performance analysis of reputation-based mechanisms for multi-hop wireless networks
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Performance Analysis of Reputation-based Mechanisms for Multi-hop Wireless Networks
Fabio MilanDipartimento di Elettronica
Politecnico di TorinoTurin, Italy
Email: fabio.milan@polito.it
Juan José Jaramillo and R. SrikantCoordinated Science Laboratory
Dept. of Electrical and Computer EngineeringUniversity of Illinois at Urbana-Champaign
Email: {jjjarami, rsrikant}@uiuc.edu
March 22, 2006 CISS 2006, Princeton, NJ, USA 2
Outline
• Problem Formulation
• Cooperation without Collisions
• Cooperation with Collisions
• Performance Analysis
March 22, 2006 CISS 2006, Princeton, NJ, USA 3
Packet Forwarding
A B C
+α –β
• When B forwards a packet for A, node A gains α units and node B loses β units due to energy expenditure
March 22, 2006 CISS 2006, Princeton, NJ, USA 4
Utility
ui = βpi – αp-i
• 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
• βpi is the gain of dropping packets from the neighbor
• αp-i is the loss for packets being dropped by the neighbor
March 22, 2006 CISS 2006, Princeton, NJ, USA 5
Utility
• Payoff of mutual cooperation 0
• Payoff of mutual defection β – α
• Packet value is greater than transmission cost
• Mutual cooperation is preferable to mutual defection
1
March 22, 2006 CISS 2006, Princeton, NJ, USA 6
It’s a Prisoner’s Dilemma
• Each node drops all packets to maximize its utility
• The Nash Equilibrium is
• Individual selfishness leads to zero throughput
• In multi-hop wireless networks, packet relaying requires cooperation
• Need for mechanisms to sustain cooperation among selfish nodes
pi* = p-i
* = 1
March 22, 2006 CISS 2006, Princeton, NJ, USA 7
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 8
Outline
• Problem Formulation
• Cooperation without Collisions
• Cooperation with Collisions
• Performance Analysis
March 22, 2006 CISS 2006, Princeton, NJ, USA 9
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 10
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
March 22, 2006 CISS 2006, Princeton, NJ, USA 11
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 12
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 13
Outline
• Problem Formulation
• Cooperation without Collisions
• Cooperation with Collisions
• Performance Analysis
March 22, 2006 CISS 2006, Princeton, NJ, USA 14
The Hidden Terminal is Back
B C D E
– α –β
A
• 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 15
Perceived Defection
( )( ) ( )p pik
ik 1
• Packet collisions with “hidden terminals” result in a distorted reputation
• 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 16
Queueing Model
λ
Dropped Traffic
∞Generated Traffic
Transit 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
• The network load λ is independent of the dropping probabilities if
March 22, 2006 CISS 2006, Princeton, NJ, USA 17
Tit-for-tat
p p
ki
kik( ) ( )
1
0
• Cooperate on the first move, then do what you believe the opponent did in the previous move
pi(0) = 0
March 22, 2006 CISS 2006, Princeton, NJ, USA 18
Retaliation
• Due to collisions, simple Tit-for-tat is not sufficient to sustain cooperation
p
~p
0 1
1
λ
Tit-for-tat
Perceived Defection
• Even if nodes initially cooperate, unjust punishment of perceived defection progressively leads to zero throughput
March 22, 2006 CISS 2006, Princeton, NJ, USA 19
Generous Tit-for-tat
p
~p
0 1
1
λ
Generous Tit-for-tat
Perceived Defection
• Add a tolerance threshold to mitigate throughput loss
• The optimal tolerance to avoid both retaliation and exploitation is λ
March 22, 2006 CISS 2006, Princeton, NJ, USA 20
Generous Tit-for-tat
p p
ki
kik( ) ( )m ax{ , }
1 0
0
pi(0) = 0
• Cooperate on the first move, then cooperate more than what you believe the opponent did in the previous move
March 22, 2006 CISS 2006, Princeton, NJ, USA 21
Equilibrium
11
1 2
( )
• Deviation from Generous Tit-for-tat is not profitable if
• 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 22
Outline
• Problem Formulation
• Cooperation without Collisions
• Cooperation with Collisions
• Performance Analysis
March 22, 2006 CISS 2006, Princeton, NJ, USA 23
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 24
Throughput Upper Bound
0
Cooperative Nodes
Selfish Nodes
1 1
Throughput
Offered Load
• Beyond this critical threshold, nodes perceive no incentive to cooperate
March 22, 2006 CISS 2006, Princeton, NJ, USA 25
Packet Value Lower Bound
1
1 2( )
9
4
1
3
1/3 1/3 1/3
• The capacity of a wireless network is limited (Gupta – Kumar, 2000)
• If α is sufficiently large, there exists a value of δ that achieves cooperation for every feasible load
1
March 22, 2006 CISS 2006, Princeton, NJ, USA 26
Conclusion• Developed a game-theoretic framework to evaluate the performance of hop-
by-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…
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