Two-Dimensional Route Switching in Cognitive Radio Networks: A Game-Theoretical Framework

1. Two-Dimensional Route Switching in Cognitive Radio Networks: A Game-Theoretical Framework Qingkai Liang, Xinbing Wang, Xiaohua Tian, Fan Wu, Qian Zhang

2. Outline Introduction Network Model Complete-Information Scenario Incomplete-Information Scenario Game Analysis Conclusion 2

3. Background • Spectrum Scarcity • Growth of WLAN, Mobile Communications, etc. • Cisco: most mobile data are in unlicensed bands (ISM bands) • Unlicensed bands are heavily-utilized • Licensed bands are under-utilized I. F. Akyildiz, W.Lee, M. Vuran, S. Mohanty, "NeXt generation/dynamic spectrum access/cognitive radio wireless networks: A survey", Computer Networks (Elsevier), 2127-2159, 2006.

4. Cognitive Radio Networks (CRN) • Cognitive Radio • A promising solution to spectrum shortage • Dynamic Spectrum Access Secondary User (SU) Primary User (PU)

5. Cognitive Radio Networks (CRN) • Spectrum Mobility • High-priority PUs can reclaim their licensed channels at any time. • SUs must cease their transmission on the licensed channels. • Spectrum availability is dynamic (or mobile) to secondary users.

6. Potential Location for Building Bridges (correspond to a physical data link) Route Switching • Spectrum MobilityRoute BreakRoute Switching Bridge (Correspond to a Licensed Channel) Routing Costs Re-select a new spatial route (switch to a new spatial route) ? Channel Switching Costs Build a new bridge at the same location? (switch to a new channel) ?

7. Route Switching In order to balance routing and switching costs, joint switching in both Spatial and Frequency domains is necessary! Two-Dimensional Route Switching

8. Route Switching • Two-Dimensional Route Switching

9. Existence of the potential function Existence of the Nash Equilibrium (NE) Complete Information An algorithm for finding the NE A low-complexity algorithm for finding the approximate NE Game Model Game Analysis Improvement Existence of Bayesian Nash Equilibria (BNE) Incomplete Information A simple algorithm for finding the BNE Price of Anarchy Be upper-bounded Be deterministically bounded Bayesian Price of Anarchy Overview of Results Route Switching in CRN Complete

10. Outline Introduction Network Model Network Architecture Flow & Interference Model Cost Model Complete-Information Scenario Incomplete-Information Scenario Game Analysis Conclusion 10

11. If channel jwas assigned to link e Network Architecture • Two-Tier Network • Primary Network • C licensed channels (orthogonal) • Secondary Network • Representedby graph G=(V,E) • Channel assignment history (matrix A) • Currently unavailable channels: set

12. Flow & Interference Model • Flow Model • Mconcurrent and constant data flows • Routing Source and Destination: • Flow parameters: rate and packet size • Interference Model • Transmission succeeds if the interference neighborhood is silent. • Resemble CSMA/CA in IEEE 802.11 The interference neighborhood of link e: Contention for transmission opportunities!

13. Flows’ strategies are mutually influenced Game Theory Cost Model • Routing Cost • Delay Cost • Proportional to end-to-end delay • Characterize congestion level • Depend on other flows’ strategies • Energy Cost • Reflect the energy consumption for data transmission • Arbitrary form: related to Data Rate, AWGN, Path Loss, etc. • Switching Cost • Incurred during the channel switching process • Reflect the extra wear and tear, switching delay, etc.

14. Cost Model TotalCosts=Delay Costs+Energy Costs+Switching Costs • Routing Cost • Delay Cost • Expected waiting time: • Reflect congestion level • Depend on other flows’ strategies • Total Delay Costs: • Energy Cost • Representedby • Arbitrary form: related to Data Rate, AWGN, Path Loss, etc. • Total Energy Costs: • Switching Cost • One switching costs • Total Energy Costs:

15. Outline Introduction Network Model Complete-Information Scenario Game Formulation Potential Game Nash Equilibrium Incomplete-Information Scenario Game Analysis Conclusion 15

16. Flows’ strategies are mutually influenced! Route-Switching Game! Game Formulation • Why is this problem a game? • Each flow’s costs depends on other flows’ strategies • Each flow aims at minimizing its own costs

17. Data rate & Packet Size Game Formulation • Complete Information: flows’ parameters are publicly-known • Game Formulation • Player: flow initiator (flow) • Strategy Space: • Strategy: selection of new spatial routes and channels • Cost Function:

18. Potential Game Definition 1: A game is referred as the potential game if and only if there exists a potential function. • Property 1: Each potential game has at least one pure Nash Equilibrium (NE) • Remark: Any minimum of the potential function is an NE! • Property 2: Each potential game has the Finite Improvement Property (FIP) • Remark: Any minimum can be reached within finite improvement steps! Challenge: constructing a potential function is difficult!

19. Theorem 1: Under complete information, Route-Switching Game has the potential function: Theorem 2: Under complete information, there existsa Nash Equilibrium (NE) in the proposed game and this NE minimizes the above potential function. Existence of the Nash Equilibrium

20. Theorem 3: Each improvement step in Algorithm 1 can reduce the potential function to the maximal extent and guarantee the route connectivity in polynomial time O(|E|M+|V|2). Algorithm to find the NE • Following Finite Improvement Property. • Based on Dijsktra Algorithm • Correctness and time complexity

21. Algorithm to find the NE • Convergence of Algorithm 1 Converge to a small but non-zero value Convergence is fast (less than 20 iterations for 20 flows)！

22. Problem with Algorithm 1 • Theoretically, it doesn’t converge in polynomial time • Solution • Fast Algorithm to find Approximate NE ( -NE) • Existence of -NE (Theorem 4) • Algorithm for finding -NE (omitted) • Correctness and Time-Complexity (Theorem 5)

23. Approximate NE • Efficiency of -NE

24. Approximate NE • Accuracy of -NE

25. Tradeoff • Tradeoffs between routing and switching costs One type of costs can be reduced by raising the other type of costs. Routing and switching costs cannot be simultaneously minimized.

26. Outline Introduction Network Model Complete-Information Scenario Incomplete-Information Scenario Game Analysis Conclusion 26

27. Incomplete Information • Complete-Information Games • Parameters of flows are publicly known • In practice, such information is very hard to obtain! • Incomplete-information Games • Parameters of flows are private knowledge • Each flow only knows the type distribution (stochastic model) • Bayesian Nash Equilibrium (BNE) is considered • Instead, obtaining statistics of flows is much easier!

28. Theorem 6: Algorithm 2 can compute a pure BNE of the Route-Switching Game with incomplete information. Incomplete Information • Main Results • Existence of BNE • A simple method for computing the BNE (Algorithm 2) • Correctness of Algorithm 2

29. Incomplete Information • Incomplete Information vs. Complete Information The game yields less social costs under complete information than under incomplete information but their gap becomes smaller with the increasing number of flows

30. Outline Introduction Network Model Complete-Information Scenario Incomplete-Information Scenario Game Analysis Price of Anarchy Bayesian Price of Anarchy Conclusion 30

31. Definition 2: Social costs are the sum of all players’ costs, i.e., Definition 3: The Price of Anarchy is the ratio of social costs between the NE and the optimalityin centralized schemes, i.e.,. Theorem 7: The price of anarchy is upper-bounded by Price of Anarchy (PoA) • Complete-Information Scenario • Measure the Social Costs yielded by the NE

32. Theorem 8: The Bayesian Price of Anarchy is upper-bounded by Bayesian Price of Anarchy (BPoA) • Incomplete-information Scenario • Measure the Expected Social Costs yielded by the NE

33. Price of Anarchy • Simulation Results for Price of Anarchy In the simulation, PoA is not significant!

34. Outline Introduction Network Model Complete-Information Scenario Incomplete-Information Scenario Game Analysis Conclusion 34

35. Two-Dimensional Route Switching in the CRN [1] K. Jagannathan, I. Menashe, G. Zussman, E. Modiano, “Non-cooperative Spectrum Access - The Dedicated vs. Free Spectrum Choice,” IEEE Journal on Selected Areas in Communications (JSAC), 2012. Game-Theoretical Model [2] Gaurav Kasbekar and Saswati Sarkar, "Spectrum Auction Framework for Access Allocation in Cognitive Radio Networks" IEEE/ACM Transactions on Networking, 2010. Incomplete Information Complete Information [3] R. Southwell, J. Huang and X. Liu, "Spectrum Mobility Games," IEEE INFOCOM, 2012. Frequency Domain Potential Function Existence of the BNE Generalization Existence of the NE Our Work Algorithm to find the NE Algorithm to find the BNE Spatial Domain Approximate NE [4] M. Caleffi, I. F. Akyildiz and L. Paura, “OPERA: Optimal Routing Metric for Cognitive Radio Ad Hoc Networks,” in IEEE Transactions on Wireless Communications, 2012. Bayesian Price of Anarchy Extensive Simulations Price of Anarchy [5] I. Pefkianakis, S. Wong and S. Lu, "SAMER: Spectrum Aware Mesh Routing in Cognitive Radio Networks," in IEEE DySPAN, 2008. Efficiency Improvement: Virtual Charging Scheme Conclusion

36. Thank you!