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

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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

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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

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

Secondary User (SU)
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.

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Route Switching

• Spectrum Mobility Route Break
  Route Switching

Routing Costs
Re-select a new spatial route (switch to a new
spatial route) ?
Channel Switching Costs
Build a new bridge at the same location? (switch
to a new channel) ?
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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
Complete
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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
• 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
• Flow parameters rate and packet size
• Interference Model
• Transmission succeeds if the interference
  neighborhood is silent.
• Resemble CSMA/CA in IEEE 802.11

The interference neighborhood of link e
Contention for transmission opportunities!
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Cost Model

• Routing Cost
• Delay Cost
• Proportional to end-to-end delay
• Characterize congestion level
• Depend on other flows strategies
• 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
Total CostsDelay CostsEnergy CostsSwitching
Costs

• Routing Cost
• Delay Cost
• Expected waiting time
• Reflect congestion level
• Depend on other flows strategies
• Total Delay Costs
• Energy Cost
• 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 flows costs depends on other flows
  strategies
• Each flow aims at minimizing its own costs

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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

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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.

• 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
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Algorithm to find the NE

• Following Finite Improvement Property.
• Based on Dijsktra Algorithm
• Correctness and time complexity

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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 doesnt 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!
• 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!
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Incomplete Information

• Main Results
• Existence of BNE
• A simple method for computing the BNE (Algorithm
  2)
• Correctness of Algorithm 2

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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

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Bayesian Price of Anarchy (BPoA)

• Incomplete-information Scenario
• Measure the Expected Social Costs yielded by the
  NE

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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
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Thank you!