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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.Jiang 28-08-2004. Outline. Overview of Adaptive Routing Related Work Probabilistic Routing Scheme

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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.Jiang

28-08-2004

outline
Outline
  • Overview of Adaptive Routing
  • Related Work
  • Probabilistic Routing Scheme
  • Convergence Analysis
  • Simulation Results
  • Conclusion
where are you
Where are you?
  • Overview of Adaptive Routing
  • Related Work
  • Probabilistic Routing Scheme
  • Convergence Analysis
  • Simulation Results
  • Conclusion
introduction to adaptive routing
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
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
Illustration of source routing

n1-n2-n3-n4-n5

n1

n2

n3

n4

n5

problems i oscillation
Problems I -- Oscillation
  • Ring Network (Data Networks)
  • Simultaneous Overlay Network

1+ Mbps

(L2)

Primary Paths

Alternate Paths

2 Mbps

L1

Sources

Bottleneck

Phy. Link

Destinations

1 Mbps

(L3)

Ov.Nw. Nodes

(2 Ovns)

problem ii performance degradation
Problem II -- Performance Degradation
  • Nash Equilibrium
  • Well known that Nash Equilibrium do not in general optimize social welfare.
  • Braess’s Paradox

1

x

1

Performance degradation:selfish routing : global optimal= 2/(0.5+1) = 4/3

1/2

0

s

t

1/2

1

x

where are you1
Where are you?
  • Overview of Adaptive Routing
  • Related Work
  • Probabilistic Routing Scheme
  • Convergence Analysis
  • Simulation Results
  • Conclusion
related work
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
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 cont1
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 you2
Where are you?
  • Overview of Adaptive Routing
  • Related Work
  • Probabilistic Routing Scheme
  • Convergence Analysis
  • Simulation Results
  • Conclusion
routing scheme data path component
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.
routing scheme control path component
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
Routing Scheme: Notation
  • ljithe latency of link from node i to its neighbor j
  • Ljikthe estimated delay from i to destination k through node j
  • qjikthe internal probability from node i to destination k through neighbor j
  • pjikthe routing probability from node i to destination k through neighbor j
  • {qjik} will converge to the Wardrop equilibrium
  • {pjik} are ε- approximate of {qjik}
update of routing probabilities 1
Update of routing probabilities (1)
  • Node i first computes the new delay Δjik = lji + Ljk
  • Ljkis the estimated latency from node j to node k
  • node i update the new latency estimationLjik = (1-α(n)) Ljik + α(n) Δjik
  • α(n) is the delay learning factor.
  • then node i computes its overall delay estimation Lik to destination k
update of routing probabilities 2
Update of routing probabilities (2)
  • Node i reports Lik to its neighbors after some delay, and 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
  • ξjik is i.i.d uniform random routing vectors to add disturbance to avoid non-Wardrop solutions
update of routing probabilities 3
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:
update of routing probabilities 4
Update of routing probabilities (4)
  • Node i compute the routing probabilities:
comments on measuring
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- Δjik = 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
probabilistic scheme for network optimal routing
Probabilistic Scheme for network optimal routing
  • Overview of network optimal routingto solve the convex programming:
probabilistic scheme for network optimal routing cont
Probabilistic Scheme for network optimal routing (cont)

Proved in “How bad is selfish routing”.

probabilistic scheme for network optimal routing cont1
Probabilistic Scheme for network optimal routing (cont)
  • For network optimal routing, replace lji with marginal cost function: mcji = lji + fjisji
  • sji is the rate of change in the latency from node 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 you3
Where are you?
  • Overview of Adaptive Routing
  • Related Work
  • Probabilistic Routing Scheme
  • Convergence Analysis
  • Simulation Results
  • Conclusion
convergence analysis intuition
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
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 -
where are you4
Where are you?
  • Overview of Adaptive Routing
  • Related Work
  • Probabilistic Routing Scheme
  • Convergence Analysis
  • Simulation Results
  • Conclusion
evaluation methodologies
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
conclusion
Conclusion
  • Overview of Adaptive Routing
  • Related Work
  • Probabilistic Routing Scheme
  • Convergence Analysis
  • Simulation Results
  • Conclusion
conclusion1
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).