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

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

The Autonomous Systems (ASs) number increases very fast!

Sources: www.caida.org; the CIDR report


Internet as an interconnection of ass

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


Intra and inter autonomous system as routing

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


Inter as business relationships transit agreement

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


Inter as business relationships peering agreement

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


Hot potato and least med bgp rules bgpv4

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.


Rationales

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


A simple 2 link peering game example

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


Simple 3 link clubmed game examples

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.


The clubmed game

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


The clubmed game properties

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


Dealing with igp weight optimizations igp wo

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


Clubmed based peering link congestion controls

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 iCi the egress capacity of li

    • Gc practically not considered when


Nash equilibrium multipath nemp routing

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


Results for a internet2 geant2 peering emulation

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


Results igp routing cost

Results: IGP routing cost

17


Results maximum link utilization

Results: maximum link utilization

18


Results nash equilibria dynamic

Results: Nash equilibria dynamic

19


Results route stability

Results: route stability

20


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) ≤ 0ANDφ (xj,yj) – φ (x0,y0) ≤ 0 (2)


Results route stability under intra as congestion pemp

Results: route stability under intra-AS congestion (PEMP)

22

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)

23

(with decimated link capacities)


Results pemp policy trade offs link utilization

Results: PEMP policy trade-offs (link utilization)

24

With decimated link capacities


But is route stability a real issue

But is route stability a real issue?

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


Giochi non cooperativi per l instradamento di pacchetti ip nella rete internet

But is route stability a real issue?

26


Giochi non cooperativi per l instradamento di pacchetti ip nella rete internet

But is route stability a real issue? (2)

27

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


Summary

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


Related publications

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.


Giochi non cooperativi per l instradamento di pacchetti ip nella rete internet

Contact

Stefano Secci

Tel. +33 1 4581 8399

[email protected]

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