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### Multi-Radio Channel Allocation in Wireless Networks

Prospective wireless networks

Relaxing spectrum licensing:

- small network operators in unlicensed bands
- inexpensive access points
- flexible deployment
- community and ad hoc networks
- no authority
- peer-to-peer network operation
- cognitive radio
- restricted operation in any frequency band
- no interference with licensed (primary) users
- adaptive behavior

Márk Félegyházi (EPFL)

Motivation

- more complexity at the network edges
- decentralization
- ease of programming for wireless devices
- rational users

- more adaptive wireless devices
- potential selfish behaviorof devices

TRENDS

OUTCOME

What is the effect of selfish behavior in wireless networks?

Márk Félegyházi (EPFL)

Related work (1/2)

- Peer-to-peer networks
- free-riding [Golle et al. 2001, Feldman et al. 2007]
- trust modeling [Aberer et al. 2006]
- Wired networks
- congestion pricing [Korilis et al. 1995, Korilis and Orda 1999, Johari and Tsitsiklis 2004]
- bandwidth allocation [Yaïche et al. 2000]
- coexistence of service providers [Shakkottai and Srikant 2005/2006, He and Walrand 2006]
- Wireless networks
- power control [Goodman and Mandayam 2001, Alpcan et al. 2002, Xiao et al. 2003]
- resource/bandwidth allocation [Marbach and Berry 2002, Qui and Marbach 2003]
- medium access [MacKenzie and Wicker 2003, Yuen and Marbach 2005, Čagalj et al. 2005]
- Wi-Fi pricing [Musacchio and Walrand 2004/2006]

Márk Félegyházi (EPFL)

Related work (2/2)

Security

Cooperation

12. Behavior enforcement

8. Privacy protection

11. Operators in shared spectrum

7. Secure routing

10. Selfishness in PKT FWing

6. Secure neighbor discovery

9. Selfishness at the MAC layer

5. Security associations

4. Naming and addressing

3. Trust

Appendix A:

Security and crypto

Appendix B:Game theory

2. Upcoming networks

1. Existing networks

http://secowinet.epfl.ch

Márk Félegyházi (EPFL)

Summary of my research

Part I:

Introduction to game theory

- Ch 1: A tutorial on game theory
- Ch. 2: Multi-radio channel allocation in wireless networks
- Ch. 3: Packet forwarding in static ad-hoc networks
- Ch. 4: Packet forwarding in dynamic ad-hoc networks
- Ch. 5: Packet forwarding in multi-domain sensor networks
- Ch. 6: Cellular operators in a shared spectrum
- Ch. 7: Border games in cellular networks

Part II:

Non-cooperative users

Part III:

Non-cooperative network operators

Márk Félegyházi (EPFL)

The channel allocation (CA) game

c1

c2

f1

f2

f3

- two channels: c1 and c2
- total available throughput: and
- two devices: p1 and p2
- throughput is fairly shared
- users of the devices are rational

- Channel Allocation (CA) game: GCA = (N, S, U)
- N – players: p1 and p2
- S – strategies: choosing the channels
- and
- U – payoff functions: received throughputs
- and

strategy of player i

strategy profile

payoff of player i

Márk Félegyházi (EPFL)

Stability: Nash equilibrium

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

Nash equilibrium: No player has an incentive to unilaterally deviate.

Márk Félegyházi (EPFL)

Efficiency: Pareto-optimality

Pareto-optimality: The strategy profile spois Pareto-optimal if:

with strict inequality for at least one player i

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

Márk Félegyházi (EPFL)

Non-Cooperative Users

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]

Márk Félegyházi (EPFL)

Problem

- multi-radio devices
- set of available channels

How to assign radios to available channels?

Márk Félegyházi (EPFL)

System model (1/3)

- C – set of orthogonal channels (|C| = C)
- N – set of communicating pairs of devices (|N| = 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

Márk Félegyházi (EPFL)

System model (2/3)

number of radios by sender i

on channel x

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

→

Intuition:

example:

Use multiple radios on one channel ?

Márk Félegyházi (EPFL)

System model (3/3)

- channels with the same properties
- τt(kx)– total throughput on any channel x
- τ(kx) – throughput per radio

Márk Félegyházi (EPFL)

Multi-radio channel allocation (MRCA) game

- selfish users (communicating pairs)
- non-cooperative game GMRCA
- players→ senders
- strategy → channel allocation
- payoff → total throughput
- strategy:
- strategy matrix:
- payoff:

Márk Félegyházi (EPFL)

Use of all radios

p4

p4

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

Each player should use all of his radios.

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

all channel allocations

Lemma

Márk Félegyházi (EPFL)

Load-balancing channel allocation

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

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

all channel allocations

Lemma

Proposition

Márk Félegyházi (EPFL)

Nash equilibria (1/2)

p2

p4

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

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

- dx,y≤ 1and
- ki,x≤ 1.

Nash Equilibrium:

Use one radio per channel.

all channel allocations

NE type 1

Lemma

Proposition

Márk Félegyházi (EPFL)

Nash equilibria (2/2)

- Consider two arbitrary channels x and y in C, where kx ≥ ky
- distance: dx,y = kx – ky
- loaded and less loaded channels: C+ andC–

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

- dx,y≤ 1,
- for any player i who haski,x≥ 2, x in C,
- for any player i who haski,x≥ 2 and x inC+, ki,y≥ ki,x– 1, for all y inC–

Nash Equilibrium:

Use multiple radios on certain channels.

all channel allocations

NE type 1

Lemma

Proposition

C–

C+

Márk Félegyházi (EPFL)

NE type 2

Efficiency (1/2)

Theorem: In GMRCA , the price of anarchy is:

where

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

Márk Félegyházi (EPFL)

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

Márk Félegyházi (EPFL)

Convergence to NE (1/3)

Algorithm with imperfect info:

- move links from “crowded” channels to other randomly chosen channels
- desynchronize the changes
- convergence is not ensured

N = 5, C = 6, k = 3

p5

p4

p5

p4

p3

p4

p3

p3

p2

p5

p1

p2

p2

p1

p1

time

p5: c2→c5

p1: c4→c6

c4

c5

channels

c6

c1

c2

c3

p1

p5

c6→c4

c5→c2

p4

p3

p3: c2→c5

p4: idle

p2

c6→c4

c1→c3

p1

p2: c2→c5

p1: c2→c5

c6→c4

Márk Félegyházi (EPFL)

Convergence to NE (2/3)

Algorithm with imperfect info:

move links from “crowded” channels to other randomly chosen channels

desynchronize the changes

convergence is not ensured

Balance:

best balance (NE):

unbalanced (UB):

Efficiency:

Márk Félegyházi (EPFL)

Convergence to NE (3/3)

Márk Félegyházi (EPFL)

Summary – Multi-radio channel allocation

- 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

Márk Félegyházi (EPFL)

Summary of my research

Part I:

Introduction to game theory

- Ch 1: A tutorial on game theory
- Ch. 2: Multi-radio channel allocation in wireless networks
- Ch. 3: Packet forwarding in static ad-hoc networks
- Ch. 4: Packet forwarding in dynamic ad-hoc networks
- Ch. 5: Packet forwarding in multi-domain sensor networks
- Ch. 6: Cellular operators in a shared spectrum
- Ch. 7: Border games in cellular networks

Part II:

Non-cooperative users

Part III:

Non-cooperative network operators

Márk Félegyházi (EPFL)

Future research directions (1/3)

- Cognitive networks
- Chapter 2: multi-radio channel allocation
- adaptation is a fundamental property of cognitive devices
- selfishness is threatening network performance
- primary (licensed) users
- secondary (cognitive) users
- incentives are needed to prevent selfishness
- frequency allocation
- interference control

submitted: M. Félegyházi, M. Čagalj and J.-P. Hubaux, “Efficient MAC in Cognitive Radio Systems: A Game-Theoretic Approach,” submitted to IEEE JSAC, Special Issue on Cognitive Radios, 2008

Márk Félegyházi (EPFL)

Future research directions (2/3)

- Coexistence of wireless networks
- Chapter 6 and 7: wireless operators in shared spectrum
- advancement of wireless technologies
- alternative service providers
- small operators
- social community networks
- competition becomes more significant
- coexistence results in nonzero-sum games
- mechanism to enforce cooperation
- competition improves services

in preparation: M. H. Manshaei, M. Félegyházi, J. Freudiger, J.-P. Hubaux, and P. Marbach, “Competition of Wireless Network Operators and Social Networks”

Márk Félegyházi (EPFL)

Future research directions (3/3)

- Economics of security and privacy
- cryptographic building blocks are quite reliable (some people might disagree)
- implementation fails due to economic reasons (3C)
- confusion in defining security goals
- cost of implementation
- complexity of usage
- privacy is often not among the security goals
- incentives to implement correct security measures
- share liabilities
- better synchronization
- collaboration to prevent attacks

submitted: J. Freudiger, M. Raya, M. Félegyházi, and J.-P. Hubaux, “On Location Privacy in Vehicular Mix-Networks”

Márk Félegyházi (EPFL)

My research

Non-cooperative users

- Multi-radio channel allocation in wireless networks
- Packet forwarding in static ad-hoc networks
- Packet forwarding in dynamic ad-hoc networks

Non-cooperative network operators

- Packet forwarding in multi-domain sensor networks
- Cellular operators in a shared spectrum
- Border games in cellular networks

Márk Félegyházi (EPFL)

Thesis contributions (Ch. 1: A tutorial on game theory)

- facilitate the application of game theory in wireless networks

M. Félegyházi and J.-P. Hubaux, “Game Theory in Wireless Networks: A Tutorial,” submitted to ACM Communication Surveys, 2006

Márk Félegyházi (EPFL)

Thesis contributions(Ch. 2: Multi-radio channel allocation in wireless networks)

- NE are efficient and sometimes fair, and they can be reached even if imperfect information is available

- load-balancing Nash equilibria
- each player has one radio per channel
- some players have multiple radios on certain channels
- NE are Pareto-efficient both in theory and practice
- fairness issues
- coalition-proof equilibria
- convergence algorithms to efficient NE

M. Félegyházi, M. Čagalj, S. S. Bidokhti, and J.-P. Hubaux, “Non-cooperative Multi-radio Channel Allocation in Wireless Networks,” in Proceedings of Infocom 2007, Anchorage, USA, May 6-12, 2007

Márk Félegyházi (EPFL)

Thesis contributions(Ch. 3: Packet forwarding in static ad-hoc networks)

- incentives are needed to promote cooperation in ad hoc networks

- model and meta-model using game theory
- dependencies / dependency graph
- study of NE
- in theory, NE based on cooperation exist
- in practice, the necessary conditions for cooperation do not hold
- part of the network can still cooperate

M. Félegyházi, L. Buttyán and J.-P. Hubaux, “Nash Equilibria of Packet Forwarding Strategies in Wireless Ad Hoc Networks,” in Transactions on Mobile Computing (TMC), vol. 5, nr. 5, May 2006

Márk Félegyházi (EPFL)

Thesis contributions(Ch. 4: Packet forwarding in dynamic ad-hoc networks)

- mobility helps cooperation in ad hoc networks

- spontaneous cooperation exists on a ring (theoretical)
- cooperation resistant to drift (alternative cooperative strategies) to some extent
- in reality, generosity is needed
- as mobility increases, less generosity is needed

M. Félegyházi, L. Buttyán and J.-P. Hubaux, “Equilibrium Analysis of Packet Forwarding Strategies in Wireless Ad Hoc Networks - the Dynamic Case,” Technical report - LCA-REPORT-2003-010, 2003

Márk Félegyházi (EPFL)

Thesis contributions(Ch. 5: Packet forwarding in multi-domain sensor networks)

- sharing sinks is beneficial and sharing sensors is also in certain scenarios

- energy saving gives a natural incentive for cooperation
- sharing sinks
- with common sinks, sharing sensors is beneficial
- in sparse networks
- in hostile environments

M. Félegyházi, L. Buttyán and J.-P. Hubaux, “Cooperative Packet Forwarding in Multi-Domain Sensor Networks,” in PerSens 2005, Kauai, USA, March 8, 2005

Márk Félegyházi (EPFL)

Thesis contributions(Ch. 6: Cellular operators in a shared spectrum)

- both cooperation (low powers) and defection (high powers) exist, but cooperation can be enforced by punishments

- wireless operators compete in a shared spectrum
- single stage game
- various Nash equilibria in the grid scenario, depending on cooperation parameters
- repeated game
- RMIN (cooperation) is enforceable with punishments
- general scenario = arbitrary ranges
- the problem is NP-complete

M. Félegyházi and J.-P. Hubaux, “Wireless Operators in a Shared Spectrum,” in Proceedings of Infocom 2006, Barcelona, Spain, April 23-29, 2006

Márk Félegyházi (EPFL)

Thesis contributions(Ch. 7: Border games in cellular networks)

- operators have an incentive to adjust their pilot power on the borders

- competitive power control on a national border
- power control game
- operators have an incentive to be strategic
- NE are efficient, but they use high power
- simple convergence algorithm
- extended game corresponds to the Prisoner’s Dilemma

M. Félegyházi, M. Čagalj, D. Dufour, and J.-P. Hubaux, “Border Games in Cellular Networks,” in Proceedings of Infocom 2007, Anchorage, USA, May 6-12, 2007

Márk Félegyházi (EPFL)

Selected publications (à la Prof. Gallager)

- M. Félegyházi, M. Čagalj, S. S. Bidokhti, and J.-P. Hubaux, “Non-Cooperative Multi-Radio Channel Allocation in Wireless Networks,” in Infocom 2007
- M. Félegyházi, M. Čagalj, D. Dufour, and J.-P. Hubaux, “Border Games in Cellular Networks,” in Infocom 2007
- M. Félegyházi, L. Buttyán and J.-P. Hubaux, “Nash Equilibria of Packet Forwarding Strategies in Wireless Ad Hoc Networks,” in IEEE Transactions on Mobile Computing (TMC), vol. 5, nr. 5, 2006

Márk Félegyházi (EPFL)

Fairness

Nash equilibria (unfair)

Nash equilibria (fair)

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

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

Márk Félegyházi (EPFL)

Centralized algorithm

Assign links to the channels sequentially.

p4

p4

p4

p4

p2

p2

p3

p3

p3

p3

p2

p1

p1

p1

p2

p1

Márk Félegyházi (EPFL)

Thesis contributions

- Ch 1: A tutorial on game theory
- facilitate the application of game theory in wireless networks
- Ch. 2: Multi-radio channel allocation in wireless networks
- NE are efficient and sometimes fair, and the fair NE can be reached even if imperfect information is available
- Ch. 3: Packet forwarding in static ad-hoc networks
- incentives are needed to promote cooperation in ad hoc networks
- Ch. 4: Packet forwarding in dynamic ad-hoc networks
- mobility helps cooperation in ad hoc networks
- Ch. 5: Packet forwarding in multi-domain sensor networks
- sharing sinks is beneficial and sharing sensors is also in certain scenarios
- Ch. 6: Cellular operators in a shared spectrum
- both cooperation (low powers) and defection (high powers) exist, but cooperation can be enforced by punishments
- Ch. 7: Border games in cellular networks
- operators have an incentive to adjust their pilot power on the borders

Márk Félegyházi (EPFL)

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