in [4], a content delivery scheme based on opportunistic spatial gossip was proposed for mobile social networks. In this scheme, for delivering content, a network ...
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.
A Controlled Coalitional Game for Wireless Connection Sharing and Bandwidth Allocation in Mobile Social Networks Dusit Niyato∗ , Zhu Han† , Walid Saad‡ , and Are Hjørungnes‡ ∗ Centre for Multimedia and Network Technology (CeMNet) School of Computer Engineering, Nanyang Technological University (NTU), Singapore † Electrical and Computer Engineering, University of Houston, USA ‡ UNIK - University Graduate Center, University of Oslo, Norway Abstract—Mobile social networks have been introduced as a new efficient (i.e., minimize resource usage) and effective (i.e., maximize the number of target recipients) way to disseminate content and information to a particular group of mobile users sharing the same interests. In this paper, we investigate how the content providers and the network operator can interact to distribute content in a mobile social network. The objective of each content provider is to minimize the cost pertaining to the time used for distributing the content to all subscribed mobile users as well as the cost due to the price paid to network operator for transferring the content over a wireless connection via a base station. While the content providers can cooperate by establishing coalitions for sharing a wireless connection, the network operator can control the amount of bandwidth of the wireless connection. We introduce a novel coalitional game model, referred to as “controlled coalitional game”, to investigate the decision makings of the content providers and the network operator. The numerical studies show that, given the allocated bandwidth from network operator, the content providers can selforganize into coalitions while minimizing their individual cost for wireless connection sharing. Also, the results demonstrate that the revenue of the network operator can be maximized when the bandwidth allocation is performed considering the coalitional structure of the content providers.
Keywords – Mobile social network, content provider, game theory. I. I NTRODUCTION The concept of social networks has been introduced to enable people to keep in touch with friends, build social ties of people with the same or similar interest, and facilitate communications and information sharing. This concept was extended to mobile environments and it constitutes the basis of mobile social networks [1]. In mobile social network, the content distribution relies not only on the broadband connection from base stations, but also on the local connection when mobile users move and meet with each other. This content distribution can reduce the radio resource usage of the base station and, hence, lower the cost for content providers by utilizing the social relation and physical mobility of the mobile users. While content delivery and data routing among users in mobile social networks have been widely studied (e.g., [3]), none of these existing works considered jointly the rationality of content providers for sharing the wireless This work was supported by the Research Council of Norway through the project 197565/V30, 183311/S10, and 176773/S10.
connection and the selfishness of the wireless infrastructure owner (i.e., network operator) to optimally manage the radio resources (i.e., bandwidth). In this paper, we consider a mobile social network where multiple content providers seek to buy a wireless connection from a network operator to distribute desired content to their subscribed mobile users. For efficiently sharing of their wireless connection, the content providers can cooperate by forming coalitions. Although this sharing will lower the cost due to the price paid to network operator, the performance of content distribution may be degraded (e.g., due to larger delay). For the network operator, the amount of bandwidth allocated to a wireless connection used by content providers can be controlled so that the revenue is maximized. For this scenario, we introduce the idea of a controlled coalitional game which is a game theoretical model developed to address jointly the coalition formation and bandwidth allocation problems. This model is composed of a coalitional game formulation for the content providers and an optimization formulation for the network operator. Similar in spirit to the well known Stackelberg framework, the proposed game model allows to provide a solution for scenarios where these two formulations are intertwined. Using the proposed controlled coalitional game, the numerical results show that the network operator can optimize the allocated bandwidth given that the content providers form coalitions accordingly. II. R ELATED W ORK Recently, there has been an increasing interest in studying models suited for mobile social networks. For instance, in [4], a content delivery scheme based on opportunistic spatial gossip was proposed for mobile social networks. In this scheme, for delivering content, a network node selects not only the forwarder, but also the message to be forwarded according to a past relationship. In [5], a routing scheme, named “SocialCast”, was proposed for publish-subscribe mobile social networks. This routing scheme estimates the social interaction metrics based on the patterns of movement among communities of users. Subsequently, in this approach, the best information carrier is selected. The authors in [6] propose a content delivery scheme for mobile social networks. This scheme performs the selection of carrier by taking into account both the mobility pattern and
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the meeting time of the people. As a result, content delivery can be optimized for time-critical applications by significantly reducing the end-to-end delay. In [7], a community-based data transmission scheme was proposed to limit the content distribution and, hence, reduce the overhead in mobile social networks. This scheme divides mobile users into different communities based on the contact frequency. The number of content copies to be distributed to the users in the different communities is adjusted adaptively. In [8], an optimal bandwidth allocation scheme was developed to transmit content from content provider to users. The objective is to maximize the utility of all users whereby the utility is defined as a decreasing function of the content age. However, in all the above and other related works, the problems of rational cooperation among content providers and radio resource management of network operator were ignored. To the best of our knowledge, this paper presents the first contribution in this area.
U < Ni ). The rest of the mobile users can obtain the content via direct transfer. In particular, the content can be transferred directly among the subscribed users when they move and meet each other. We assume that the speed of direct content transfer between the mobile users is much larger than that between the base station and the mobile users. From base station to mobile user
From mobile user to mobile user
Content provider 1 Content provider 2 Content provider 3
Base station of network operator
User mobility
Fig. 1.
Content transfer
Example of mobile social network.
III. S YSTEM M ODEL A. Mobile Social Network We consider a mobile social network which is composed of the following components (see Fig. 1): • Content Providers: We consider a mobile social network having a total of I content providers. We let I = {1, . . . , I} denote the set of all the providers. These providers create desired content for their subscribed mobile users (e.g., news, business data, and mobile applications). To transfer content, each content provider uses a wireless connection from a base station belonging to a network operator. The main objectives of the content providers are: (i)- to minimize the time used to transfer new content to all subscribed mobile users, and (ii)- to minimize the cost due to the price paid to the network operator for obtaining a wireless connection. Multiple content providers can cooperate and form coalitions (i.e., a coalition S ⊆ I is established between the members of S) for sharing a wireless connection from network operator. • Network Operator: A network operator provides a wireless data transfer service (i.e., a wireless connection) to the content providers. The content received from the providers using this service is buffered in a queue. Subsequently, the content at the head of the queue is transferred to U mobile users at any base station (e.g., using broadband wireless access) owned by the network operator. We consider that the network operator can control the amount of bandwidth b (in kbps) allotted by each base station for transferring content to the mobile users. The price of the wireless connection charged to each content provider is denoted by bθ where θ is a price constant. The objective of the network operator is to maximize the revenue from selling wireless connections to content providers. • Mobile Users: For any content provider i, there are Ni subscribed mobile users. To reduce the cost on the content provider, only a number U of subscribed mobile users will receive the new content via the base station (i.e.,
In the aforementioned mobile social network, two issues arise for the content providers and the network operator. By cooperating and forming coalitions, the content providers can reduce the cost paid to the network operator for sharing a wireless connection. However, the time taken to transfer the content (i.e., delay) will increase since a limited bandwidth is shared. Thus, the formation of coalitions among content providers strongly depends on the amount of allocated bandwidth by the network operator. The optimal decisions of the network operator (i.e., bandwidth allocation) and content providers (i.e., coalition formation) will be investigated using the proposed controlled coalitional game framework. The details of this framework are presented later in this paper. IV. C OST OF C ONTENT P ROVIDER Each content provider in the considered network must be able to deliver its content to the mobile users in a timely manner. Hence, for any content provider, we define a cost that is a function of the time duration needed until all subscribed mobile users receive the content (i.e., delay). In addition, this cost is also a function of the price paid to the network operator. Without loss of generality, the cost of content provider i which is a member of a coalition S (i.e., i ∈ S) is defined as follows: Ci (S, b) = ζd Di (S, b) +
bθ , |S|
(1)
where Di (S, b) is the delay for content to be transferred to all mobile users subscribed to content providers in coalition S and ζd is a weight for the delay. θ is a price constant and b is the amount of allocated bandwidth per connection. |S| is the Cardinality of set S (i.e., number of content providers in coalition S). The delay of content distribution is obtained from (2) Di (S, b) = Q(S, b) + T (S), where Q(S, b) is the waiting time of the content at the base station and T (S) is the time duration used by the mobile users to transfer content among each other. Note that the time taken to transfer content from content provider to network operator
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(i.e., base station) is negligible as it is performed over a wired network. A. Waiting Time at a Base Station Any content received from content providers in coalition S is buffered in a queue at a given base station. We assume that the content generation follows a Poisson process with an average rate αi using an M/D/1 queueing model1 . Thus, the waiting time of any content at a given base station can be obtained from LU ρS Q(S, b) = 1+ , (3) b 2(1 − ρS ) where L is the content size. b is amount of bandwidth allocated by network operator, U is the number of mobile users that are downloading new content from the base station, and ρS is the LU i∈S αi . traffic intensity for coalition S where ρS = b B. Content Transfer among Mobile Users The mobile users who receive new content from a base station can transfer/forward this new content directly to other users as they move and meet one another. We assume that the inter-encounter time interval of mobile users is exponentially distributed with mean 1/λ [2]. The time taken for some content to be transferred to all mobile users subscribed to content provider i ∈ S after U mobile users obtained this content from a base station can be modeled as a phase-type Each phase (i.e., row s distribution with parameters S and β. of transition rate matrix S and initial probability vector β) represents the number of mobile users having the content. Matrix S is of size i∈S Ni − 1 × i∈S Ni − 1 and element Ss,s at row s and column s is defined as follows: Ss,s+1 = λs Ni − s , (4) i∈S
and Ss,s = −Ss,s+1 for s ∈ 1, . . . , i∈S Ni − 2 . For s = i∈S Ni − 1, Ss,s = −λs. Element βs at row s of vector is defined as follows: β 1, if s = U, βs = (5) 0, otherwise. That is, the phase-type distribution starts with phase U . The average time duration used to transfer content to all mobile T S−11 where 1 is a users is obtained from T (S) = −β column vector of ones. V. C ONTROLLED C OALITIONAL G AME F ORMULATION In this section, we introduce the proposed controlled coalitional game to address the issues of coalition formation for content providers and bandwidth allocation for the network operator. To obtain the optimal strategies of leaders and followers, this controlled coalitional game is decomposed into the optimization formulation based on a Markov decision process 1 This
model is selected for simplicity, other models such as M/M/1 can also be accommodated.
(MDP) [9] for the network operator and a coalitional game formulation for the content providers. These optimization and coalitional game formulations are interrelated. In particular, the optimal action of network operator is obtained given the coalitional structure (i.e., coalitional state)2 of content providers. Also, the coalitional state transition of content providers is controlled by the action of the network operator. A. Coalitional Game Formulation of Content Providers Given the amount of allocated bandwidth b by network operator (i.e., leader), a coalitional game is formulated for the rational content providers (i.e., followers) that seek to minimize their costs. The set of coalitions of all content providers can be defined as the coalitional state w = {S1 , . . . , Sx , . . . , SX } X where Sx ∩ Sx = ∅ for x = x , and x=1 Sx = I, and X is the total number of coalitions in state w, i.e., X = |w|. The state space of the coalitional structures is then defined as follows: Ω = {(wy ) such that y = {1, . . . , KI }},
(6)
where KI is the Bell number given the total of I content providers. The change of coalitional state is due to the strategies of the content providers to split or merge their formed coalitions. These strategies are defined as follows. Split: Given the original coalition Sx , content providers in this coalition can collectively form (i.e., split into) multiple new coalitions Sx† whose corresponding set is denoted by M† , if the following condition is satisfied Ci (Sx† , b)
