Non-Cooperative Multi-Radio Channel Allocation in Wireless Networks

Non-Cooperative Multi-Radio Channel Allocation

in Wireless Networks

Márk Félegyházi*, Mario Čagalj†, Shirin Saeedi Bidokhti*, Jean-Pierre Hubaux*

* Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne, Switzerland

† University of Split, Croatia

Infocom 2007

Infocom 2007

Márk Félegyházi (EPFL) 2

Problem

► multi-radio devices► set of available channels

How to assign radios to available channels?

3d4d5d

6d

1d 2d

Infocom 2007


System model (1/3)

3d4d5d

6d

1d 2d

2p

1p

3p

► – set of orthogonal channels (|| = C)

► – set of communicating pairs of devices (|| = N)

► sender controls the communication (sender and receiver are synchronized)

► single collision domain if they use the same channel

► devices have multiple radios► k radios at each device, k ≤ C

Infocom 2007


System model (2/3)

► N communicating pairs of devices► C orthogonal channels► k radios at each device

,i xknumber of radios

by sender i on channel x

→

,i i xx C

k k

,x i xi N

k k

example:

3 2, 2p ck

Use multiple radios on one channel ?

, 1i xk Intuition:

23ck

34pk

Infocom 2007


System model (3/3)► channels with the same properties► τ t(kx) – total throughput on any channel x

► τ(kx) – throughput per radio

Infocom 2007


► selfish users (communicating pairs)► non-cooperative game GMRCA

– players → senders – strategy → channel allocation – payoff → total throughput

► strategy:

► strategy matrix:

► payoff:

Multi-radio channel allocation (MRCA) game

,1 ,,...,i i i Cs k k

1

N

s

S

s

, ( )i i i x xx C

u k k

Infocom 2007


Game-Theoretic Concepts

Nash equilibrium: No player has an incentive to unilaterally deviate.* * *( , ) ( , ),i i i i i i iu s s u s s s S

Best response: Best strategy of player i given the strategies of others.

' '( ) : ( , ) ( , ),i i i i i i i i i ibr s s u s s u s s s S S

Price of anarchy: The ratio between the total payoff of players playing a socially-optimal (max. Pareto-optimal) strategy and a worst Nash equilibrium.

soi

iw NEi

i

uPOA

u

Pareto-optimality: The strategy profile spo is Pareto-optimal if:

' ': ( ) ( ),poi is u s u s i with strict inequality for at least one player i

Infocom 2007


Lemma: If S* is a NE in GMRCA, then .

Use of all radios

Each player should use all of his radios.

p4 p4

,ik k i

Intuition: Player i is always better off deploying unused radios.

all channel allocations

Lem

ma

Infocom 2007


Proposition: If S* is a NE in GMRCA, then dy,x ≤ 1, for any channel x and y.

Load-balancing channel allocation► Consider two arbitrary channels x and y in , where kx ≥ ky► distance: dx,y = kx – ky


Lem

ma

Pro

posi

tion

Infocom 2007


Nash equilibria (1/2)

Theorem 1: A channel allocation S* is a Nash equilibrium in GMRCA if for all i:

► dx,y ≤ 1 and

► ki,x ≤ 1.

p2

Nash Equilibrium: p4

Use one radio per channel.


Lem

ma

Pro

posi

tion NE type 1

► Consider two arbitrary channels x and y in , where kx ≥ ky► distance: dx,y = kx – ky

Infocom 2007


Nash equilibria (2/2)

Nash Equilibrium:

Theorem 2: A channel allocation S* is a Nash equilibrium in GMRCA if:

► dx,y ≤ 1,

► for any player i who has ki,x ≥ 2, x in ,

► for any player i who has ki,x ≥ 2 and x in +, ki,y ≥ ki,x – 1, for all y in –

Use multiple radios on certain channels.all channel allocations

Lem

ma

Pro

posi

tion NE type 1

NE type 2

,

( 1) ( 1)

( 1) ( )x x

i xx x

k kk

k k

► Consider two arbitrary channels x and y in , where kx ≥ ky► distance: dx,y = kx – ky

► loaded and less loaded channels: + and –

+–

Infocom 2007


Efficiency (1/2)

1

1 1 1

t

t t tx x x x

POAN k

k k k kC

Corollary: If τt(kx) is constant (i.e., ideal TDMA), then any Nash equilibrium channel allocation is Pareto-optimal in GMRCA.

Theorem: In GMRCA , the price of anarchy is:

, 1x x

N k N kk k

C C

where

Infocom 2007


Efficiency (2/2)

► In theory, if the total throughput function τt(kx) is constant POA = 1► In practice, there are collisions, but τt(kx) decreases slowly with kx (due to the

RTS/CTS method)

G. Bianchi, “Performance Analysis of the IEEE 802.11 Distributed Coordination Function,” in IEEE Journal on Selected Areas of Communication (JSAC), 18:3, Mar. 2000

Infocom 2007


Summary► wireless networks with multi-radio devices► users of the devices are selfish players► GMRCA – multi-radio channel allocation game► results for a Nash equilibrium:

– players should use all their radios– load-balancing channel allocation– two types of Nash equilibria– NE are efficient both in theory and practice

► fairness issues► coalition-proof equilibria► algorithms to achieve efficient NE:

– centralized algorithm with perfect information– distributed algorithm with imperfect information

http://people.epfl.ch/mark.felegyhazi

Infocom 2007


Future work

► general scenario – conjecture: hard► approximation algorithms► extend model to mesh networks

(multihop communication)

Extensions

Infocom 2007


Related work► Channel allocation

– in cellular networks: fixed and dynamic: [Katzela and Naghshineh 1996, Rappaport 2002]

– in WLANs [Mishra et al. 2005]– in cognitive radio networks [Zheng and Cao 2005]

► Multi-radio networks– mesh networks [Adya et al. 2004, Alicherry et al. 2005]– cognitive radio [So et al. 2005]

► Competitive medium access– Aloha [MacKenzie and Wicker 2003, Yuen and Marbach 2005]– CSMA/CA [Konorski 2002, Čagalj et al. 2005]– WLAN channel coloring [Halldórsson et al. 2004]– channel allocation in cognitive radio networks [Cao and Zheng 2005, Nie

and Comaniciu 2005]

Infocom 2007


Fairness

Nash equilibria (fair) Nash equilibria (unfair)

Theorem: A NE channel allocation S* is max-min fair iff

min min

, , , ,i x j xx x

k k i j

C C

N

Intuition: This implies equality: ui = uj, i,j

Infocom 2007


Centralized algorithm

Assign links to the channels sequentially.

p1 p1 p1p1 p2p2

p2p2 p3 p3 p3p3

p4 p4 p4p4

Infocom 2007


Convergence to NE (1/3)

p1 p1

N = 5, C = 6, k = 3

p2 p2

p4

p1

p3 p2 p5

p4

p5

p3

p3

p4

p5

c1 c2 c3c4 c5 c6

timep5: c2→c5

c6→c4p3: c2→c5

c6→c4c1→c3

p2: c2→c5p1: c2→c5

c6→c4

p1: c4→c6c5→c2

p4: idle

channelsp5

p3

p2

p1

p1

p4

Algorithm with imperfect info:► move links from “crowded”

channels to other randomly chosen channels

► desynchronize the changes► convergence is not ensured

Infocom 2007



3UB

Algorithm with imperfect info:► move links from “crowded”

channels to other randomly chosen channels

► desynchronize the changes► convergence is not ensured

xx

N kS k

C

C

Balance:

unbalanced (UB): best balance (NE):

Efficiency: ( ) ( )

( ) ( )UB

UB NE

S SS

S S

0 1S

15UB 7S

15 7 3

15 3 4S

Infocom 2007



N (# of pairs) 10

C (# of channels) 8

k (radios per device) 3

τ(1) (max. throughput) 54 Mbps

Documents

Non-Cooperative Multi-Radio Channel Allocation in Wireless Networks