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

22 Outline Introduction Network Model Complete-Information Scenario Incomplete-Information Scenario Game Analysis Conclusion

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), , 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 Route Switching  Spectrum Mobility Route Break Route Switching Build a new bridge at the same location? (switch to a new channel) ? Re-select a new spatial route (switch to a new spatial route) ? Channel Switching Costs Routing Costs Potential Location for Building Bridges Potential Location for Building Bridges (correspond to a physical data link) Bridge Bridge (Correspond to a Licensed 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 Overview of Results Comp lete Complete Information Incomplete Information Existence of the potential function Existence of the Nash Equilibrium (NE) An algorithm for finding the NE A low-complexity algorithm for finding the approximate NE Existence of Bayesian Nash Equilibria (BNE) A simple algorithm for finding the BNE Game Analysis Be upper-bounded Be deterministically bounded Improvement Price of Anarchy Bayesian Price of Anarchy Game Model Route Switching in CRN

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

11 Network Architecture  Two-Tier Network  Primary Network C licensed channels (orthogonal) C licensed channels (orthogonal)  Secondary Network Represented by graph G=(V,E) Represented by graph G=(V,E) Channel assignment history (matrix A) Channel assignment history (matrix A) Currently unavailable channels: set Currently unavailable channels: set If channel j was assigned to link e

12 Flow & Interference Model  Flow Model  M concurrent 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 The interference neighborhood of link e: Contention for transmission opportunities!

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

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

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

16 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 Flows’ strategies are mutually influenced! Route-Switching Game!

17 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: Data rate & Packet Size

18 Potential Game  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! Definition 1: Definition 1: A game is referred as the potential game if and only if there exists a potential function. Challenge: constructing a potential function is difficult!

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

20 Algorithm to find the NE  Following Finite Improvement Property.  Based on Dijsktra Algorithm  Correctness and time complexity Theorem 3: 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 ).

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

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

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

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

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

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

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

35 Conclusion Two-Dimensional Route Switching in the CRN Game-Theoretical Model Complete Information Incomplete Information Potential Function Existence of the NE Algorithm to find the NE Approximate NE Price of Anarchy Existence of the BNE Algorithm to find the BNE Bayesian Price of Anarchy Efficiency Improvement: Virtual Charging Scheme Extensive Simulations [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), [3] R. Southwell, J. Huang and X. Liu, "Spectrum Mobility Games," IEEE INFOCOM, [2] Gaurav Kasbekar and Saswati Sarkar, "Spectrum Auction Framework for Access Allocation in Cognitive Radio Networks" IEEE/ACM Transactions on Networking, Frequency Domain [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, [5] I. Pefkianakis, S. Wong and S. Lu, "SAMER: Spectrum Aware Mesh Routing in Cognitive Radio Networks," in IEEE DySPAN, Spatial Domain Our Work Generalization

36 Thank you!