Transcript Presentation Slide

Performance Analysis of
Reputation-based Mechanisms
for Multi-hop Wireless Networks
Fabio Milan
Dipartimento di Elettronica
Politecnico di Torino
Turin, Italy
Email: [email protected]
Juan José Jaramillo and R. Srikant
Coordinated Science Laboratory
Dept. of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
Email: {jjjarami, rsrikant}@uiuc.edu
Outline
•
•
•
•
Problem Formulation
Cooperation without Collisions
Cooperation with Collisions
Performance Analysis
March 22, 2006
CISS 2006, Princeton, NJ, USA
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Packet Forwarding
+α
–β
A
B
C
• When B forwards a packet for A, node A gains α units and node B loses β
units due to energy expenditure
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CISS 2006, Princeton, NJ, USA
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Utility
•
•
•
•
α is the packet value
β is the transmission cost
pi is the dropping probability of node i
p-i is the dropping probability of the neighbor of node i
ui = βpi – αp-i
• βpi is the gain of dropping packets from the neighbor
• αp-i is the loss for packets being dropped by the neighbor
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CISS 2006, Princeton, NJ, USA
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Utility
• Payoff of mutual cooperation
• Payoff of mutual defection
0
β–α

1

• Packet value is greater than transmission cost
• Mutual cooperation is preferable to mutual defection
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CISS 2006, Princeton, NJ, USA
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It’s a Prisoner’s Dilemma
• Each node drops all packets to maximize its utility
• The Nash Equilibrium is
pi* = p-i* = 1
• Individual selfishness leads to zero throughput
• In multi-hop wireless networks, packet relaying requires cooperation
• Need for mechanisms to sustain cooperation among selfish nodes
March 22, 2006
CISS 2006, Princeton, NJ, USA
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Incentives for Cooperation
• Micro-payments
• Reputation-based Mechanisms
– End-to-end
– Hop-by-hop
• With Information Exchange
• Without Information Exchange
– Advantages
» No Control Overhead
» Collusion Resistance
» Full Decentralization
– Disadvantages
» Performance Degradation due to Packet Collisions
March 22, 2006
CISS 2006, Princeton, NJ, USA
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Outline
•
•
•
•
Problem Formulation
Cooperation without Collisions
Cooperation with Collisions
Performance Analysis
March 22, 2006
CISS 2006, Princeton, NJ, USA
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Reputation-based Mechanism
• Nodes take into account the effect of their actions on their future payoff
• The weight of the k-th future payoff is δk
• δ is the discount parameter
0≤δ≤1
• Nodes play a Repeated Game
• δ is the probability to continue to play after each stage
March 22, 2006
CISS 2006, Princeton, NJ, USA
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Tit-for-tat
• Cooperate on the first move, then do what the opponent did in the previous
move
pi(0) = 0
pi(k) = p-i(k-1)
k>0
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CISS 2006, Princeton, NJ, USA
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One-step Deviation
• If both nodes cooperate, their payoff is 0.
• Assume that node i deviates, by setting a dropping probability p>0
– Node i initially benefits from this deviation
– As the neighbor reacts, node i suffers packet losses
– Node i reacts to the punishment by punishing its neighbor
– …
• The discounted payoff of i in case of deviation is a function of α, β, δ and p
• If it is not greater than 0, then being the first to defect is not rational
March 22, 2006
CISS 2006, Princeton, NJ, USA
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Equilibrium
• Deviation from Tit-for-tat is not profitable if
1  


• If δ is sufficiently large, the outcome is mutual cooperation
• If transmission cost is close to packet value, then cooperation emerges only
if the users are farsighted or stay in the system for a very long time
March 22, 2006
CISS 2006, Princeton, NJ, USA
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Outline
•
•
•
•
Problem Formulation
Cooperation without Collisions
Cooperation with Collisions
Performance Analysis
March 22, 2006
CISS 2006, Princeton, NJ, USA
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The Hidden Terminal is Back
A
B
–α
–β
C
D
E
• When D forwards a packet from C to E, interference may prevent C to hear
this transmission
• C does not know if D is cooperating or not
March 22, 2006
CISS 2006, Princeton, NJ, USA
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Perceived Defection
• Packet collisions with “hidden terminals” result in a distorted reputation
p i( k )    (1   ) pi( k )
• Estimate of neighbor’s dropping probability: either cannot “hear”
neighbors transmission due to another neighbor’s transmission () or
can hear and neighbor drops a relay packet
March 22, 2006
CISS 2006, Princeton, NJ, USA
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Queueing Model
• The network load λ is independent of the dropping probabilities if
Generated Traffic
∞
λ
Transit Traffic
Dropped Traffic
• Infinite Backlog, no end-to-end Congestion Control
• A node always transmits, within the MAC constraints: either it transmits its
own packet or a relay packet
March 22, 2006
CISS 2006, Princeton, NJ, USA
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Tit-for-tat
• Cooperate on the first move, then do what you believe the opponent did in
the previous move
pi(0) = 0
pi( k )  p ( ki 1)
k0
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CISS 2006, Princeton, NJ, USA
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Retaliation
• Due to collisions, simple Tit-for-tat is not sufficient to sustain cooperation
1
Tit-for-tat
Perceived Defection
~
p
λ
0
p
1
• Even if nodes initially cooperate, unjust punishment of perceived defection
progressively leads to zero throughput
March 22, 2006
CISS 2006, Princeton, NJ, USA
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Generous Tit-for-tat
• Add a tolerance threshold to mitigate throughput loss
• The optimal tolerance to avoid both retaliation and exploitation is λ
1
Generous Tit-for-tat
Perceived Defection
~
p
λ
0
March 22, 2006
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CISS 2006, Princeton, NJ, USA
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Generous Tit-for-tat
• Cooperate on the first move, then cooperate more than what you believe the
opponent did in the previous move
pi(0) = 0
pi( k )  max{ p ( ki 1)   ,0}
k0
March 22, 2006
CISS 2006, Princeton, NJ, USA
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Equilibrium
• Deviation from Generous Tit-for-tat is not profitable if
 1
1  
 (1   ) 2
• If δ is sufficiently large, the outcome is mutual cooperation
• Need an even larger δ now due to imperfect knowledge of neighbor’s actions
March 22, 2006
CISS 2006, Princeton, NJ, USA
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Outline
•
•
•
•
Problem Formulation
Cooperation without Collisions
Cooperation with Collisions
Performance Analysis
March 22, 2006
CISS 2006, Princeton, NJ, USA
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Game Parameters
• λ is a measure of the network load, if every node transmits at the same rate
• δ is a measure of the session length
– If a session involves a great number of packets, it is reasonable to assume δ → 1
• α is a measure of the information contained in a packet, with respect to the
overall information flow transferred from source to destination
– For a multimedia stream source, tolerant to packet losses, the packet value is
small. For a file transfer source, the packet value is high.
• β is a measure of the energy spent to transmit a packet, with respect to the
total energy available to the node
– For a terminal connected to the AC power, the transmission cost is low. For a
terminal running out of battery, the transmission cost is high.
March 22, 2006
CISS 2006, Princeton, NJ, USA
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Throughput Upper Bound
1


  1

Throughput
Cooperative Nodes
Selfish Nodes
0
Offered Load
• Beyond this critical threshold, nodes perceive no incentive to cooperate
March 22, 2006
CISS 2006, Princeton, NJ, USA
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Packet Value Lower Bound

  1



1

 (1   ) 2
• The capacity of a wireless network is limited (Gupta – Kumar, 2000)
1/3
1/3

1
3

1/3
 9

 4
• If α is sufficiently large, there exists a value of δ that achieves cooperation for
every feasible load
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CISS 2006, Princeton, NJ, USA
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Conclusion
• Developed a game-theoretic framework to evaluate the performance of hopby-hop reputation-based mechanisms for multi-hop wireless network, in
presence of packet collisions with “hidden terminals”
• Explored the conditions for the emergence of cooperation in a network of
selfish users, in terms of network load, session length, application type and
energy constraints
• Ongoing work: How does the network topology affects the conditions for
the emergence of cooperation?
• Ongoing work: Simulation experiments to study how the externalities
introduced by an end-to-end congestion control affect the stability of the
mechanism
• As for now, our model suggests that if nodes use Skype™ while running out
of battery, then they are unlikely to cooperate…
March 22, 2006
CISS 2006, Princeton, NJ, USA
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Thank You!
March 22, 2006
CISS 2006, Princeton, NJ, USA
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