A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

1. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks Lin Gao, Xinbing Wang Dept. of Electronic Engineering Shanghai Jiao Tong University Shanghai, China

2. Outline • Introduction • Motivations • Objectives • System Model and Game Theory • Existence of MMCPNE • Convergence Algorithm and Simulation • Conclusions A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

3. Motivation • The appearance of Multi-hop mobile ad hoc networks (MANETs) • A good channel allocation scheme in multi-hop MANET can improve the system performance dramatically. • Distributed algorithm shows potential ability in channel allocation problem due to the lacking of global central node in multi-hop MANETs. MANETs A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

4. Objectives -- How to Solve the Problem? • Fixed channel allocation(FCA), dynamic channel allocation(DCA) and hybrid channel allocation(HCA), e.g., [1], [2], [3] • Weighted graph coloring method, e.g., [4] • In this paper, We model the channel allocation problem as a static cooperative game, in which some players collaborate to achieve high date rate. [1] J. van den Heuvel, R. A. Leese, and M. A. Shepherd. Graph labeling and radio channel assignment. Journal of Graph Theory, 29:263-283, 1998. [2] I. Katzela and M. Naghshineh. Channel assignment schemes for cellular mobile telecommunication systems: a comprehensive survey. IEEE Personal Communications, 3(3):10-31, Jun 1996. [3] Hac A and Z. Chen. Hybrid channel allocation in wireless networks. In Proceedings of the IEEE Conference on Vehicular Technology Conference (VTC'99), 50(4):2329-2333, Sept. 1999. [4] A. Mishra, S. Banerjee, and W. Arbaugh. Weighted coloring based channel assignment for WLANs. Mobile Computing and Communications Review (MC2R), 9(3), 2005. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

5. Outline • Introduction • System Model and Game Formulation • System Model: Multi-hop MANET • Game Theory: Nash Equilibrium • Existence of MMCPNE • Convergence Algorithm and Simulation • Conclusions A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

6. System Model -- I • We assume that there exist several communication sessions in our model and we further assume each user participates in only one session. An example of 3 communication sessions and 7 users. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

7. System Model -- II • We assume each user owns a device equipped with several radio transceivers, denoted by TS and RS respectively, which used to transmit the data packets respectively. • We assume that there is a mechanism that enables the multiple radios in any TS (or RS) to communicate simultaneously by using orthogonal channels. TS TS RS RS TS RS An example of 3 radios in TS (and RS). A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

8. System Model -- III • We assume that the total available bandwidth on channel c is shared equally among the radios deployed on this channel. • Utility function: A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

9. Game Formulation -- I • We formulate the channel allocation problem with a single stage game, which corresponds to a fixed channel allocation among the players. Each player's strategy consists in defining the number of radios on each of the channels. The strategy of the previous system model. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

10. Game Formulation -- II • Nash Equilibrium (NE): NE expresses the resistance to the deviation of a single player in non-cooperative game. In other words, in a NE none of the players can unilaterally change its strategy to increase its utility. An example of the Nash Equilibrium. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

11. Game Formulation – III • Non-cooperative game is not suitable for the multi-hop networks for the following two reasons: (1) In one hand, the achieved date rate of any player in multi-hop link is not only determined by the utility itself, but also by the utilities of other players in the same link. (2) In the other hand, it is possible that the players in the same multi-hop link cooperatively choose their strategies for the purpose of high achieved date rate. An example of the Nash Equilibrium with poor performance where u1 and u2 belong to the same multi-hop link. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

12. Game Formulation – IV • we define a novel coalition-proof Nash equilibrium in cooperative game, named as min-max coalition-proof Nash equilibrium (MMCPNE), in which players make their decisions so as to improve the minimal payoff of players in the coalition. An example of the MMCPNE. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

13. Game Theory – V • By jointly searching the strategy in the strategies set of | li | players. The computation of achieving MMCPNE increases exponentially with the size of link. • To reduce the large computation in finding MMCPNE, we introduce three approximate solutions, denoted by minimal coalition-proof Nash equilibrium (MCPNE), average coalition-proof Nash equilibrium (ACPNE) and i coalition-proof Nash equilibrium (ICPNE). The definitions of MCPNE, ACPNE and ICPNE are shown in Section IV. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

14. Definition of MMCPNE • We define a novel coalition-proof Nash equilibrium in cooperative game, named as min-max coalition-proof Nash equilibrium (MMCPNE), in which players make their decisions so as to improve the minimal payoff of players in the coalition. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

15. Definition of MCPNE • In MCPNE, players in a coalition select their strategies to maximize the minimal utilities of players in the coalition. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

16. Definition of ACPNE • In ACPNE, players in a coalition select their strategies to maximize the average utility while do not decrease the minimal utility of players in the coalition. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

17. Definition of ICPNE • In ICPNE, however, players in a coalition select their strategies to maximize their own utilities while do not decrease the minimal utility of players in the same coalition. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

18. Intuition among these NE definitions A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

19. Outline • Introduction • System Model and Game Formulation • Existence of MMCPNE • Theorem 1 • Proposition 1, Lemma 2 ~ 5 • Theorem 2 • Convergence Algorithm and Simulation • Conclusions A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

20. Theorem 1 • The existence of Nash Equilibrium [5]: [5] M. Felegyhazi, M. Cagalj, S. S. Bidokhti, and J. P. Hubaux. Non-cooperative Multi-radio Channel Allocation in Wireless Networks. In Proceedings of the IEEE Conference on Computer Communications (INFOCOM '07), March 13-17 2007. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

21. Proposition 1 • We divide the MMCPNE states into two sets according to theorem 1. We denote the MMCPNE states which satisfy the theorem 1 by MMCPNE-1 and denote the remainder MMCPNE states by MMCPNE-2. We find that the multi-hop links in MMCPNE-1 states always occupy more bandwidth compared with those in MMCPNE-2 states. • The basic criterion of finding MMCPNE • The value of Proposition 1 is that it provides a method to choose the MMCPNE with the high bandwidth occupied, i.e., MMCPNE-1. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

22. Lemma 2&3 • Moving from NE to MMCPNE: link members relocate their radios to improve the payoff of others when two members share any channels. An example of a NE channel allocation corresponding to Lemma 2. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

23. Lemma 4&5 • Moving from NE to MMCPNE: link members helping each other is that they mutually exchange some radios with each other. An example of a NE channel allocation corresponding to Lemma 4. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

24. Theorem 2 • The necessary conditions that enables a NE to be MMCPNE: A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

25. Conjecture 1 • The sufficient conditions that enables a NE to be MMCPNE: The unknown region converges to NULL set according to Conjecture 1. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

26. Outline • Introduction • System Model and Game Formulation • Existence of MMCPNE • Convergence Algorithm and Simulation • Convergence algorithm • Simulation Results • Conclusions A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

27. Convergence Algorithm -- I • MMCP Algorithm (1) In the first stage, the coalitions move their radios to achieve high utility. Thus we call this stage as inter-link competition stage. (2) In the second state, players in the same link mutually adjust their radios to achieve higher date rate. We call this stage as intra-link improvement stage. link to the code A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

28. Convergence Algorithm -- II • DCP Algorithm By transforming the mutual operation of multiple players into multiple independent operations of the players, DCP algorithm efficiently reduces the computational complexity, specifically, from exponentially increasing with the number of players to linear increasing with it. link to the code A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

29. Simulation Results -- I • Performance criterion: A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

30. Simulation Results -- II • Average Coalition Utility vs. Time • Channel Number: 8 User number: 5 Link number: 4 Radio number: 4 Coalition: {u1,u2} A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

31. Simulation Results – III • Average Coalition Efficiency vs. Time Channel Number: 8 User number: 5 Link number: 4 Radio number: 4 Coalition: {u1,u2} A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

32. Simulation Results – IV • Average Coalition Usage Factor vs. Time Channel Number: 8 User number: 5 Link number: 4 Radio number: 4 Coalition: {u1,u2} A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

33. Simulation Results – V • Average Coalition Usage Factor vs. Users Number Channel Number: 8 Radio number: 4 Coalition: {u1,u2} A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

34. Outline • Introduction • System Model and Game Theory • Existence of MMCPNE • Convergence Algorithm and Simulation • Conclusions • Conclusions A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

35. Conclusions • In this paper, we have studied the problem of competitive channel allocation among devices which use multiple radios in the multi-hop system. • We propose a novel coalition-proof Nash equilibrium, denoted by MMCPNE, to ensure the multi-hop links to achieve high date rate without worsening the date rates of single-hop links. • We investigate the existence of MMCPNE and propose the necessary conditions for the existence of MMCPNE. • Finally, we provide several algorithms to achieve the exact and approximate MMCPNE states. We study their convergence properties theoretically. Simulation results show that MMCPNE outperforms CPNE and NE schemes in terms of achieved data rates of links due to cooperation gain. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

36. Thank you !

37. Reference • [1] J. van den Heuvel, R. A. Leese, and M. A. Shepherd. Graph labeling and radio channel assignment. Journal of Graph Theory, 29:263-283, 1998. • [2] I. Katzela and M. Naghshineh. Channel assignment schemes for cellular mobile telecommunication systems: a comprehensive survey. IEEE Personal Communications, 3(3):10-31, Jun 1996. • [3] Hac A and Z. Chen. Hybrid channel allocation in wireless networks. In Proceedings of the IEEE Conference on Vehicular Technology Conference (VTC'99), 50(4):2329-2333, Sept. 1999. • [4] A. Mishra, S. Banerjee, and W. Arbaugh. Weighted coloring based channel assignment for WLANs. Mobile Computing and Communications Review (MC2R), 9(3), 2005. • [5] M. Felegyhazi, M. Cagalj, S. S. Bidokhti, and J. P. Hubaux. Non-cooperative Multi-radio Channel Allocation in Wireless Networks. In Proceedings of the IEEE Conference on Computer Communications (INFOCOM '07), March 13-17 2007. A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

38. MMCP-Algorithm back A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks

39. DCP-Algorithm back A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks