a social group utility maximization framework with applications in database assisted spectrum access...

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A Social Group Utility Maximization Framework with Applications in Database

Assisted Spectrum Access

Xu Chen Xiaowen Gong Lei Yang Junshan Zhang

School of Electrical, Energy, and Computer EngineeringArizona State University

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Outline

• Introduction• Social Group Utility Maximization Framework• Database-assisted Spectrum Access under SGUM• Conclusion and Future Work

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• Mobile networks are ubiquitous– Mobile phone shipments is projected to reach 1.9 billion in 2014 (about 7

times that of desktop and laptop combined), mobile data traffic more than doubled in 2013

– Advanced wireless technology (e.g., MIMO, OFDM), powerful wireless devices (e.g., smartphone, wearable smart devices)

• Social networks shape people’s behavior– Social relationships have pervasive impact (e.g., social media, social

recommendation)– Online social networks users in 2013 crossed 1.7 billion (about one

quarter of world’s population)

When Mobile Network Meets Social Network

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Social Dimension on Mobile Networking

• Key observations on mobile networko Mobile devices are personal communication devices carried and

operated by human beingso People have diverse social ties and care about their social neighbors

at different levels (e.g., family, friend, acquaintance)

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Virtual Social Network Underlays Physical Communication Network

Social Domain

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2

3

4 5Social Coupling

Physical Domain

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3

5Physical Coupling

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• Physical-social coupling among mobile deviceso Physical domain: physical coupling subject to physical relationshipo Social domain: social coupling due to social ties among users

Question: Can we exploit social ties among mobile users to improve the interactions of their mobile

devices in communication networks? How can we leverage it cleverly?

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From Non-cooperative Game to Network Utility Maximization

• Network utility maximization (NUM)o Users are altruistic, aiming to maximize social welfare o Extensively studied for network resource allocation

• Non-cooperative game (NCG)o Each user is selfish, aiming to maximize its individual utilityo Widely used to study strategic interaction among autonomous users

• NCG and NUM are two extreme cases: selfish (social-oblivious) or altruistic (fully social-aware)

Question: What is between these two extremes?

Non-Cooperative Game Network Utility Maximization

Users’ Social Awareness

Selfish Altruistic

Answer: Social group utility maximization (SGUM): A new paradigm on mobile social networking

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Outline


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Physical Graph Model

• A set of mobile users

• User-specific feasible strategy set (e.g., channel selection, power level selection)

• Physical graph o Two users are connected by a physical edge if they have physical couplingo Capture the physical relationships among users (e.g., interference)o the set of users having physical coupling with user

• Individual utility o User’s payoff under strategy profile (e.g., SINR, data rate)o Depend on the physical graph (e.g., interference graph)

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Social Graph Model

• Social graph o Two users are connected by a social edge if they have a social tieo Capture the social coupling among users (i.e., kinship, friendship)o : the set of users user has social ties witho : social tie strength from user to user

• From individual utility to social group utility

user ’s individual utility

weighted sum of individual utilities of user ’s social neighbors

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Social Group Utility Maximization Game• Distributed decision making among users

o Each user aims to maximize its social group utility

• Social group utility maximization (SGUM) game o player seto strategy space of player o payoff function of player

• Social-aware Nash equilibrium (SNE)

o is a SNE if no user can improve its social group utility by unilaterally changing its strategy

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Social Group Utility Maximization• SGUM provides rich modeling flexibility

o If no social tie exists (i.e., ), SGUM degenerates to NCG as o If all social ties have the maximum strength (i.e., ), SGUM becomes NUM as o Span the continuum space between NCG and NUM

1 2

3 4

𝑎21

𝑎23

𝑎34SGUM

1 2

3 4NCG

selfish 1 2

3 4

1

1

1NUM

11 1altruistic

NCG NUM

Social-aware Altruistic

SGUM

Selfish

Social group utility maximization (SGUM) framework captures diverse social ties of mobile users and

diverse physical relationships of mobile devices; it spans the continuum space between non-cooperative game and

network utility maximization.

Related Work

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• Explore social aspect for wireless networkso Exploit social contact pattern for efficient data forwarding [Gao et al, 2009];

leverage social trust and reciprocity to improve D2D communication [Chen et al, 2013]

o Routing game among altruistic users [Chen et al, 2008] [Hoefer et al, 2009], random access game between two symmetrically social-aware users [Kesidis 2010]

• SGUM game is not coalition game (CG)o Each user in a CG only cares about its own utility (though it is achieved through

cooperation with others)o A user in a CG can only join one coalition, while it can be in multiple social

groups in a SGUM game

1 134

522

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5coalitions in a CG: {1,2,3}, {4,5}

social groups under SGUM: {1,2,3},{3,4,5}

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Outline

• Introduction• Social Group Utility Maximization Framework• Database Assisted Spectrum Access under SGUM• Conclusion and Future Work

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Database Assisted Spectrum Access

• FCC recent ruling on TV spectrum utilization o White-space users determine vacant channels via geo-location databaseo Obviate the need of spectrum sensing for individual users

• Challenges for achieving efficient shared spectrum accesso Access the same vacant channel cause severe interferenceo Effective cooperation incentives for spectrum access is needed

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• Individual utility o Each user aims to minimize its total interference plus noise

SGUM-based Spectrum Access Game

• A set of white-space users

• Each user selects a vacant channel from a specific set

• Physical graph o Two users are connected by a physical edge they can cause

interference to each other

• Social group utility

• Potential game: if the game has a potential function such that

o Property: any strategy that locally maximizes the potential function is a Nash equilibrium

SGUM-based Spectrum Access Game

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THEOREM: Social group utility maximization game for database assisted spectrum access is a potential game and always admits a SNE.

• Potential function of the SGUM game

Due to physical coupling Due to social coupling

Distributed Spectrum Access Algorithm

• Distributed spectrum access algorithmo Inspired by adaptive CSMA for NUM [Jiang et al, 2010]o Key idea: coordinate users’ asynchronous channel selection updates to

form a Markov chain, and drive it to the stationary distribution, which asymptotically maximizes the potential function

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• How to achieve a SNE with a good social welfare?o The strategy that (globally) maximizes the potential function is appealing,

but it is a combinatorial problem that is hard to solve in generalo Distributed algorithm is desirable


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• Each user repeats following steps in parallel:o Compute the social group utility on the current channel based on the

individual utilities reported by social neighbors

o Set a random timer following the exponential distributiono Count down until the timer expires


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• Each user repeats following operations in parallel:o When the timer expires, choose a new channel randomly

o Compute the social group utility on the new channel o Decision update: stay in the new channel with probability ; or move back to the original channel with probability


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• The distributed algorithm induces a Markov chain o System state: the channel selection profile of all userso Each state transition involves one user: due to the property of exponential

distribution for channel update countdowno Two-user Markov chain example:

Channel of User A: Channel of User B:

Vacant Channel Set

{1, 2} {2, 3}

(1,2) (1,3)

(2,2) (2,3)

Markov Chain For Dynamic Channel Selection

Channel 1 Channel 2


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distribution for channel update count-downo Two-user Markov chain example:


Vacant Channel Set

{1, 2} {2, 3}

(1,2) (1,3)

(2,2) (2,3)


User B Updates Channel Selection

Channel 1 Channel 3


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Vacant Channel Set

{1, 2} {2, 3}

(1,2) (1,3)

(2,2) (2,3)


Channel 2 Channel 3

User A Updates Channel Selection


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Vacant Channel Set

{1, 2} {2, 3}

(1,2) (1,3)

(2,2) (2,3)


Channel 2 Channel 2

User B Updates Channel Selection


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distribution for channel update count-downo Two-user Markov chain example: diagram of all feasible state transitions

User A User B

Vacant Channel Set

{1, 2} {2, 3}

(1,2) (1,3)

(2,2) (2,3)



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distribution for channel update count-downo Two-user Markov chain example

THEOREM: The distributed spectrum access algorithm induces a time-reversible Markov chain with the unique stationary distribution given as

• As , the SNE can be achieved• For finite , the gap from is bounded by , where is the number of states in

Markov chain

Performance Gap

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• Performance gap from the social optimal strategy by NUMo maximum social welfare: where THEOREM: The performance gap of the SNE found by the distributed spectrum access algorithm is at most

• decreases as the social tie strength increases• when all users are altruistic, i.e.,

Numerical Results• N=100 users randomly scatter over a square area

• Physical graph is generated based on users’ distances

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Numerical Results• Social graph is generated by Erdos-Renyi random graph model

o There exists a social link between two users with probability

• Performance improves as the social link probability increases• The SNE for the SGUM game migrates monotonically from the NE for NCG to

the social optimal strategy for NUM28

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Outline


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Conclusion

• Contributiono Developed the social group utility maximization (SGUM)

framework, which captures diverse social ties of mobile users and diverse physical relationships of mobile devices, and spans the continuum between non-cooperative game and network utility maximization

o Studied SGUM game for database assisted spectrum access, showed that it is a potential game, developed a CSMA-like distributed algorithm to achieve a social-aware Nash equilibrium, and quantified the impact of social ties

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Future Work

• Study a variety of applications under the SGUM framework– E.g, power control, random access control

• Zero-sum game (ZSG)o Users aim to minimize others’ welfareo Employed for security applicationso If total strength of social ties to each user is zero (i.e., ), SGUM

degenerates to ZSG as (e.g, , )

• Extend the SGUM framework to “negative” social ties– Social tie can be “negative” (i.e., ) such that a user intends to damage

another’s welfare (e.g., against opponent or enemy)

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Future Work

NCG NUM

Positive Social Tie Malicious Altruistic

SGUMSGUM

Negative Social Tie

ZSG

Selfish

1 2

3 4

𝑎21

𝑎23

𝑎34SGUM

1 2

3 4NCG

selfish 1 2

3 4

1

1

1NUM

11 1altruistic

1 2

3 4

−1

−1ZSG

−1 −1selfish

malicious

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Thank You!

a social group utility maximization framework with applications in database assisted spectrum access...

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