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Giochi non cooperativi per linstradamento 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
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Internet dissected
The Autonomous Systems (ASs) number increases
very fast!
Sources www.caida.org the CIDR report
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Internet as an interconnection of ASs
Source The CIDR report
AS number detected on a backbone BGP router
routing table
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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

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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 your preferences via the MED
SURE! ( ?)
Client
ISP national
ISP national
ISP national
ISP national
Can you give me more bw?
IGP?MED Id prefer you use link A, then C, B
?MED10
?MED100
?MED50

• Transit agreements directly imply infrastructure
  upgrades
• Upgrade of inter-AS link capacity, routers (the
  customer pays for)

ISP regional
ISP regional
ISP regional
ISP regional
ISP regional
ISP regional
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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 Id 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
ISP national
ISP national
ISP national
ISP national

• 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 regional
ISP regional
ISP regional
ISP regional
ISP regional
ISP regional
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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.

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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 others 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

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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 BGPMED 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

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Simple 3-link ClubMED game examples

The Nash equilibrium is unique and
Pareto-efficient
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13 14 15
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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 players cost
  can be decreased from s to s without increasing
  the other players 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.

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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 XmYmnm

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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 Gc guides
  the Nash equilibrium

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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 d 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
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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 function H set of
  inter-peer flow pairs ?ih the outgoing bit-rate
  of the flow pair h on link i Ci the egress
  capacity of li
• Gc practically not considered when

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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

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Results for a Internet2 Geant2 peering emulation
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• 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

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Results IGP routing cost
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Results maximum link utilization
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Results Nash equilibria dynamic
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Results route stability
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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)
  ? (xj,yj) - ? (x0,y0) f (xj,yj) f (x0,y0) lt 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) ? (xj,yj) - ? (x0,y0) 0 AND f
  (xj,yj) f (x0,y0) 0 (2)

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Results route stability under intra-AS
congestion (PEMP)
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With decimated link capacities
The route stability performance depends on the
IGP-WO cost function
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Results PEMP policy trade-offs (IGP routing cost)
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(with decimated link capacities)
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Results PEMP policy trade-offs (link utilization)
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With decimated link capacities
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But is route stability a real issue?
Dataset source  A Radar for the Internet , M.
Latapy et al.
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But is route stability a real issue?
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But is route stability a real issue? (2)
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Dataset source  A Radar for the Internet , M.
Latapy et al.
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Summary
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• 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

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Related publications
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1. 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.
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 2009 5th Euro-NGI
   Conference on Next Generation Internet Networks
   (NGI 2009), Aveiro, Portugal, 1-3 July 2009. Best
   Paper Award.

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Contact
Stefano Secci
Tel. [phone]
secci_at_enst.fr
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