Routing Games for Traffic
Engineering
F. Larroca and J.L. Rougier
IEEE International Conference on
Communications (ICC 2009)
Dresden, Germany, June 14-18 2009
Introduction
 Current
traffic is highly dynamic and unpredictable
 How may we define a routing scheme that performs well
under these demanding conditions?
 Possible answer: Dynamic Load-Balancing
• We connect each Origin-Destination (OD) pair with
several pre-established paths
• Traffic distribution depends on current TM and network
condition
 Greedy algorithms on path cost function fP:
• Minimum coordination
• Ideal case study for game theory: Routing Game
page 1
F. Larroca and J.L. Rougier
IEEE ICC 2009
Introduction
 First
Contribution:
• New routing game designed for elastic traffic
• Basic Idea: use load-balancing to further maximize the
utility obtained by TCP flows
 Second Contribution:
• Performance comparison of three routing games
• Considered games:
- Congestion Game
- Bottleneck Game
- Our proposition
page 2
F. Larroca and J.L. Rougier
IEEE ICC 2009
Agenda
Introduction
Basic
New
Definitions and Results
Routing Game
Evaluation
Conclusions
page 3
F. Larroca and J.L. Rougier
IEEE ICC 2009
Definitions
3
functions to define a Routing Game:
• Link cost: fl(rl)
• Path cost: fP=g ({fl(rl)}lϵP)
• Social Cost: SC(d)
 Congestion Game:
fl (r l ) 
1
cl  r l
g ( A )  a
SC ( d ) 
a A

s
rl
• Equilibrium minimizes  ( d )   l 0
d si f Psi  
i
f l ( x ) dx
l
rl
cl  r l
instead of SC(d)
• To converge to the optimum we should use
fˆl ( r l ) 
cl
c l
• Example: MPLS adaptive traffic engineering (MATE)
[EJLW01]
page 4
F. Larroca and J.L. Rougier
IEEE ICC 2009
 rl 
2
Definitions
3
functions to define a Routing Game:
• Link cost: fl(rl)
• Path cost: fP=g ({fl(rl)}lϵP)
• Social Cost: SC(d)
 Bottleneck
Game:
fl (r l ) 
rl
cl
g ( A )  max a
a A
SC ( d )  max f P  max
P
l
rl
cl
• Equilibrium and social optimum coincide!
• Examples: TeXCP [KKDC05] and REPLEX [FKF06]
page 5
F. Larroca and J.L. Rougier
IEEE ICC 2009
Agenda
Introduction
Basic
New
Definitions and Results
Routing Game
Evaluation
Conclusions
page 6
F. Larroca and J.L. Rougier
IEEE ICC 2009
New Routing Game: Intuition
 Assume
each OD pair s has exactly Ns TCP flows
 Congestion Control Problem (x = TCP rate):

maximize
x
N
si
U si ( x si )
OD pairs ( s ) Paths ( i )
s.t.
N
s
si
x si  c l
i :l  i
 Nsi
(flows per path) are given. Why not optimize in both
x and N?
 First idea: à la Multi-Path TCP (optimized by end-users)
 Our idea: keep the separation between end-to-end
congestion control (maximization on x) and routing
(maximization on N)
page 7
F. Larroca and J.L. Rougier
IEEE ICC 2009
New Routing Game: Definition
 First
problem: Considered time-scale
• Time-Scale(TCP) << Time-Scale(Routing)
• Approximations of xsi and Nsi are necessary:
x si  ABW
N si  d si
si
 min c l  r l 
l  si
(number
of flows  amount
of traffic)
 Second
problem: Usi(x) is not known by routing
• Use arbitrary U(x)
 Result:
maximize
Umax
maximize
f
( r l ) UN sicUl si (rxlsi ) g ( A
)  max a 
SC ( d )
 d 
dmin
fcUl c lrl r l 
si
l
si
l  si P
d
l  si
x
OD pairs ( s ) Paths ( i )
a A
OD pairs ( s ) Paths ( i )s
si
i
s.t.s.t. not
d sid si 
0 0 
d sid si d sd s
SC optimum are
the
same!
i i
s i :l  i
However,
we provide an adaptation of fl(r
l)
 Equilibrium
s.t.   N si x siand
 cl
page 8
F. Larroca and J.L. Rougier
IEEE ICC 2009
Agenda
Introduction
Basic
New
Definitions and Results
Routing Game
Evaluation
Conclusions
page 9
F. Larroca and J.L. Rougier
IEEE ICC 2009
Evaluation: simple examples
 Example
1:
 Congestion
Game is reluctant to use longer paths =>
bigger maximum link utilization
page 10
F. Larroca and J.L. Rougier
IEEE ICC 2009
Evaluation: simple examples
 Example
2:
 Path
lengths relatively similar (even if link capacities
are different) => UM and CG obtain similar results (plus:
difference with BG not as important)
page 11
F. Larroca and J.L. Rougier
IEEE ICC 2009
Evaluation: simple examples
 Example
3:
 The
only mechanism that enforce fairness at a path
level is Utility Maximization
page 12
F. Larroca and J.L. Rougier
IEEE ICC 2009
Evaluation: Realistic Topologies
 ABWsi
is always bigger in our proposal
• Not very big over CG in mean (<5%) but significant in the
minimum (>15%). Origin: fairness
• More important with respect to BG
 Link utilization relatively similar among all games
• CG obtains a bigger maximum (5-10%)
page 13
F. Larroca and J.L. Rougier
IEEE ICC 2009
Agenda
Introduction
Basic
New
Definitions and Results
Routing Game
Evaluation
Conclusions
page 14
F. Larroca and J.L. Rougier
IEEE ICC 2009
Conclusions and Future Work
 The
proposed game is the most balanced one:
• It generally outperforms the rest
• When it does not, the difference is not important
 However, it is more difficult to implement
 We are interested in the total mean delay
• Answer: Congestion Routing Game
• Heavily depends on the assumed model
• Load-balancing mechanism that converges to the
minimum-delay configuration without assuming any
model? Yes! [LR09][LR09a]
page 15
F. Larroca and J.L. Rougier
IEEE ICC 2009
References
• [EJLW01]: A. Elwalid; C. Jin; S. Low and I. Widjaja "MATE: MPLS adaptive
traffic engineering" INFOCOM 2001.
• [KKDC05]: S. Kandula; D. Katabi; B. Davie and A. Charny "Walking the
tightrope: responsive yet stable traffic engineering" ACM SIGCOMM '05
• [FKF06]: S. Fischer; N. Kammenhuber and A. Feldmann "REPLEX: dynamic
traffic engineering based on wardrop routing policies" CoNEXT '06
• [LR09]: F. Larroca and J.L. Rougier "Minimum-Delay Load-Balancing Through
Non-Parametric Regression" IFIP/TC6 NETWORKING 2009
• [LR09a]: F. Larroca and J.L. Rougier "Robust Regression for Minimum-Delay
Load-Balancing" 21st International Teletraffic Congress (ITC 21)
Thank you
Questions?
page 16
F. Larroca and J.L. Rougier
IEEE ICC 2009