Traffic Management and Traffic Engineering for the Future Internet, 7-8 Dec. 2009, Paris, France. 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. S. Secci, J.-L. Rougier, A. Pattavina, F. Patrone, G. Maier, "ClubMED: Coordinated Multi-Exit Discriminator Strategies for Peering Carriers", in Proc. of 2009 5th Euro-NGI Conference on Next Generation Internet Networks (NGI 2009), Aveiro, Portugal, 1-3 July 2009. Best Paper Award.

  30. Contact Stefano Secci Tel. +33 1 4581 8399 secci@enst.fr Torna alla presentazione

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