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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
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Outline
Introduction
Network Model
Complete-Information Scenario
Incomplete-Information Scenario
Game Analysis
Conclusion
2
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
Spectrum Utilization of Licensed Bands
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.
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Cognitive Radio Networks (CRN)
Cognitive Radio
A promising solution to spectrum shortage
Dynamic Spectrum Access
Fixed Channel Access
ISM Bands
Dynamic Channel Access
Licensed Bands
ISM Bands
Licensed Bands
idle
1
Unlicensed Users
2
Licensed Users
3
1
Unlicensed Users
Secondary User (SU)
2
3
Licensed Users
Primary User (PU)
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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.
Time 1
Time 2
idle
1
SU
idle
2
PU
3
1
SU
2
3
PU
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Route Switching
Spectrum Mobility
Route Break
Potential Location for Building Bridges
(correspond to a physical data link)
Route Switching
Bridge
(Correspond to a Licensed Channel)
Source
Destination
Re-select a new spatial route (switch to a new spatial route) ?
Build a new bridge at the same location? (switch to a new channel) ?
Routing Costs
Channel Switching Costs
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Route 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 Switching
Two-Dimensional Route Switching
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Overview of Results
Route Switching
in CRN
Existence of the potential function
Comp
Complete
lete
Existence of the Nash Equilibrium (NE)
Information
An algorithm for finding the NE
A low-complexity algorithm for finding the approximate NE
Game Model
Existence of Bayesian Nash Equilibria (BNE)
Incomplete
Information
A simple algorithm for finding the BNE
Price of Anarchy
Be upper-bounded
Bayesian Price of Anarchy
Be deterministically bounded
Game Analysis
Improvement
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Outline
Introduction
Network Model
Network Architecture
Flow & Interference Model
Cost Model
Complete-Information Scenario
Incomplete-Information Scenario
Game Analysis
Conclusion
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Network Architecture
Two-Tier Network
Primary Network
C licensed channels (orthogonal)
Secondary Network
Ae, j 1
If channel j was assigned to link e
Represented by graph G=(V,E)
Channel assignment history (matrix A)
Currently unavailable channels: set
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Flow & Interference Model
Flow Model
M concurrent and constant data flows
Routing Source and Destination: (Sk , Dk )
Flow parameters: rate rk and packet size k
Interference Model
Transmission succeeds if the interference neighborhood is silent.
Resemble CSMA/CA in IEEE 802.11
Interference link
The interference neighborhood of link e: I (e)
Contention for transmission opportunities!
link e
Interference
neighborhood I(e)
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Cost Model
Routing Cost
Delay Cost
Proportional to end-to-end delay
Characterize congestion level
Depend on other flows’ strategies
Flows’ strategies are mutually influenced
Game Theory
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.
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Cost Model
Routing Cost
Delay Cost
Expected waiting time:
Reflect congestion level
Depend on other flows’ strategies
Total Delay Costs:Costs+Energy
TotalCosts=Delay
Energy Cost
Costs+Switching Costs
Represented by
Arbitrary form: related to Data Rate, AWGN, Path Loss, etc.
Total Energy Costs:
Switching Cost
One switching costs
Total Energy Costs:
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Outline
Introduction
Network Model
Complete-Information Scenario
Game Formulation
Potential Game
Nash Equilibrium
Incomplete-Information Scenario
Game Analysis
Conclusion
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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!
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Game Formulation
Complete Information: flows’ parameters are publicly-known
Data rate & Packet Size
Game Formulation
Player: flow initiator (flow)
Strategy Space:
Strategy: selection of new spatial routes and channels
Cost Function:
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Potential Game
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
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!
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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.
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Algorithm to find the NE
Following Finite Improvement Property.
Based on Dijsktra Algorithm
Correctness and time complexity
Theorem 3: Each improvement
step in Algorithm 1 can reduce
the potential function to the
maximal extent and guarantee
the route connectivity in
2
polynomial time O(|E|M+|V| ).
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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)!
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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)
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Approximate NE
Efficiency of
-NE
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Approximate NE
Accuracy of
-NE
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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.
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Outline
Introduction
Network Model
Complete-Information Scenario
Incomplete-Information Scenario
Game Analysis
Conclusion
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Incomplete Information
Complete-Information Games
Parameters of flows are publicly known
In practice, such information is very hard to obtain!
Instead, obtaining statistics of flows is much easier!
Incomplete-information Games
Parameters of flows are private knowledge
Each flow only knows the type distribution (stochastic model)
Bayesian Nash Equilibrium (BNE) is considered
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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 RouteSwitching Game with incomplete information.
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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
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Outline
Introduction
Network Model
Complete-Information Scenario
Incomplete-Information Scenario
Game Analysis
Price of Anarchy
Bayesian Price of Anarchy
Conclusion
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Price of Anarchy (PoA)
Complete-Information Scenario
Measure the Social Costs yielded by the NE
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 optimality in centralized schemes, i.e.,.
Theorem 7: The price of anarchy is upper-bounded by
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Bayesian Price of Anarchy (BPoA)
Incomplete-information Scenario
Measure the Expected Social Costs yielded by the NE
Theorem 8: The Bayesian Price of Anarchy is upper-bounded by
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Price of Anarchy
Simulation Results for Price of Anarchy
In the simulation, PoA is not significant!
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Outline
Introduction
Network Model
Complete-Information Scenario
Incomplete-Information Scenario
Game Analysis
Conclusion
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Conclusion
Two-Dimensional Route
Switching in the CRN
[1] K. Jagannathan, I. Menashe, G. Zussman, E. Modiano, “Non-cooperative Spectrum Access - The Dedicated vs.
Game-Theoretical
Model
Free Spectrum Choice,” IEEE Journal on
Selected Areas in Communications
(JSAC), 2012.
[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
Existence of the NE
Generalization
Algorithm to find the NE
Approximate NE
Our Work
Algorithm to find the BNE
Spatial Domain
[4] M. Caleffi, I. F. Akyildiz and L. Paura, “OPERA: Optimal Routing Metric for Cognitive Radio Ad Hoc Networks,” in
Bayesian Price of Anarchy
Price on
of Wireless
AnarchyCommunications, 2012.
IEEE Transactions
[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
Extensive Simulations
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Thank you!
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