giochi non cooperativi per l’instradamento di pacchetti ip nella rete internet stefano secci a, in...
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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. Maierb
a Telecom ParisTech, France b Politecnico di Milano, Italyc Università di Genova, Italy
Corso di Teoria dei Giochi, ApplicazioniCollegio Borromeo, Università di Pavia, 29-30 Marzo 2010, Pavia
Stefano SecciDEI
2Internet dissected
Sourc
es:
ww
w.c
aid
a.o
rg;
the C
IDR
re
port
The Autonomous Systems (ASs) number increases very fast!
Stefano SecciDEI
3Internet as an interconnection of ASs
AS uAS w
AS x
AS z
AS y
ISP 1
ISP 2
ISP 3Multi-homed AS
Border Gateway
ISP 4 ...
ISP 4 ...
Internet Exchange point
Stub AS
Carrier AS
Sourc
e:
The C
IDR
report
AS number detected on a backbone BGP router routing table
Stefano SecciDEI
4Intra- and Inter- Autonomous System (AS) Routing
An EGP protocol, i.e., the Border Gateway Protocol (BGP) for inter-AS routingMany IGP protocols, e.g., OSPF, ISIS, RIP, for intra-AS routing
BGP and IGP routing is coupled
AS 13Address Range:
27.0.0.0/8
EGPEGPAS 1712
Address Range: 137.194.0.0/16
AS 1972Address Range: 192.65.10.0/24
IGPIGP137.194.10.0
137.194.20.0137.194.30.0
137.194.40.0
137.194.50.0
Stefano SecciDEI
5Inter-AS business relationships: transit agreement
Client
Provider
ISPregional
ISPregional
ISPregional
ISPregional
ISPregional
ISPregional
ISPnational
ISPnational
ISPnational
ISPnational
ISPinternational
ISPinternational
A provider announces to its clients all the routes customers have full access to its network
€
Can
you
give
me
mor
e bw
?
IGP
MED
I’d p
refe
r you
use
link
A, th
en C
, B
M
ED
=10
M
ED
=100
M
ED
=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 SecciDEI
6Inter-AS business relationships: peering agreement
ISPregional
ISPregional
ISPregional
ISPregional
ISPregional
ISPregional
ISPnational
ISPnational
ISPnational
ISPnational
ISPinternational
ISPinternational
A provider announces to its peer its network and all the routes by its clients
Peer provider
Peer provider
For free! Can you give me more bw?
Well . only if you do the same OK
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
IGPMED mapping :I’d prefer you use link G,
then H, IUhm.. why should I?
Stefano SecciDEI
7Hot potato and least MED BGP rules – BGPv4
AS YDestination
AS XMEDA=25
25
15
Paris
Bucharest
NiceMEDA=15
Rome
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.
AS Y
AS BDestinationAS A
IGP weight=25 IGP weight=15
Bucharest
RomeParis
Stefano SecciDEI
8Rationales
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
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9A simple 2-link peering game example
AS I and AS II exchange their internal routing cost via the MEDfor NET A and NET B (resp.)
Game strategy set = possible egress linksTable 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
AS II
NET A
NET B
MED=5
25 15
AS I
550
l1 l2
MED=50 MED=5
Rb
Ra
R1I
R2I
R2II R1
II
MED=25 MED = 15
Stefano SecciDEI
10Simple 3-link ClubMED game examples
Community A
Community B
9
10
15
5
6
11
9
8
l2 l3l1
13 23
7
10
AS I
AS II
Community A
Community B
9
10
15
5
3
8
9
8
l2 l3l1
9 1
6
10
AS I
AS II
10
The Pareto-superior Nash equilibrium is not Pareto-efficient any longer!
The Nash equilibrium is unique and Pareto-efficient
13
13 13 14
15
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
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11The ClubMED game
The resulting ClubMED game can be described as G = Gs + Gd + Gc
Gs, a selfish game (endogenous)Gd , a dummy game, of pure externalityGc, a congestion game (endogenous)
For m pairs and n links: permutation of m single-pair n-link ClubMED games |Xm|=|Ym|=nm
Generalization
Mono-directional costs
Many peering links
Multiple pairs of destination communities
Congestion costs on peering links
xlEiHh
ihi
ihic
i CKx
,
1)()(
Stefano SecciDEI
12The ClubMED game: properties
It is a potential gameThe 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 minimumAnd a Nash equilibrium always existsFrequent occurrence of multiple equilibria
A ClubMED Nash equilibrium is not necessarily a Pareto-efficient profileThe Pareto-frontier may not contain Nash equilibriaGd guides the Pareto-efficiency, Gs + Gc guides the Nash equilibrium
Stefano SecciDEI
13Dealing 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
Iji
IjixXxji
I c ,,,
),( maxmin
Tp
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14ClubMED-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 pairsρi
h the outgoing bit-rate of the flow pair h on link iCi the egress capacity of li
Gc practically not considered when
Hh iEih Cmin
xlEiHh
ihi
ihic
i CKx
,
1)()(
Hh iiiiih CKKC else ; , If
Stefano SecciDEI
15Nash 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
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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
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17Results: IGP routing cost
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18Results: maximum link utilization
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19Results: Nash equilibria dynamic
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20Results: route stability
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21Peering 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 (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)
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22Results: route stability under intra-AS congestion (PEMP)
With decimated link capacities
The route stability performance depends on the IGP-WO cost function
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23Results: PEMP policy trade-offs (IGP routing cost)
(with decimated link capacities)
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24Results: PEMP policy trade-offs (link utilization)
With decimated link capacities
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But is route stability a real issue? 25
Dataset source: « A Radar for the Internet », M. Latapy et al.
Stefano SecciDEI
26But is route stability a real issue?
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27But is route stability a real issue? (2)
Dataset source: « A Radar for the Internet », M. Latapy et al.
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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 SecciDEI
29
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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