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Is Random Access Fundamentally Inefficient ?

CH-1015 EcublensPatrick.Thiran@epfl.chhttp://lcawww.epfl.ch

Patrick Thiran (EPFL)

LCA

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Random Access Can be spatially efficient

“Top down” approaches: distributed scheduling algorithms by message passing methods optimize utility functions and hence able to reach (at least some controlled) level of fairness. (Srikant et al, 2007, Modiano, Shah, Zussman, 2006, Jiang Walrand, 2007, Tassiulas 98, ...)

Bootstrap phase needed to have all the nodes talking first to each other, overhead to distribute schedules in dynamic situations (mobility, time-varying channel) is a challenge.

“Bottom-up” approaches: asynchronous CSMA/CA algorithms. Here approx: continuous expo() back-off distributions , instantaneous CS mechanism, saturated conditions. Metrics: spatial reuse and per link fairness.

(Wang, Kar, 2005, Durvy T, 2006, Bordenave, McDonald, Proutière, 2007, Liew et al, 2008). Other models with collisions show some similar spatial efficiency, Jindal Psounis, 2008).

4Channel Access intensity

Sp

ati

al re

use

Reversible Markov chain Reversible Markov chain (= Kelly loss network) -> product

solution: Stationary probability that k links are active is k / ∑i N(i) i

with N(i) = number of independent sets with i active links. When ∞, Prob(max nr active links) 1. CSMA/CA protocols finds spontaneously maximal independent sets

for any graph G(V,E).

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Fairness vs spatial reuse

= 1 = 400

Line 50 nodes

= 0.19 = 0.32

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1-dim lattice 2-dim latticeL smallL large

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1-dim lattice 2-dim latticeSpati

al re

use

Ja

in F

air

ness

Ind

ex

L smallL large

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p(j) = prob(link j is active)

Phase transition in 2 dim networks. In 2-dim, one can have one or

multiple Gibbs measures. Theorem (Durvy,Dousse,T 08):

There is 0 < 1 ≤ 2 < ∞ such that

i) unique Gibbs measure if < 1

ii) multiple Gibbs measures if > 2

Multiple Gibbs measures -> starvation occurs just because of topology (even without collisions, TCP, etc).

Remedy: can compute a lower bound on 1 keeping unique Gibbs measure..

=26

=78

=78

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Asymmetric Exclusion Domain with Capture

CSRange = RxRange Can consider non directed links.

CSRange > RxRange and Capture Effect Must take directed links New connection acceptance depends of order of arrival of neighboring

connections

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Limited capture model: spatial reuse What is lost in terms of spatial reuse is gained in terms of

fairness.

=(∑i i N(i) (i)) / L

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Fairness vs spatial reuse

= 600 Line 50 nodes

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Comparison between loss network model and 802.11

Performance ns-2 gagged node problem solved jammed node problem solved focused node problem solved reduction of RTS/CTS overhead theoretical limit

Possible to trace all the effects that explain differences between model and more realistic simulations, minor fixes sometimes possible (DurvyT06)

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Spatial reuse vs fairness

Two levels of decentralization. Distributed algorithms by message passing. CSMA/CA.

Random Access Algorithms can be spatially efficient. Starvation is the price to pay for max spatial reuse (even

without collisions) in CSMA/CA protocols, it is a fundamental feature.

Solutions might be simpler: Trade-off between spatial reuse and fairness can be adapted by

playing on (average back-off time). Asymmetric exclusion domains (CSRange > RXRange) lower spatial

reuse but increase fairness if some amount of capture is possible. Irregularity often helps ! Need explanatory models to get insight and fundamental

properties, with explicit even if strong assumptions.