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

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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


Network ModelNetwork Model Network ArchitectureNetwork Architecture Flow & Interference ModelFlow & Interference Model Cost ModelCost Model





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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



Complete-Information ScenarioComplete-Information Scenario Game FormulationGame Formulation Potential GamePotential Game Nash EquilibriumNash Equilibrium




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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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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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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




Incomplete-Information Scenario Incomplete-Information Scenario

Game AnalysisGame Analysis


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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





Game AnalysisGame Analysis Price of AnarchyPrice of Anarchy Bayesian Price of AnarchyBayesian Price of Anarchy


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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





Game AnalysisGame Analysis


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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



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!

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

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