Is Random Access Fundamentally Inefficient ?

1. LCA Is Random Access Fundamentally Inefficient ? Patrick Thiran (EPFL) CH-1015 Ecublens Patrick.Thiran@epfl.ch http://lcawww.epfl.ch

2. 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(l) 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).

3. Spatial reuse s Channel Access intensity l 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). l 1

4. Fairness vs spatial reuse Line 50 nodes  = 0.32  = 0.19  = 1  = 400

5. 1-dim lattice 2-dim lattice L small L large

6.     1-dim lattice 2-dim lattice L small L large Spatial reuse Jain Fairness Index

7. 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.. =78 =78 =26

8. 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

9.  =(∑i i N(i)(i)) / L   Limited capture model: spatial reuse • What is lost in terms of spatial reuse is gained in terms of fairness.

10. Fairness vs spatial reuse  = 600 Line 50 nodes

11. 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)

12. 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.