Non-Cooperative Multi-Radio Channel Allocation in Wireless Networks

1. 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

2. Problem • multi-radio devices • set of available channels How to assign radios to available channels? Márk Félegyházi (EPFL)

3. 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)

4. 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)

5. 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)

6. 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)

7. Game-Theoretic Concepts Best response: Best strategy of player i given the strategies of others. Nash equilibrium: No player has an incentive to unilaterally deviate. 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)

8. 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)

9. 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)

10. 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)

11. 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

12. 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)

13. 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)

14. 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 Márk Félegyházi (EPFL)

15. Future work • general scenario – conjecture: hard • approximation algorithms • extend model to mesh networks (multihop communication) Márk Félegyházi (EPFL)

16. Extensions

17. 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)

18. 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)

19. 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)

20. 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)

21. 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)

22. Convergence to NE (3/3) Márk Félegyházi (EPFL)