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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

Internet dissected
Internet dissected nella rete Internet

The Autonomous Systems (ASs) number increases very fast!

Sources:; the CIDR report

Internet as an interconnection of ass
Internet as an interconnection of ASs nella rete Internet

Carrier AS

Internet Exchange point




AS x




AS z

Multi-homed AS


AS w

AS y

AS u

Border Gateway

Stub AS

Source: The CIDR report

AS number detected on a backbone BGP router routing table

Intra and inter autonomous system as routing

IGP nella rete Internet

Intra- and Inter- Autonomous System (AS) Routing


AS 1972

Address Range:

AS 1712

Address Range:

AS 13

Address Range:

  • 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

Inter as business relationships transit agreement
Inter-AS business relationships: transit agreement nella rete Internet


A provider announces to its clients all the routes

 customers have full access to its network





SURE! announce me yourpreferences via the MED

SURE! ($$$ )










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
















Inter as business relationships peering agreement
Inter-AS business relationships: peering agreement nella rete Internet

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?







  • 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





















Hot potato and least med bgp rules bgpv4
Hot potato and least MED BGP rules – BGPv4 nella rete Internet

  • 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.

Rationales nella rete Internet

  • 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

A simple 2 link peering game example
A simple 2-link peering game example nella rete Internet

  • 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

Simple 3 link clubmed game examples
Simple 3-link ClubMED game examples nella rete Internet

The Nash equilibrium is unique and Pareto-efficient


13 13 14




The Pareto-superior Nash equilibrium is not Pareto-efficient any longer!


  • 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.

The clubmed game
The ClubMED game nella rete Internet

  • 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

The clubmed game properties
The ClubMED game: properties nella rete Internet

  • 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

Dealing with igp weight optimizations igp wo
Dealing with IGP Weight Optimizations (IGP-WO) nella rete Internet

  • 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


Clubmed based peering link congestion controls
ClubMED-based peering link congestion controls nella rete Internet

  • 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

Nash equilibrium multipath nemp routing
Nash Equilibrium MultiPath (NEMP) routing nella rete Internet

  • 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

Results for a internet2 geant2 peering emulation
Results for a Internet2 – Geant2 peering emulation nella rete Internet


  • 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 igp routing cost
Results: IGP routing cost nella rete Internet


Results maximum link utilization
Results: maximum link utilization nella rete Internet


Results nash equilibria dynamic
Results: Nash equilibria dynamic nella rete Internet


Results route stability
Results: route stability nella rete Internet


Peering equilibrium multipath pemp routing policies cont
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)

Results route stability under intra as congestion pemp
Results: route stability under intra-AS congestion (PEMP) (cont.)


With decimated link capacities

The route stability performance depends on the IGP-WO cost function

Results pemp policy trade offs igp routing cost
Results: PEMP policy trade-offs (IGP routing cost) (cont.)


(with decimated link capacities)

Results pemp policy trade offs link utilization
Results: PEMP policy trade-offs (link utilization) (cont.)


With decimated link capacities

But is route stability a real issue
But is route stability a real issue? (cont.)

Dataset source: « A Radar for the Internet », M. Latapy et al.

But is route stability a real issue? (2) (cont.)


Dataset source: « A Radar for the Internet », M. Latapy et al.

Summary (cont.)


  • 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

Related publications
Related publications (cont.)


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.

Contact (cont.)

Stefano Secci

Tel. +33 1 4581 8399

[email protected]

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