On Self Adaptive Routing in Dynamic Environments
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Transcript of On Self Adaptive Routing in Dynamic Environments
On Self Adaptive Routing in Dynamic Environments
-- A probabilistic routing scheme
Haiyong Xie, Lili Qiu, Yang Richard Yang and Yin Zhang@ Yale, MR and AT&T
Presented by Joe, W.J.Jiang28-08-2004
Outline
• Overview of Adaptive Routing• Related Work• Probabilistic Routing Scheme• Convergence Analysis• Simulation Results• Conclusion
Where are you?
• Overview of Adaptive Routing• Related Work• Probabilistic Routing Scheme• Convergence Analysis• Simulation Results• Conclusion
Introduction to adaptive routing
• Routing in the Internet:interior gateway routing – OSPFexterior gateway routing – BGP
• Static routing, based on hop counts• There is an inherent inefficiency in IP routing
from user’s perspective: latency, bandwidth, loss rate, etc
• Adaptive routing, allowing end hosts to select routes by themselves.
Selfish Routing (user-optimal routing)
• Each end host selects a route with minimum latency.
• Shortest path routing, metric -- latency, additive
• Two approaches:source routing -- Nimrodoverlay routing -- Detour, RON
• Selfish by nature -- selfish routing
Illustration of source routing
n1 n2 n3 n4 n5
n1-n2-n3-n4-n5
Illustration of overlay routing
Problems I -- Oscillation
• Ring Network (Data Networks)• Simultaneous Overlay Network
Primary Paths
BottleneckPhy. Link
1+ Mbps(L2)
2 MbpsL1
1 Mbps(L3)
Sources
Destinations
Alternate Paths
Ov.Nw. Nodes(2 Ovns)
Problem II -- Performance Degradation
• Nash Equilibrium• Well known that Nash Equilibrium do not in general o
ptimize social welfare.• Braess’s Paradox
x 1
s t
x1
1/2
1/2
0
1
Performance degradation:selfish routing : global optimal= 2/(0.5+1) = 4/3
Where are you?
• Overview of Adaptive Routing• Related Work• Probabilistic Routing Scheme• Convergence Analysis• Simulation Results• Conclusion
Related Work
• Wardrop equilibrium: a research aspect in economics of transportation.
• The proof of existence of unique equilibrium and some extensions.
• Network optimal routing - Data Networks- Frank-Wolfe Method- Projection MethodThese are centralized algorithms.
• Distributed version for optimal routing - Parallel and Distributed Computation
Related Work (Cont)
• “How bad is selfish routing?”- There exists unique Nash Equilibrium for selfish routing under network flow model.- The performance (average delay) ratio between selfish routing and global routing could be unbounded for arbitrary network.- The upper bound for network with linear delay function is 4/3.
• “On selfish routing in Internet-like environment”- Based on simulation, selfish routing and global optimal routing exhibit similar performance, under different network topology and traffic models.
Related Work (cont)
• If individual users are allowed to select routes selfishly without coordination, how to ensure these behaviors will converge to an equilibrium?
• “Dynamic Cesaro-Wardrop equilibration in Networks”- a model to ensure the convergence of probabilistic routing scheme
• “On self adaptive routing in dynamic environments”
Where are you?
• Overview of Adaptive Routing• Related Work• Probabilistic Routing Scheme• Convergence Analysis• Simulation Results• Conclusion
Routing Scheme - Data Path Component• Data path component
- similar to distance vector routing- destination could be all overlay nodes.-
- a generalization of normal Internet routing.
0 1 ikj
j
ikj pp ,
Routing Scheme - Control Path Component
• Control path component - how routing probabilities are updated.
• Selfish routing, Wardrop routing, user-optimal routing
• property - Given a source-destination pair with a given amount of traffic, the routes with positive traffic should have equal latency, no larger than those unused routes for this source-destination pair.
Routing Scheme: Notation
• lji the latency of link from node i to its neighbo
r j• Lj
ik the estimated delay from i to destination k through node j
• qjik the internal probability from node i to desti
nation k through neighbor j• pj
ik the routing probability from node i to destination k through neighbor j
• {qjik} will converge to the Wardrop equilibrium
• {pjik} are ε- approximate of {qj
ik}
Update of routing probabilities (1)• Node i first computes the new delay
Δjik = lj
i + Ljk
• Ljk is the estimated latency from node j to node k• node i update the new latency estimation
Ljik = (1-α(n)) Lj
ik + α(n) Δjik
• α(n) is the delay learning factor.• then node i computes its overall delay estimation Lik t
o destination k
)('
''iNj
jkj
ikj
ik LpL
Update of routing probabilities (2)• Node i reports Lik to its neighbors after some delay, a
nd the delay is a random value between T/2 to T, to avoid synchronization.
• node i updates its internal routing probabilities:
• β(n’) is routing learning factor• ξj
ik is i.i.d uniform random routing vectors to add disturbance to avoid non-Wardrop solutions
ikj
ikj
ikikj
ikj
ikj LLqnqq '
Update of routing probabilities (3)• Projection: node i projects the internal routing
probabilities to the subspace of [0,1]N(i), which is equivalent to solving the following problem:
jx
x
qx
j
iNjj
iNj
ikjj
allfor 10over
1 subject to
minimize
)(
)(
2
Update of routing probabilities (4)• Node i compute the routing probabilities:
)(
1iN
qp ikj
ikj
Protocol to implement user-optimal routing
Comments on measuring
• About measuring lji , two approaches:
- measured by node i- measured by node j
• The advantage of the second method:- unnecessary for clock synchronization- Δj
ik = lji + Ljk, there is an offset which is just the clock
difference between i and the destination, independent of j.- - overhead is to stamp packets
ikj
ikj
ikikj
ikj
ikj LLqnqq '
Probabilistic Scheme for network optimal routing
• Overview of network optimal routingto solve the convex programming:
)()( ,)()( minimize eeeeeEe
ee fflfcfcfC
PP
P f
Eeff
,...,k}{irf
P
PePpe
iPP
P
i
0
1
:
Probabilistic Scheme for network optimal routing (cont)
eeeeeeeeeeee fflflfflfcfl )()())(()()(*
. instancefor
mequilibriuNash at isit ifonly and if optimal is
for feasible flow aThen above. as defined function
cost marginal with , edgeeach for function convex a is
in which instancean be Let :
)(G,r,l
(G,r,l)
fl
e
(x)lx(G,r,l)Theorem
*
*
e
Proved in “How bad is selfish routing”.
Probabilistic Scheme for network optimal routing (cont)
• For network optimal routing, replace lji with m
arginal cost function: mcj
i = lji + fj
isji
• sji is the rate of change in the latency from no
de i to node j at traffic amount fji
• Without knowing the analytical expression of latency functions.
• However, the paper does not mention the scheme to measure the rate of change in the latency.
Where are you?
• Overview of Adaptive Routing• Related Work• Probabilistic Routing Scheme• Convergence Analysis• Simulation Results• Conclusion
Convergence analysis - Intuition
• Consider a network with only two links
• p1, p2 >=0, p1+p2=1• Five cases.
- (a) link 1 has higher latency- (b) link 1 has lower latency- (c) link 1 and 2 has the same latency- (d) link 1 has all of the traffic- (e) link 2 has all of the traffic
Convergence Analysis - Assumption
• A1 - latency function is continuous, non-decreasing and bounded.
• A2 - the updates are frequent enough compared with the change rate in the underlying network states.
• A3 -
Convergence Analysis - Assumption
• A4 -
Where are you?
• Overview of Adaptive Routing• Related Work• Probabilistic Routing Scheme• Convergence Analysis• Simulation Results• Conclusion
Evaluation Methodologies
• Network topologies: ATT, Sprint, Tiscali• Traffic demands• Traffic stimuli:
- Traffic spike- Step function- Linear function
• Performance metrics:- average latency- average convergence time- link utilization
Dynamics of user-optimal routing and network-optimal routing
Conclusion
• Overview of Adaptive Routing• Related Work• Probabilistic Routing Scheme• Convergence Analysis• Simulation Results• Conclusion
Conclusion
• This paper introduces a probabilistic routing scheme to achieve both user-optimal (selfish) routing and network optimal routing.
• An application of enforcement learning.• Not consider the issue of fairness
between users (or overlays).
Thank you!