Transcript iwct.sjtu.edu.cn

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
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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
TotalCosts=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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