Making Cooperation Valuable: a Delay-Centric, Pricing-Based User Cooperation Strategy Chen Chen and Shalinee Kishore Department of Electrical and Computer Engineering Lehigh University, Bethlehem, PA 18015

CISS 2011

C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Outline

1

Introduction

2

Two-User Cooperation Model

3

Distributed Cooperation Strategy

4

Performance Evaluation

5

Conclusions

C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Outline

1

Introduction

2

Two-User Cooperation Model

3

Distributed Cooperation Strategy

4

Performance Evaluation

5

Conclusions

C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Introduction Cooperative Communications Take advantage of the broadcast nature of wireless channel. Relay node as a virtual antenna to improve system performance. User cooperative communications – users act as relays to help each other. User Cooperation Strategy The user who gets relay help has a more reliable communication link — a lower delay. The user who provides relay help sacrifices part of his own transmission time — a higher delay. From a system perspective, the benefit of cooperation is not obvious. Design cooperation strategy – centralized or distributed.

C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Outline

1

Introduction

2

Two-User Cooperation Model

3

Distributed Cooperation Strategy

4

Performance Evaluation

5

Conclusions

C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Two-User Cooperation Model Two-User Communication Model Two users wish to communicate to a common destination node (e.g., a base station), using orthogonal channels.

A

pA D

pB

B

Uplinks AD and BD have packet error rates (PER) pA and pB , respectively. The PER is computed as p = 1 − (1 − e)l , where l is the length of the packet, and e is the physical layer BER. Users A and B can overhear each other’s uplink transmission and these interlinks are assumed error-free. The destination D sends an ACK/NACK, indicating the receiving status. C. Chen, S. Kishore (Lehigh University)

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Two-User Cooperation Model (Cont’d) Four Cooperation Modes: Tx Phase

Tx/Relay Phase

Tx Phase

Tx/Relay Phase

A Tx

B Tx

B Tx

A Tx

T/4

T/4

T/4

T/4

b)

A Tx + B Rx

B Relay

B Tx + A Rx

A Relay

T/4

T/4

T/4

T/4

c)

A Tx + B Rx

B Relay

B Tx

A Tx

T/4

T/4

T/4

T/4

d)

A Tx

B Tx

B Tx + A Rx

A Relay

T/4

T/4

T/4

T/4

a) Both A and B do not cooperate; a)

b) Both A and B cooperate; c) B cooperates but A does not; d) A cooperates but B does not.

Two Types of Phases: Tx/Relay Phase (phase 2,4) — One user relays the other user’s packet or transmits his own packet. Tx Phase (phase 1,3) — Both users only transmit his own packet.

C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Two-User Cooperation Model (Cont’d) Centralized Cooperation Strategy Assume packets arrive at user i according to a Poisson process with rate λi . Model packets transmission at each user as an M/G/1 queue. Compute the distribution of service time Xs , i.e., the time needed to successfully transmit a packet, for user i in each of the four modes. According to Pollaczek-Khinchin Formula for M/G/1 queue, the expected delay of a packet is: Dsi = E(Xs ) +

λi E(Xs2 ) . 2(1 − λi E(Xs ))

Strategy: The control center may choose the cooperation mode that minimizes the maximum expected delay of the two users: min max [DsA , DsB ]. s

C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Outline

1

Introduction

2

Two-User Cooperation Model

3

Distributed Cooperation Strategy

4

Performance Evaluation

5

Conclusions

C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Distributed Cooperation Strategy Centralized Versus Distributed Centralized strategy — Requires a control center, that has global information on packet arrival rate λi and PERs pi,t of each user i. Distributed strategy — Cooperation decisions are made by each individual user based on local information, e.g., its PER pi,t and the length of its packet queue Li,t for user i. ◮ Rational users may act selfishly, i.e., both users would enjoy relay help rather than provide help to each other. ◮ Thus social welfare for the system may not be guaranteed.

Our Methods: We model the distributed scenario as a non-cooperative game to analyze strategies of each user. Based on the result, we propose a pricing-based user cooperation strategy. C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Distributed Cooperation Strategy (Cont’d) Two-Player Non-cooperative Game Two players: user A and user B. Actions: ‘Cooperate’ (C) or ‘Do Not Cooperate’ (DNC). Utility (Payoff) functions: the minus of the expected delay for the user using only local pi,t and Li,t . ◮ For action profile {DNC, DNC}, the utility function for user i ∈ {A, B} is   1 Li,t i UN = − , + 1 − pi,t 1 − p¯i,t The first term — The expected time to successfully transmit the current packet; The second term — The expected time to transmit the packets in the queue with length of Li,t . p¯i,t — the mean PER for user i, by averaging PER of previous periods. C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Distributed Cooperation Strategy (Cont’d) Two-Player Non-cooperative Game (Cont’d) Utility (Payoff) functions: ◮ For action profile {C, C}, the utility function UCi for user i ∈ {A, B} is   2 Li,t i UC = − + . 1 − pi,t pj,t 1 − p¯i,t ◮ For action profiles {C, DNC} and {DNC, C}, the free-riding user (who gets relay help) has utility function UFi as   Li,t 2 i + UF = − 2 − pi,t − pi,t pj,t 1 − p¯i,t ◮ For action profiles {C, DNC} and {DNC, C}, the free-ridden user (who provides help) has utility function URi as   Li,t 2 i + . UR = − 1 − pi,t 1 − p¯i,t C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Distributed Cooperation Strategy (Cont’d) Analysis of Users’ Strategy Table: Strategic form of two-user game XXX X

Player B XXX Cooperate XX Player A XX Cooperate [UCA , UCB ] Do Not Cooperate

Do Not Cooperate

[UFA , URB ]

[URA , UFB ] A, U B ] [UN N

It is easy to see that for any user i, i UFi > UCi , UN > URi ,

indicating action DNC is a dominating action, i.e., the action profile {DNC, DNC} is the only Nash Equilibrium. There is no incentive for users to cooperate.

C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Distributed Cooperation Strategy (Cont’d) System Perspective Consider the social welfare utility, i.e., the sum of utility functions of users A and B: A USmn = Um + UnB ,

where (m, n) ∈ {(C, C), (N, N ), (F, R), (R, F )} corresponding to the four action profiles {C, C}, {DNC, DNC}, {DNC, C}, {C, DNC}. Superiority of {C, C} to {DNC, DNC}

The action profile {C, C} is superior to {DNC, DNC} if A B UCA + UCB > UN + UN

⇒f (pA , pB ) = [6 − (pA + pB )](3 + pA pB ) − 16 < 0. The more negative f (pA , pB ) is, the more {C, C} is superior to {DNC, DNC}. C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Distributed Cooperation Strategy (Cont’d) Superiority of {C, C} to {DNC, DNC} (Cont’d) This condition requires pA + pB be large while pA pB be small, i.e., the value of pA and pB should be distinct; otherwise action profile {C, C} has no advantage.

(a) f(pA,pB)

2

1.5

B

f(p ,p )

1

A

0.5 0

−0.5 −1 1

0.5

pA

0

0

0.2

0.4

0.6

0.8

1

Lemma 1: If two users have the same PER, i.e., pA = pB , the profile {DNC, DNC} is always better than {C, C} in terms of social welfare utility. p

B

Superiority of {DNC, C} ({C, DNC}) to {DNC, DNC} The action profile {DNC, C} (when only B engages in cooperation) is superior to {DNC, DNC} if A B UFA + URB > UN + UN

⇒g(pA , pB ) = p2A (pB + 1) + pA pB (1 − pB ) + 2 − 4pA < 0. C. Chen, S. Kishore (Lehigh University)

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Distributed Cooperation Strategy (Cont’d) Superiority of {DNC, C} ({C, DNC}) to {DNC, DNC} (Cont’d) (b) g(p ,p ) The more negative g(pA , pB ) is, the more {C, C} is superior to {DNC, DNC}. A

B

2

Distinctiveness of pA and pB needed. User A has a bad channel condition and its PER has a minimum value.

g(pA,pB)

1.5 1 0.5 0

1

−0.5 −1 1

pA=0.586, pB=0 0.8

0.6

0.4

p

0.2

0.5

0

0

p

B

A

Lemma 2: The profile {DNC, C} is superior to {DNC, DNC} in terms of social welfare only if user √ A suffers from high packet error rate, specifically, pA > 2 − 2 ≈ 0.586.

If pB > 0, the minimum value of pA such that g(pA , pB ) < 0 will be larger.

C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Distributed Cooperation Strategy (Cont’d) Social Welfare under Different PERs p =0.8

p =0.2

A

A

0

−2 −4

−5

−6

−10

−10 S

U

U

S

−8

−15

−12 −14 −16

−20

−25

−18

{DNC,DNC} {DNC,C} {C,C} 0

0.2

0.4

{DNC,DNC} {DNC,C} {C,C}

−20 0.6

0.8

1

−22

0

p

0.2

0.4

0.6

0.8

1

p

B

B

When pA is 0.8, both {DNC, C} and {C, C} profile outperform the {DNC, DNC} profile when pB is less than 0.6.

The more distinct the two channels are, the better the improvement. When pA is 0.2, if pB is small, the profile {DNC, DNC} is better.

From a system perspective, distinct PER scenarios are preferred when there is cooperation. C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Distributed Cooperation Strategy (Cont’d) Individual Utilities under Different PERs 0

−2

−4

Utility

−6

−8 UA

N

p =0.8

UB

−10

A

N A

UF

UB

−12

R A

B

UC=UC −14

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

p

B

In action profile {DNC, C}, the improvement to A in terms of utility is larger than the cost of cooperation to user B — ‘B’s help’ is valuable cooperation. Action profile {DNC, C} is superior to {C, C} in this scenario. If only valuable cooperation is allowed, due to highly dynamic feature of wireless channel, both users have the opportunity to get this ‘valuable’ help when his own channel condition is bad. C. Chen, S. Kishore (Lehigh University)

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Distributed Cooperation Strategy (Cont’d) Pricing Scheme Encourage this valuable cooperation: The free-riding user pays the free-ridden user some (virtual or otherwise) currency γ to reimburse the cost of cooperative help. Table: Strategic form of two-user game (pricing-based) XX XX X Player B XXX Cooperate Do Not Cooperate XXX Player A Cooperate [UCA , UCB ] [URA + γ, UFB ] A A B B Do Not Cooperate [UF , UR + γ] [UN , UN ]

As long as γ is larger than the degradation to the free-ridden user, i , he has incentive to cooperate. In this case, action i.e., URi + γ > UN profile {DNC, C} or {C, DNC} is Nash Equilibrium. The currency γ: the improvement to the free-rider compared to the i . case when he does not get the help, i.e., γ = UFi − UN

C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Distributed Cooperation Strategy (Cont’d) Four Conditions for This Cooperation Strategy a) Cooperation request condition. User i needs the other user’s cooperation when pi > η, where η is a constraint which should be at least 0.586. Satisfying this condition means user i needs help. b) Budget condition. For a user i who seeks ‘help’, his balance should be enough to reimburse the ‘helper’. Mi > 0, where Mi is the currency balance of user i. Satisfying this condition means user i is capable of getting the help. C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Distributed Cooperation Strategy (Cont’d) Four Conditions for This Cooperation Strategy (Cont’d) c) Delay constraint condition. For user i who receives a cooperation request, he must first check whether relaying the packet (instead of transmitting his own packet) will satisfy his delay constraint. −URi < Dc Dc is the delay constraint. Satisfying this condition means user i is capable of helping the other user. d) Reimbursement condition. User i will be paid γ currency for his cooperation. If the value γ can reimburse his cost, i.e., i γ > UN − URi ,

he will actually cooperate. Satisfying this condition means user i has the incentive to cooperate. C. Chen, S. Kishore (Lehigh University)

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Distributed Cooperation Strategy (Cont’d) Algorithm 1 — Decide Whether to Require Relay Help Algorithm 1 For Tx phase of user i 1: if Cooperation request condition is satisfied then 2: if Budget condition is satisfied then 3: Issue a cooperation request, i.e., set Cop rqst=1. 4: else 5: Cop rqst=0. 6: end if 7: else 8: Cop rqst=0. 9: end if 10: Tx packet (contains pi and Cop rqst). Cop rqst: cooperation request flag. Cop rqst==1 indicates there is a cooperation need. C. Chen, S. Kishore (Lehigh University)

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Distributed Cooperation Strategy (Cont’d) Algorithm 2 — Decide Whether to Accept to Provide Relay Help Algorithm 2 For Relay/Tx phase of user i 1: if There is a cooperation request (Cop rqst==1) then 2: if Delay constraint condition is satisfied and Reimbursement condition is satisfied then 3: Accept the offer, and set Cop acpt=1. 4: Update his currency balance Mi = Mi + γ. 5: Relay the packet (containing Cop acpt and γ). 6: else 7: Reject the offer, and set Cop acpt=0. 8: Tx his own packet. 9: end if 10: else 11: Tx his own packet. 12: end if C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Distributed Cooperation Strategy (Cont’d) Algorithm 3 — In Rx State Algorithm 3 For Rx state of user i 1: Receive a packet. 2: if In phase 1 or 3 then 3: Get Cop rqst flag. 4: end if 5: if In phase 2 or 4 then 6: Get Cop acpt flag and γ. 7: if The other user relays his packet (Cop acpt==1) then 8: Update his currency balance Mi = Mi − γ. 9: end if 10: end if Cop acpt: cooperation acceptance flag. Cop acpt==1 indicates the user accepts to help the other user. C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Outline

1

Introduction

2

Two-User Cooperation Model

3

Distributed Cooperation Strategy

4

Performance Evaluation

5

Conclusions

C. Chen, S. Kishore (Lehigh University)

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March, 2011

25 / 31

Performance Evaluation

Simulation Setup Simulate the delay performance of our pricing-based cooperation strategy. Simulate ‘Non-cooperation’ strategy and ‘Always-cooperation’ strategy for comparison. Model the arrival of packets at users A and B as Poisson processes with equal rates of λ. Assume channel of users A and B are good (PER ∼ U (0, 0.25)) or adverse (PER ∼ U (0.75, 1)) with equal probability.

Plot average delay versus λ under three cooperation strategies for user A, user B and the overall (social welfare), respectively.

C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Performance Evaluation (Cont’d) Delay Performance

(a) Average delay vs λ for user A

(b) Average delay vs λ for user B

12

10 Average Delay

10 Average Delay

Our proposed pricing-based cooperation strategy has lower delay than the other two strategies.

12 Non−Cooperation Always−Cooperation Pricing−based Cooperation

8

6

4

Compared to the ‘Non-cooperation’ strategy: 15.73% and 11.54% less, respectively.

2 0.05

8

6

4

0.1

0.15 0.2 Arrival Rate λ

0.25

2 0.05

0.3

(c) Average delay vs λ for overall delay

0.1

0.15 0.2 Arrival Rate λ

0.25

0.3

(d) Average delay comparison

24

Average Delay

Non−Cooperation Always−Cooperation Pricing−based Cooperation

10 Average Delay (time slot)

22 20

Compared to the ‘Always-cooperation’ strategy: 7.90% and 6.68% less, respectively.

Non−Cooperation Always−Cooperation Pricing−based Cooperation

18 16 14 12 10 8

Non−Cooperation Always−Cooperation Pricing−based Cooperation

8 6 4 2

6 4 0.05

0.1

0.15 0.2 Arrival Rate λ

0.25

0.3

0

User A

User B

Overall(Social welfare)

For large arrival rate, the delay performance of the ‘Always-cooperation’ strategy is even worse than that of the ‘Non-cooperation’ strategy — long queue effect. C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Performance Evaluation (Cont’d) Influence of Threshold η and Dc Cooperation request constraint η ◮ There is a slight increase of delay when η becomes large. (a) Influence of η

8.5 8 7.5 7

(b) Influence of D

c

9 Average overall delay

Average overall delay

9

0.5 0.6 0.7 0.8 0.9 Cooperation request threshold η

8.5 8 7.5 7

0

2 4 6 8 Delay constraint threshold Dc

Delay constraint Dc ◮ When Dc is small, average delay is large – delay constraint is so tight. ◮ As Dc increases, average delay decreases – more valuable cooperation of qualified users. ◮ After Dc reaches some value, average delay does not decrease (increases slightly instead) – some actually ‘unqualified’ users are permitted by loose delay constraint, degrading delay performance. C. Chen, S. Kishore (Lehigh University)

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March, 2011

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Outline

1

Introduction

2

Two-User Cooperation Model

3

Distributed Cooperation Strategy

4

Performance Evaluation

5

Conclusions

C. Chen, S. Kishore (Lehigh University)

CISS2011

March, 2011

29 / 31

Conclusions Contributions Propose a distributed pricing-based cooperation strategy for two-user cooperation from a delay perspective. This strategy only allows ‘valuable cooperation’; i.e., users with good channels help users with adverse channel conditions. The pricing policy guarantees both users have the opportunity to benefit from the relay help and encourages users to help the other whenever he is qualified to help. Simulation results show this strategy has lower average delay than the ‘Non-cooperation’ and ’Always-cooperation’ strategies. Future Work We intend to analytically bound the average delay when using our cooperation strategy. Extend to multi-user scenarios, in which users have more choices to select relay nodes. C. Chen, S. Kishore (Lehigh University)

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Thank you! Questions?

C. Chen, S. Kishore (Lehigh University)

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