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Two-Dimensional Route Switching in Cognitive Radio Networks: A Game-Theoretical Framework. Qingkai Liang, Xinbing Wang, Xiaohua Tian, Fan Wu, Qian Zhang. Outline. Introduction Network Model Complete-Information Scenario Incomplete-Information Scenario Game Analysis Conclusion. 2. - PowerPoint PPT Presentation
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Two-Dimensional Route Switching in Two-Dimensional Route Switching in Cognitive Radio Networks: Cognitive Radio Networks:
A Game-Theoretical FrameworkA Game-Theoretical Framework
Qingkai Liang, Xinbing Wang, Xiaohua Tian, Fan Wu, Qian Zhang
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OutlineOutline
IntroductionIntroduction
Network ModelNetwork Model
Complete-Information ScenarioComplete-Information Scenario
Incomplete-Information ScenarioIncomplete-Information Scenario
Game Analysis Game Analysis
ConclusionConclusion
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BackgroundBackground Spectrum ScarcitySpectrum Scarcity
Growth of WLAN, Mobile Communications, etc.Growth of WLAN, Mobile Communications, etc. Cisco: most mobile data are in unlicensed bands (ISM bands)Cisco: most mobile data are in unlicensed bands (ISM bands) Unlicensed bandsUnlicensed bands are heavily-utilized are heavily-utilized Licensed bandsLicensed bands are under-utilized are under-utilized
I. F. Akyildiz, W.Lee, M. Vuran, S. Mohanty, "NeXt generation/dynamic spectrum access/cognitive radio wireless networks: A survey", Computer 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.Networks (Elsevier), 2127-2159, 2006.
Spectrum Utilization of Licensed Bands
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Cognitive Radio Networks (CRN)Cognitive Radio Networks (CRN) Cognitive RadioCognitive Radio
A promising solution to spectrum shortageA promising solution to spectrum shortage
Dynamic Spectrum AccessDynamic Spectrum Access
ISM Bands Licensed Bands
Licensed UsersUnlicensed Users
Fixed Channel Access
1 2 3
ISM Bands Licensed Bands
Licensed UsersUnlicensed Users
idle
Dynamic Channel Access
1 2 3
Secondary User (SU)Secondary User (SU) Primary User (PU)Primary User (PU)
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Cognitive Radio Networks (CRN)Cognitive Radio Networks (CRN) Spectrum MobilitySpectrum Mobility
High-priority PUs can High-priority PUs can reclaimreclaim their licensed channels at any time. their licensed channels at any time. SUs must cease their transmission on the licensed channels.SUs must cease their transmission on the licensed channels. Spectrum availability is Spectrum availability is dynamicdynamic (or (or mobilemobile) to secondary users.) to secondary users.
PUSU
1 2 3
idle
Time 2
PUSU
1 2 3
Time 1idle
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Route SwitchingRoute Switching
Spectrum MobilitySpectrum Mobility Route BreakRoute Break Route SwitchingRoute Switching
Source
Destination
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 CostsChannel Switching Costs
Routing CostsRouting Costs
Potential Location for Building BridgesPotential Location for Building Bridges
(correspond to a physical data link)(correspond to a physical data link)
BridgeBridge
(Correspond to a Licensed Channel)(Correspond to a Licensed Channel)
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Route SwitchingRoute Switching
In order to balance routing and switching costs, joint switching in both Spatial
and Frequency domains is necessary!
Two-Dimensional Route Switching
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Route SwitchingRoute Switching Two-Dimensional Route SwitchingTwo-Dimensional Route Switching
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Overview of ResultsOverview of Results
Compl
eteComplete
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
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OutlineOutline
IntroductionIntroduction
Network ModelNetwork Model Network ArchitectureNetwork Architecture Flow & Interference ModelFlow & Interference Model Cost ModelCost Model
Complete-Information ScenarioComplete-Information Scenario
Incomplete-Information ScenarioIncomplete-Information Scenario
Game Analysis Game Analysis
ConclusionConclusion
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Network ArchitectureNetwork Architecture
Two-Tier NetworkTwo-Tier Network Primary NetworkPrimary Network
C C licensed channels (orthogonal)licensed channels (orthogonal)
Secondary Network Secondary Network RepresentedRepresented by graph by graph G=(V,E)G=(V,E)Channel assignment Channel assignment historyhistory (matrix (matrix A)A)Currently Currently unavailableunavailable channels: set channels: set
, 1e jA
If channel If channel jj waswas assigned to link assigned to link ee
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Flow & Interference ModelFlow & Interference Model Flow ModelFlow Model
MM concurrentconcurrent and and constantconstant data flows data flows Routing Source and Destination: Routing Source and Destination: Flow parameters: rate and packet sizeFlow parameters: rate and packet size
Interference ModelInterference Model Transmission succeeds if the Transmission succeeds if the interference neighborhoodinterference neighborhood is silent. is silent. Resemble CSMA/CA in IEEE 802.11Resemble CSMA/CA in IEEE 802.11
kr( , )k kS D
k
The interference neighborhood of link The interference neighborhood of link ee:: ( )I elink e
Interference neighborhood I(e)
Interference link
ContentionContention for transmission opportunities! for transmission opportunities!
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Cost ModelCost Model Routing CostRouting Cost
Delay CostDelay CostProportional to end-to-end delayProportional to end-to-end delayCharacterize congestion levelCharacterize congestion levelDepend on Depend on other flows’ strategiesother flows’ strategies
Energy Cost Energy Cost Reflect the energy consumption for data transmissionReflect the energy consumption for data transmissionArbitrary form: related to Data Rate, AWGN, Path Loss, etc.Arbitrary form: related to Data Rate, AWGN, Path Loss, etc.
Switching CostSwitching CostIncurred during the channel switching processIncurred during the channel switching processReflect the extra wear and tear, switching delay, etc.Reflect the extra wear and tear, switching delay, etc.
Flows’ strategies are Flows’ strategies are mutually influencedmutually influenced
Game TheoryGame Theory
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Cost ModelCost Model Routing CostRouting Cost
Delay CostDelay CostExpected waiting time:Expected waiting time:
Reflect congestion levelReflect congestion levelDepend on other Depend on other flows’ strategiesflows’ strategiesTotal Delay Costs:Total Delay Costs:
Energy Cost Energy Cost RepresentedRepresented bybyArbitrary 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 CostSwitching Cost One switching costsOne switching costs
Total Energy CostsTotal Energy Costs: :
Total Costs=Delay Costs+Energy Costs+Switching Costs
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OutlineOutline
IntroductionIntroduction
Network ModelNetwork Model
Complete-Information ScenarioComplete-Information Scenario Game FormulationGame Formulation Potential GamePotential Game Nash EquilibriumNash Equilibrium
Incomplete-Information ScenarioIncomplete-Information Scenario
Game Analysis Game Analysis
ConclusionConclusion
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Game FormulationGame Formulation
Why is this problem a game?Why is this problem a game? Each flow’s costs Each flow’s costs depends ondepends on other flows’ strategies other flows’ strategies Each flow aims at Each flow aims at minimizingminimizing its own costs its own costs
Flows’ strategies are Flows’ strategies are mutually influencedmutually influenced!!
Route-Switching Game!Route-Switching Game!
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Game FormulationGame Formulation Complete Information: flows’ Complete Information: flows’ parametersparameters are publicly-known are publicly-known
Game FormulationGame Formulation Player: flow initiator (flow)Player: flow initiator (flow)
Strategy Space:Strategy Space:
Strategy: selection of Strategy: selection of newnew spatial routes and channels spatial routes and channels
Cost Function:Cost Function:
Data rate & Packet SizeData rate & Packet Size
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Potential GamePotential Game
Property 1: Each potential game has at least one pure Property 1: Each potential game has at least one pure Nash Equilibrium (NE)Nash Equilibrium (NE) Remark: Remark: Any minimum of the potential function is an NE!Any minimum of the potential function is an NE!
Property 2: Each potential game has the Property 2: Each potential game has the Finite Improvement Property (FIP)Finite Improvement Property (FIP)
Remark: Any minimum can be reached within finite improvement steps!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.
Costs of any flow Potential Function
Challenge:Challenge: constructing a potential function is difficult! constructing a potential function is difficult!
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Existence of the Nash EquilibriumExistence of the Nash Equilibrium
Theorem 1: Under complete information, Route-Switching Game has the Theorem 1: Under complete information, Route-Switching Game has the
potential function:potential function:
Theorem 2: Under complete information, there existsTheorem 2: Under complete information, there exists a Nash Equilibrium a Nash Equilibrium
(NE) in the proposed game and this NE minimizes the above potential (NE) in the proposed game and this NE minimizes the above potential
function.function.
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Algorithm to find the NEAlgorithm to find the NE
Following Following Finite Improvement PropertyFinite Improvement Property.. Based on Based on Dijsktra AlgorithmDijsktra Algorithm Correctness and time complexityCorrectness 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).
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Algorithm to find the NEAlgorithm to find the NE
Convergence of Algorithm 1Convergence of Algorithm 1
Convergence is fast (less than 20 iterations for 20 flows) !
Converge to a small but
non-zero value
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Problem with Algorithm 1Problem with Algorithm 1 Theoretically, it doesn’t converge in polynomial timeTheoretically, it doesn’t converge in polynomial time
SolutionSolution FastFast Algorithm to find Algorithm to find Approximate NEApproximate NE ( -NE) ( -NE) Existence of -NE (Theorem 4)Existence of -NE (Theorem 4)
Algorithm for finding -NE (omitted)Algorithm for finding -NE (omitted) Correctness and Time-Complexity (Theorem 5)Correctness and Time-Complexity (Theorem 5)
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Approximate NEApproximate NE
Efficiency of -NE Efficiency of -NE
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Approximate NEApproximate NE
Accuracy of -NE Accuracy of -NE
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TradeoffTradeoff
Tradeoffs between routing and switching costsTradeoffs 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.
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OutlineOutline
IntroductionIntroduction
Network ModelNetwork Model
Complete-Information ScenarioComplete-Information Scenario
Incomplete-Information Scenario Incomplete-Information Scenario
Game AnalysisGame Analysis
ConclusionConclusion
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Incomplete InformationIncomplete Information Complete-Information GamesComplete-Information Games
Parameters of flows are publicly known Parameters of flows are publicly known In practice, such information is very hard to obtain!In practice, such information is very hard to obtain!
Incomplete-information GamesIncomplete-information Games Parameters of flows are private knowledgeParameters of flows are private knowledge Each flow only knows the Each flow only knows the type distribution type distribution (stochastic model)(stochastic model) Bayesian Nash Equilibrium (BNE) is consideredBayesian Nash Equilibrium (BNE) is considered
Instead, obtaining Instead, obtaining statisticsstatistics of flows is much easier! of flows is much easier!
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Incomplete InformationIncomplete Information
Main ResultsMain Results Existence of BNE Existence of BNE A simple method for computing the BNE (Algorithm 2)A simple method for computing the BNE (Algorithm 2) Correctness of Algorithm 2Correctness of Algorithm 2
Theorem 6: Algorithm 2 can compute a pure BNE of the Route-Switching Game Theorem 6: Algorithm 2 can compute a pure BNE of the Route-Switching Game
with incomplete information. with incomplete information.
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Incomplete InformationIncomplete Information
Incomplete Information vs. Complete InformationIncomplete 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
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OutlineOutline
IntroductionIntroduction
Network ModelNetwork Model
Complete-Information ScenarioComplete-Information Scenario
Incomplete-Information ScenarioIncomplete-Information Scenario
Game AnalysisGame Analysis Price of AnarchyPrice of Anarchy Bayesian Price of AnarchyBayesian Price of Anarchy
ConclusionConclusion
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Price of Anarchy (PoA)Price of Anarchy (PoA) Complete-Information ScenarioComplete-Information Scenario Measure the Measure the Social CostsSocial Costs yielded by the NE 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
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Bayesian Price of Anarchy (BPoA)Bayesian Price of Anarchy (BPoA) Incomplete-information ScenarioIncomplete-information Scenario Measure the Measure the Expected Social CostsExpected Social Costs yielded by the NE yielded by the NE
Theorem 8: Theorem 8: The Bayesian Price of Anarchy is upper-bounded by
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Price of AnarchyPrice of Anarchy
Simulation Results for Price of AnarchySimulation Results for Price of Anarchy
In the simulation, PoA is not significant!
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OutlineOutline
IntroductionIntroduction
Network ModelNetwork Model
Complete-Information ScenarioComplete-Information Scenario
Incomplete-Information ScenarioIncomplete-Information Scenario
Game AnalysisGame Analysis
ConclusionConclusion
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ConclusionConclusion
Two-DimensionalTwo-Dimensional Route Route
Switching in the CRNSwitching in the CRN
Game-Theoretical ModelGame-Theoretical Model
Complete InformationComplete Information Incomplete InformationIncomplete Information
Potential FunctionPotential Function
Existence of the NEExistence of the NE
Algorithm to find the NEAlgorithm to find the NE
Approximate NEApproximate NE
Price of AnarchyPrice of Anarchy
Existence of the BNEExistence of the BNE
Algorithm to find the BNEAlgorithm to find the BNE
Bayesian Price of AnarchyBayesian Price of Anarchy
Efficiency Improvement: Virtual Charging SchemeEfficiency Improvement: Virtual Charging Scheme
Extensive SimulationsExtensive Simulations
[1] K. Jagannathan, I. Menashe, G. Zussman, E. Modiano, “Non-cooperative Spectrum Access - The Dedicated vs. Free Spectrum [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. Choice,” IEEE Journal on Selected Areas in Communications (JSAC), 2012.
[3] R. Southwell, J. Huang and X. Liu, "Spectrum Mobility Games," IEEE INFOCOM, 2012. [3] R. Southwell, J. Huang and X. Liu, "Spectrum Mobility Games," IEEE INFOCOM, 2012.
[2] Gaurav Kasbekar and Saswati Sarkar, "Spectrum Auction Framework for Access Allocation in Cognitive Radio Networks" [2] Gaurav Kasbekar and Saswati Sarkar, "Spectrum Auction Framework for Access Allocation in Cognitive Radio Networks"
IEEE/ACM Transactions on Networking, 2010. IEEE/ACM Transactions on Networking, 2010.
Frequency DomainFrequency Domain
[4] M. Caleffi, I. F. Akyildiz and L. Paura, “OPERA: Optimal Routing Metric for Cognitive Radio Ad Hoc Networks,” in IEEE Transactions [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. on Wireless Communications, 2012. [5] I. Pefkianakis, S. Wong and S. Lu, "SAMER: Spectrum Aware Mesh Routing in Cognitive Radio Networks," in IEEE DySPAN, 2008. [5] I. Pefkianakis, S. Wong and S. Lu, "SAMER: Spectrum Aware Mesh Routing in Cognitive Radio Networks," in IEEE DySPAN, 2008.
Spatial DomainSpatial Domain
Our WorkOur WorkGeneralizationGeneralization
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Thank you!Thank you!