Information-Centric Virtualized Cellular Networks with ... - IEEE Xplore

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2016.2518658, IEEE Transactions on Vehicular Technology IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, XXX 2016

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Information-Centric Virtualized Cellular Networks with Device-to-Device (D2D) Communications Kan Wang, F. Richard Yu, Senior Member, IEEE, and Hongyan Li, Member, IEEE

Abstract—Information-centric wireless network virtualization enables the sharing of not only the infrastructure, but also the content, among different service providers, enabling the gain of not only virtualization but also in-network caching. In this paper, we propose a novel framework with information-centric wireless virtualization and device-to-device (D2D) communications, which enables content caching not only in the air, but also in the mobile device. Moreover, the content is virtualized, and can be shared by users from different virtual service providers. In this framework, we formulate the virtual resource allocation and caching strategies as a joint optimization problem, considering the gain of not only virtualization but also caching in the proposed information-centric wireless network virtualization architecture with D2D communications. In addition, to reduce computational complexity and signaling overhead, we propose a distributed algorithm to solve the formulated problem, based on recent advances in alternating direction method of multipliers (ADMM), in which different parties only need to solve their own problems without exchange of channel state information (CSI) with fast convergence rate. Extensive simulations are conducted with different system parameters to show the effectiveness of the proposed scheme. Index Terms—Information-centric networking, wireless network virtualization, D2D transmissions

I. I NTRODUCTION With the explosive growth of the wireless traffic, users pay more attention to the content itself rather than where it is physically located. To better cope with the shift from sender-driven end-to-end networking paradigm to receiverdriven content retrieval paradigm, innovative informationcentric networking (ICN) has attracted great attentions [1]. ICN promotes content to a first-class citizen in the network. With ICN, users are only interested in what the content is, but do not care where the content comes from. Compared to traditional networking paradigms, which lack natural support for content distribution, ICN can provide native support for scalable and highly efficient content retrieval, and meanwhile with enhanced capability for security and mobility [2]. By Copyright (c) 2015 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]. This work is supported by the National Science Foundation (91338115, 61231008, and 61372089), National S&T Major Project (2015ZX03002006), the Fundamental Research Funds for the Central Universities (WRYB142208, JB140117), Program for Changjiang Scholars and Innovative Research Team in University (IRT0852), the 111 Project (B08038). Kan Wang and Hongyan Li are with the State Key Laboratory of Integrated Service Networks, School of Telecommunications Engineering, Xidian University, Xi’an, Shaanxi 710071, China (e-mail: [email protected]; [email protected]). Hongyan Li is the corresponding author. F. Richard Yu is with the Depart. of Systems and Computer Eng., Carleton University, Ottawa, ON, Canada (e-mail: [email protected]).

naming information at the network layer, ICN is characterized by the built-in network caching and receiver-driven information-level delivery as well as multicast mechanisms, thus facilitating the information delivery across networks [2]. For next generation wireless cellular networks, ICN-based air caching has been considered as a promising technique [3]. Another promising technology is wireless network virtualization, with which wireless network infrastructure can be decoupled from the provided services [4]. Since different wireless virtual network operators can dynamically share the physical substrate wireless networks, the capital expenses (CapEx) and operation expenses (OpEx) of wireless (radio) access networks (RANs), as well as core networks (CNs), can be reduced significantly. In addition, virtual network operators, which provide some specific over-the-top services (e.g., video and gaming), can help attract more users, while physical substrate network providers can produce more revenue by leasing the isolated virtualized networks to them [5]. Integrating wireless network virtualization with ICN technique can further improve the end-to-end network performance in next generation wireless cellular networks [3]. Specifically, information-centric wireless network virtualization enables the sharing of not only the infrastructure, but also the content, among different service providers, enabling the gain of not only virtualization but also in-network caching. Although some works have been done on ICN and virtualization, most of existing works do not consider device-todevice (D2D) communications. With D2D communications, users can directly communicate with each other via D2D links instead of accessing base stations (BSs) exclusively [6]. Compared to traditional cellular communications, D2D communications allow radio resources to be shared between multiple cellular and D2D flows, thus introducing reuse gain. Meanwhile, due to the proximity of pair users in D2D links, high data rate and low transmission delay can be obtained, thus introducing proximity gain. Due to these advantages, D2D communication has received great interests from both academia [7]–[9] and standardization bodies (e.g., 3GPP) [10]. In this paper, we study information-centric virtualized cellular networks with D2D communications. The distinctive features of this paper are as follows. •

We propose a novel framework with information-centric wireless virtualization and D2D communications, which enables content caching not only in the air, but also in the mobile device. Moreover, the content is virtualized, and can be shared by users from different virtual service providers.

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In this framework, we formulate the virtual resource allocation and caching strategies as a joint optimization problem, considering the gain of not only virtualization but also caching in the proposed information-centric wireless network virtualization architecture with D2D communications. • To reduce computational complexity and signaling overhead, we propose a distributed algorithm to solve the formulated problem, based on recent advances in alternating direction method of multipliers [11] (ADMM), in which the infrastructure providers (InPs) and virtual resource manager (VRM) only need to solve their own problems without exchange of channel state information (CSI) with fast convergence rate. • Extensive simulations are conducted with different system parameters to show the effectiveness of the proposed scheme. It is shown that the total utility of mobile virtual network operators (MVNOs) can be improved and the backhaul usage can be reduced significantly in the proposed scheme. The remainder of this article is organized as follows: In Section II we present the system model and the proposed framework. In Section III, we formulate the virtual resource allocation and caching strategies as a sum-utility maximization problem. In Section IV, we relax and re-formulate the optimization problem as a convex problem. In Section V, we solve the problem via ADMM-based algorithm. In Section VI, we discuss the simulation results. We conclude this work in Section VII with future work.

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•

Core Networks MVNO1 Traditional Cellular Networks

Traditional Router

Bac

ICN Router with Content

kha

ul

MVNO2 ICN-based Cellular Networks

ICN BS with Content

Traditional BS

Network Functionality Virtualization

Router Content BS

Content

InP

Fig. 1: A general information-centric wireless network virtualization model. In the general network virtualization framework, a entity resource virtualization is responsible for the virtualization of the physical networks into virtual elements. Meanwhile, the virtual network controller over MVNOs is responsible for collecting the resource utilization prices negotiated with InPs, and the subscribed users information (e.g.,payment information) from MVNOs. For VRM, virtual resources are dynamically allocated to different MVNO users. Through this virtualization framework, each MVNO can possess a virtual network [18].

II. S YSTEM M ODEL In this section, we will introduce information-centric wireless network virtualization, then present a framework with D2D communications, followed by the virtual resource sharing model. A. Information-Centric Wireless Network Virtualization Network function virtualization (NFV) is an effective approach to manage substrate network infrastructure and network resources (e.g., radio spectrum, backhaul, etc.). With NFV, substrate network resources operated by multiple InPs can be dynamically shared by multiple MVNOs, thus significantly decreasing the CapEx and OpEx of InPs. After wireless network virtualization, infrastructure and radio resources are leased and managed by MVNOs [4]. Furthermore, from MVNOs’ point of view, NFV can facilitate the introduction of new communication and networking technologies [12]–[17]. A general information-centric wireless network virtualization model is illustrated in Fig. 1, where one InP is virtualized into two virtual networks, which are leased to MVNO1 and MVNO2, respectively. The first virtual network represents a traditional cellular network, and the second one represents a ICN-based cellular network. For ICN-based cellular networks, content can be cached in BSs or routers, whereas traditional cellular networks always need to fetch content from servers via backhaul.

B. Information-Centric Wireless Network Virtualization with D2D Communications Memory for content caching is an integral part in ICNbased cellular networks. In the existing works, the content caching function is assumed to be only available in BSs, since content delivery merely occurs in the downlink (i.e., BS → users), and not vice versa. However, in the context of D2D communications, all nodes (including BSs in InPs and users owned by different MVNOs) potentially have the caching capabilities. D2D communications can be conducted whenever the potential D2D link qualifies the communication requirement. Thus, caching capabilities in users are non-negligible in the proposed framework even though users generally have much smaller caching memory compared to BSs. To support D2D communications in the general informationcentric wireless network virtualization framework, not only traditional substrate network resources but also content stored in InPs should be virtualized and shared between multiple MVNO. The framework with D2D communications is illustrated in Fig. 2 where there are three concurrent content delivery occurring in the networks. User 1 subscribed to MVNO1 can only retrieve the content from core networks via backhaul, since its required content is available in neither BS nor other users. User 2 from MVNO2 is capable of receiving its required content from the BS, provided that the content is already cached in it. Meanwhile, a D2D communication is



Content Publish

Core Networks

Content Request

Content from Core Networks Content Directly from BS (Cellular Transmission) Content Directly from user (D2D Transmission)

BS without Content

MVNO1

BS with Content

User 3 MVNO2 User 1

User 2 User with Content

User 4

Fig. 2: Information-centric wireless network virtualization with D2D Communications.

established to facilitate the direct content delivery from user 3 to user 4. In the traditional D2D transmissions, two users subscribed to different MVNOs cannot communicate with each other directly even though they are in close proximity. Yet, in our proposed framework, the content cached in user 3 can also be virtualized and shared by user 4. As such, a D2D communication is conducted between different MVNOs. C. Network Resource Virtualization In this paper, we only consider the single-cell scenario (i.e., one InP) with multiple users. After virtualization, the BS may be leased to multiple MVNOs at different prices from InP. Meanwhile, there is a high probability that users are owned by different MVNOs. It should be noted that not only BS but also users can be virtualized as virtual nodes for association since D2D transmissions are considered to improve network performance. Contents located in different users and BS can also be regarded as virtual resources. Moreover, we have to consider the virtualization of caching memory, which facilitates the caching optimization, which will be discussed in Section III. How to implement the virtualization of physical networks has been described in detail in many recent works (e.g., [19]) and hence we focus on the specific virtual resource allocation among virtual nodes. Meanwhile, we assume perfect CSI estimation at InP as well as perfect information interaction between InP and MVNOs. Let M be the set of MVNOs operating on the InP. For each MVNO m ∈ M, the set of corresponding users with requirements can be denoted by Im .SFor the sake of brevity, we further denote I = {1, · · · , I} = Im as the index set of all users from multiple MVNOs. At each resource allocation

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interval, it is assumed that user i ∈ Im has a request for content ci . Let J = {1, · · · , J} be the set of users which can be considered as transmitters in potential D2D pairs. Note here that, users in J are actually handled as transmitters in InP, while those in Im are regarded as subscribers in MVNO m. For practical implementation, all transmitters in J can be virtualized to slices by means of resource isolation (at subchannel or time-slot level, or even hardware level, etc.) [4]. In the context of D2D communications, user i can associate with either BS (which can be indexed by j = 0) using cellular transmissions, or other user (indexed by j, 1 ≤ j ≤ J) with ci in its memory using D2D transmissions. Let aij be the content distribution indicator, i.e., aij = 1 represents that ci is readily stored in the memory of j and 0 otherwise. In this paper, we consider the BS downlink (DL) transmissions for cellular transmissions, since contents are typically delivered by BS to users in general. Meanwhile, BS uplink (UL) resource sharing among D2D transmissions will be studied. That is because the interference incurred by D2D transmissions in the BS UL will only impact the BS and can be mitigated easily using BS coordination techniques [7]. Obviously, this scheme with orthogonal spectrum between cellular and D2D communications can significantly decrease the complexity of analyzing mutual interference between two transmission modes. Consequently, the bandwidth in this system can be divided into two orthogonal parts: BS DL Bdl for cellular communications and BS UL Bul for D2D communications, respectively. Meanwhile, for ease of notation, we further denote B0 and Bj , ∀j ∈ J as the bandwidth assigned to BS (i.e., j = 0) and transmitting users (i.e., 1 ≤ j ≤ J), respectively. In the proposed framework, time is divided into periods with equal duration and each period is further split into three phases, namely, content request, data transmission and caching refreshment phase. In the content request phase, each user i ∈ Im will send a content request to its MVNO m, and then MVNO m forwards this requirement to VRM. In addition, user i is also with a data rate requirement which is forwarded by MVNO m to VRM as well. Eventually, VRM will determine the associated transmitter, radio resource allocation and caching strategy for each user. In the data transmission phase, user i will receive content ci via either cellular or D2D transmissions upon the reception of control signaling from VRM. In the caching refreshment phase, each user will eventually refresh the caching memory based on the caching decisions made in the content request phase. Note that it can only be executed at the end of each period, since only after the transmission are delivered contents fully available to users.

III. P ROBLEM F ORMULATION In this section, we will discuss the resource allocation constraints, then develop the utility function associated with each potential link, followed by the formulation of sum-utility maximization.



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A. Constraints

B. Utility Function

Let xij ∈ {0, 1} be the associated transmitter indicating variable, i.e., xij = 1 denotes that user i is associated with transmitter j, and xij = 0 otherwise. We do not focus on multi-homing in this paper, which can be formulated as X xij ≤ 1, ∀i ∈ Im , m ∈ M, (1)

As mentioned above, caching functions exist in both BS and users. We denote α = [α1 , . . . , αi , . . . , αI ]T as the vector of gain per unit of received data rate for receivers, β = [β0 , . . . , βj , . . . , βJ ]T the vector of price per unit of consumed radio bandwidth for transmitters, γ = [γ0 , . . . , γj , . . . , γJ ]T the vector of price per unit of consumed backhaul bandwidth on transmitters, and φ = [φ0 , . . . , φi , . . . , φI ]T the vector of unit gain that MVNO charge users who request for content ci , and ψ = [ψ1 , . . . , ψi , . . . , ψI ]T the vector of price per unit of space in the memory of receivers, respectively. Mathematically, the utility for the potential transmission between user i and transmitter j ∈ J (i.e., D2D transmission) can be defined as:

j∈J0

where, J0 = J ∪ {0}. Meanwhile, there exists only one receiver for each D2D-pair, i.e., X xij ≤ 1, ∀j ∈ J . (2) i∈Im ,m∈M

Let yij ∈ [0, 1] be the fraction of Bj allocated to user i, then the BS DL and UL bandwidth allocation constraints should be formulated as X xi0 yi0 B0 ≤ Bdl , (3) i∈Im ,m∈M

and X

X

xij yij Bj ≤ Bul ,

(4)

i∈Im ,m∈M j∈J

respectively. For user i’s data rate requirement, it can be formulated as X xij yij Bj rij ≥ di , ∀i ∈ Im , m ∈ M, (5) j∈J0

where di is user i’s data rate requirement in the corresponding QoS class, rij is the achievable spectrum efficiency of user i on transmitter j using the Shannon bound. For the caching refreshment on each user i, we introduce binary variable zij ∈ {0, 1} as the cache refreshing variable, namely, zij = 1 indicates that user i caches content ci sent by transmitter j and 0 otherwise. Since one user can only cache the content from one transmitter, the caching limit for each receiver can be formulated as X

xij zij sci ≤ Si , ∀i ∈ Im , m ∈ M,

(6)

j∈J0

where Si is the size of the memory of user i, and sci is the size of content ci . In addition, let vi ∈ {0, 1} be the caching refreshment variable on BS, i.e., vi = 1 indicates that BS caches content ci requested by user i and 0 otherwise. Note that, we do not need to focus on the caching function on transmitter j ∈ J , since all D2D transmissions are based on the fact that the required contents are already available on sending users. Considering that the size of all cached contents should not exceed the maximal size of the memory in BS, we have X xi0 vi sci ≤ S0 , (7) i∈Im ,m∈M

where S0 denotes the size of the memory of BS.

uij (xij , yij , zij ) =xij yij (αi Bj rij − βj Bj − (1 − aij )γj Bj rij ) +xij zij (φi ei − ψi sci ), (8) where αi Bj rij denotes the gain of received data rate, βj Bj is the cost of consumed radio bandwidth, (1 − aij )γj Bj rij is the cost of consumed backhaul bandwidth, φi ei is the gain achieved on estimated reduced backhaul bandwidth usage ei from caching content ci , and ψi sci is the cost of caching ci in the memory of user i, provided that only user i accesses transmitter j. In particular, if aij = 0, the term (1 − aij )γj Bj rij in (8) reduces to γj Bj rij . In this case, ∀j ∈ J , we need to set γj at an extremely large value since it is unrealistic to use D2D transmissions under the condition that there exists no content ci in the memory of j, and thus −γj Bj rij a extremely small number. However, for aij = 0 and j = 0, due to BS’s capability of backhaul, it is feasible to set γ0 at a reasonable value. For the potential transmission between user i and BS, the associated utility function could be formulated as: ui0 (xi0 , yi0 , zi0 , vi ) =xi0 yi0 (αi B0 ri0 − β0 B0 − (1 − ai0 )γ0 B0 ri0 ) +xi0 zi0 (φi ei − ψi sci ) +xi0 vi (1 − ai0 )(φi ei − ψi sci ), (9) in which the term xi0 vi (1 − ai0 )(φi ei − ψ0 sci ) evaluating the net caching gain in BS is added compared to (8). In this paper, it is assumed the there are totally C types of contents with diverse popularity in the networks, and the popularity of the c-th most popular content is characterized by a Zipf P popularity distribution with parameter α, i.e., qc = C P ǫ −1 with ǫ ≥ 1 [20]–[22]. Here, for ease , P = ( c=1 /c ) cǫ of notation, we denote qci as the requested rate for content ci (1 ≤ ci ≤ C) across networks. Therefore, for user i, the expected reduced backhaul bandwidth consumption during the next period T via caching content ci can be calculated as q s ei = ciT ci . C. Optimization Problem The resources allocated to users for transmissions should be such that the total utility seen by all MVNOs is maximized. Considering all the constraints and utility functions described



above, the sum-utility maximization problem can be mathematically formulated as follows: X X X max uij (10a) (x,y,z,v)

m∈M i∈Im j∈J0

subject to

(1) − (7),

(10b)

which is a mixed binary integer programming problem with both continuous (i.e., y) and binary variables (i.e., x, z, v) [23], [24]. IV. P ROBLEM R E - FORMULATION It is challenging to approach problem (10) due to the following observations: • x, z, v are boolean variables such that the feasible set of problem (10) is nonconvex. • The objective function is not jointly convex with respect to (x, y, z, v) even though we relax x, z, v to be continuous variables. • Problem (10) is usually large-sized due to the fact that multiple D2D transmissions may coexist within one macrocell coverage. Next, we relax binary variables such that 0 ≤ xij ≤ 1, 0 ≤ zij ≤ 1, 0 ≤ vi ≤ 1. By this means, 0 ≤ xij ≤ 1 can be interpreted as that user i can associate with multiple transmitters in a time division multiple access (TDMA) manner instead of exclusively connecting to only one transmitter [25]. In the same way, 0 ≤ zij ≤ 1, 0 ≤ vi ≤ 1 represent the time fraction of caching content ci during one period on user i and BS, respectively. However, problem (10) is still intractable due to the product term xij yij , xij zij and xi0 vi . By means of transformation y˜ij = xij yij , z˜ij = xij zij and v˜i = xi0 vi , we can re-formulate problem (10) as

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A lot of methods can be used for solving convex problems, e.g., interior point method and dual decomposition [23]. However, the size of the problem will be prohibitively large as the number of transmitters increases. Moreover, even we assume that a centralized algorithm works, the signaling overhead will be extremely large since it requires all CSI and content distribution information. Therefore, a distributed optimization algorithm executed on each transmitter needs to be developed for practical implementation. Due to the constraints, (11) is not separable with respect to each slice. That is to say, each user i has J + 1 association selections, J + 1 radio resource allocation fractions, and J + 1 caching decisions on all J + 1 slices. Thus, the coupling has to be processed properly, as discussed in Section V. V. D ISTRIBUTED O PTIMIZATION

max

(x,˜ y,˜ z,˜ v)

uij

(11a)

m∈M i∈Im j∈J0

subject to

X

xij ≤ 1, ∀i, m,

j∈J0

X

xij ≤ 1, ∀j, (11b)

i∈Im ,m∈M

xij ≥ y˜ij , xij ≥ z˜ij , ∀i, m, j, xi0 ≥ v˜i0 , ∀i, m, (11c) X X X y˜i0 ≤ 1, y˜ij ≤ 1, (11d) i∈Im ,m∈M

X

i∈Im ,m∈M j∈J

y˜ij Bj rij ≥ di , ∀i, m,

(11e)

j∈J0

X

C ONSENSUS ADMM

In this section, we first transform the problem by introducing new variables. Then, each step in the distributed algorithm is described in detail. Moreover, the convergence and implementation issues are discussed in this section. A. Problem Transformation In order to decouple the coupling variables, we introduce ˜ and ˜z for each slice j ∈ J0 , which can be local copies of x, y interpreted as each slice’s opinion about the associated global ˆj , y ˆ j and zˆj be the local copies of x, y ˜ and variables. Let x ˜z, respectively. As such, we could form the equivalent global consensus version of (11) as max subject to

X X X

VIA

XX

uij j∈J0 i∈I j j x ˆjik = xik , yîk = y˜ik , zîk = z˜ik , ∀j, i, k, X j X j x îk ≤ 1, ∀j, i, xîk ≤ 1, ∀j, k, i∈I k∈J0 j j x ˆjik ≥ yîk , xˆjik ≥ zîk , ∀j, i, k, j x î0 ≥ v˜i , ∀j, i, X

j yî0

i∈I

≤ 1,

XX

j yîk

≤ 1, ∀j

(12a) (12b) (12c) (12d) (12e) (12f)

i∈I k∈J

X

j yîk Bk rik ≥ di , ∀j, i,

(12g)

j zîk si ≤ Si , ∀j, i,

(12h)

k∈J0

X

k∈J0

z˜ij si ≤ Si , ∀i, m,

(11f)

j∈J0

X

X

v˜i si ≤ S0 ,

(12i)

i∈I

v˜i si ≤ S0 ,

(11g)

i∈Im ,m∈M

which is obviously a linear programming problem. Note that, constraint (11c) enforces that the association variable should be larger than or equal to the radio resource fraction as well as the caching variable. Intuitively, if xij > 0, y˜ij can be any nonnegative; if xij = 0, y˜ij = 0 must hold. Similarly, user i can decide to cache the content or not only when xij > 0.

with global variables {xik , y˜ik , z˜ik } and local variables j j {ˆ xjik , yîk , zîk , v˜i }j∈J0 . The consensus constraint (12b) imposes that all local variables need to be consistent with the asˆ j = {ˆ sociated global variables. Note here that, x xjik }i∈I,k∈J0 , j j j ˆ = {ˆ y yik }i∈I,k∈J0 , ˆz = {ˆ zij }i∈I,k∈J0 are the vectors of local variables with respect to transmitter j, respectively. As a result, the feasible set of local vectors for each slice j can be written as



X j X j  x îk ≤ 1, ∀i, x îk ≤ 1, ∀k,   k∈J0  i∈I    j  j j j  îk ≥ yîk , x îk ≥ zîk , ∀i, k, x   j   x  ˆ ≥ v ˜ , ∀i,  i i0 X   X X   j j  y ˆ ≤ 1, y ˆ ≤ 1,  i0 ik  i∈I j j j i∈I k∈J ˆ ,y ˆ , zˆ , v ˜ X Xj = x   j   yîk Bk rik ≥ di , ∀i,         k∈J0     X j       z ˆ s ≤ S , ∀i, k,   i i ik       k∈J   0 X           v˜i si ≤ S0 ,   i∈I (13) ˜ only makes sense for BS It should be noted that, however, v ˜ actually vanishes. (i.e., slice j = 0). For slice j ∈ J , v For each slice j ∈ J0 , the corresponding utility function can be identified as                       

6

(15), since for any feasible solution, the penalty term added to the objective is actually equal to zero [11]. Then ADMM consists of the following sequential iterations: [t+1]

ˆ j , ˆzj , v ˜ }j∈J0 := arg min{gj (ˆ ˆ j , ˆzj , v ˜) {ˆ xj , y xj , y X j[t] j X [t] j[t] j [t] + λik (ˆ xik − xik ) + µik (ˆ yik − y˜ik ) i,k

i,k

ρX j [t] (ˆ xik − xik )2 + − + 2 i,k i,k ρX j ρX j [t] 2 [t] + (ˆ yik − y˜ik ) } + (ˆ zik − z˜ik )2 } 2 2 X

[t] z˜ik )

j[t] j νik (ˆ zik

i,k

i,k

j

˜ y

[t+1]

i,k

2

ˆ j , ˆzj , v ˜) = gj (ˆ xj , y

j

j

+

j

ˆ ,ˆ ˜ ) ∈ Xj (ˆ x ,y z ,v

j

i



XX

νik (ˆ zik

− xik )2

min subject to

j

j

ˆ , zˆ , v ˜) gj (ˆ x ,y

j∈J0 x ˆjik =

(15a)

j j xik , yîk = y˜ik , zîk = z˜ik , ∀j, i, k. (15b)

It can be seen that in (15), the objective function is separable across all slices but the consensus constraints are still coupled on slices. Next, we derive a distributed consensus optimization via ADMM. The augmented Lagrangian [11] for (15) can be derived as ˆ , zˆ, v ˜ }, {x, y ˜ , z˜}, {λ, µ, ν}) = Lρ ({ˆ x, y

X

j∈J0

+

X

X

λjik (ˆ xjik − xik ) +

j∈J0 i∈I,k∈J0

X

X

+

X

j µjik (ˆ yik − y˜ik )

j∈J0 i∈I,k∈J0 j j νik (ˆ zik

XX ρ j

i,k

2

j[t+1]

(ˆ zik

(18)

− y˜ik )2 j[t]

j[t+1]

− z˜ik )

i,k

− z˜ik )2

λj[t+1] := λj[t] + ρ(ˆ xj[t+1] − x[t+1] ) ˜ [t+1] ) µj[t+1] := µj[t] + ρ(ˆ yj[t+1] − y ν

j[t+1]

:= ν

j[t]

j[t+1]

+ ρ(ˆz

[t+1]

− ˜z

(19)

),

where, the superscript [t] denotes the iteration index. The first step (17) and third step (19) can be completely seperable across slices when finding the optimal local allocation variables and local dual variables (i.e., Lagrange multipliers). The second step (18), however, needs to be implemented in VRM. Next, we will discuss each step respectively.

ˆ j , zˆj , v ˜) gj (ˆ xj , y B. Local Resource Allocation Variables Update

ρ X X (ˆ xjik − xik )2 + − z˜ik ) + 2 j∈J0 i∈I,k∈J0 j∈J0 i∈I,k∈J0 ρ X X ρ X X j j 2 + (ˆ yik − y˜ik ) + (ˆ zik − z˜ik )2 , 2 2 j∈J0 i∈I,k∈J0 j∈J0 i∈I,k∈J0 (16) where ρ is called the penalty parameter, and λ = {λjik }, j µ = {µjik } and ν = {νik } are the associated dual variables with respect to (12b). Compared to the standard Lagrangian, the addition of the quadratic penalty term in objective can improve the conditioning of the problem and thus improve the performance of the iterative method [26]. Note that, minimizing (16) is equivalent to solving the original problem X

j[t+1]

j[t]

i,k

j

and j

2

− y˜ik )

µik (ˆ yik

(ˆ yik

z˜[t+1] := arg min

+∞

otherwise, (14) where as defined in (8) and (9), uij is obviously linear with ˆ j , zˆj , v ˜ ), thus convex. Problem (12) can be respect to (ˆ xj , y equivalently written as X

i,k

j[t+1]

XX

j[t+1]

(ˆ xik

:= arg min

XX ρ

− xik )

i,k

j

 X  − uij

j[t+1]

λik (ˆ xik

j

XX ρ

j[t]

XX

x[t+1] := arg min +

(17)

The first step (17) of the ADMM is completely decoupled into J + 1 specific subproblems, one for each slice. After eliminating the constant term, the first step (17) for slice j is equivalent to solving the following problem at iteration t + 1: min

−

X

uij

i∈I

Xρ j [t] j[t] j [ (ˆ x − xik )2 + λik x îk ] 2 ik i,k Xρ j [t] j[t] j y − y˜ik )2 + µik yîk ] + [ (ˆ 2 ik i,k Xρ j [t] j[t] j + z − z˜ik )2 + νik zîk ] [ (ˆ 2 ik +

subject to

(20)

i,k j

ˆ j , zˆj , v ˜ ) ∈ Xj , (ˆ x ,y



which is a convex problem due to its quadric objective and convex feasible set. Primal-dual interior-point methods can solve it efficiently [23]. Due to the limited space, the details of these methods are omitted here. C. Global Resource Allocation Variables Update Now we focus on the global variables update, i.e., the second step (18). Due to the additional quadratic regularization term in the augmented Lagrangian (16), the unconstrained ˜ and problems (18) are strictly convex with respect to (x, y ˜z). By setting the gradients to zero, we can have 1 X j[t+1] j[t] [ˆ xkl + (1/ρ)λkl ], ∀k, l, J +1 j∈J0 1 X j[t+1] j[t] [t+1] [ˆ ykl + (1/ρ)µkl ], ∀k, l, y˜kl = J +1 j∈J0 1 X j[t+1] [t+1] j[t] z˜kl = [ˆ zkl + (1/ρ)νkl ], ∀k, l. J +1 [t+1]

xkl

=

j∈J0

From initializing the dual variables at zeros, it follows that P P P j[t] j[t] j[t] j∈J0 νkl = 0, ∀k, l, at j∈J0 µkl = 0, j∈J0 λkl = 0, each iteration t [26]. Therefore, (21) reduces to 1 X j[t+1] [t+1] xkl = xˆkl , ∀k, l, J +1 j∈J0 1 X j[t+1] [t+1] yˆkl , ∀k, l, y˜kl = (22) J +1 j∈J0

[t+1]

z˜kl

ADMM process, we have to recover the optimal fractional ∗ solutions x∗ = {x∗ij } and caching variables z ∗ = {zij } from the ADMM process into binary variables. As shown in [27], there will be “ties” when multiple slices achieve positive fractional x∗ij on users i, due to the assumption that one user can only associate with one slice. Clearly, if there exist no ties on any user, the proposed algorithm gives the optimal solution to problem (10). However, in case of ties, it is necessary to break these ties to obtain an integer association. Here, we adopt the approach in [28], i.e., computing the marginal utility for each slice j on user i. Then, the integer association variables can be recovered as follows, x∗il

(21)

1 X j[t+1] zˆkl , ∀k, l, = J +1 j∈J0

which represents that global variables are the average of local copies across all slices. For practical implementation, it can be interpreted as gathering all updated local copies from slices and averaging them out in VRM. Note that, (22) does not involve dual variables, which significantly decreases signaling overhead in information exchange. D. Dual Variables Update The final step (19) involves the dual variables update with a step size equal to the augmented Lagrangian parameter ρ. It is demonstrated in [11] that by updating variables λ, µ and ν in this way, after each sequence of updating (17), (18) and (19), the solution satisfies the second dual feasibility condition (obtained by taking gradients with respect to global variables). The first dual feasibility (obtained by taking gradients with respect to local variables) and primal feasibility actually do not hold. However, the dual residual and primal residual converge to zero, namely, the first dual feasibility and primal feasibility are achieved with t → ∞. E. Recovery of Association Variables As described above, our proposed algorithm actually consists of two procedures: the first step is the relaxation of binary variables to continuous variables, and the second step is the ADMM process. Therefore, upon the convergence of the

7

=

(

1, Qil = maxk {Qik , k ∈ J0 } 0, otherwise,

and Qil > 0,

(23) where, Qik is the first partial derivation of uik with respect to xik . zil∗ = 1 makes sense only when x∗il = 1. Therefore, given that x∗il = 1, we set zil∗ = 1 unless zil∗ takes the zero value from the ADMM process. F. Overall Algorithm: Convergence and Complexity As described in [26], the convergence of the ADMM process is regulated by the penalty parameter ρ. As can be seen in (17) and (19), ρ not only imposes penalty on consensus constraint violation, but also serves for the dual variable update. It is shown in [11] that ρ is proportional to the residual of the dual feasibility, namely, a larger value of ρ will result in increased dual residual. On the contrary, with the increase of ρ, the primal dual converges to zero fast. Therefore, a proper choice of ρ actually affects the convergence of the ADMM process. In Section VI, we will show the convergence of the proposed algorithm via various values of parameter ρ. Next, we compare the complexity of the centralized algorithm (i.e., without distributed optimization at each transmitter) and the proposed distributed algorithm. Assume that the input for the centralized algorithm is Θ. Both CSI and content distribution information from each link is updated to VRM, thus the size of Θ is 2I × (J + 1). For each input Θ, the centralized algorithm employs the primal-dual interior-point method to solve the convex problem, and thus the complexity is O((2I)k (J + 1)k ) with k > 0 (k > 1 represents a polynomial time algorithm while k = 1 a linear algorithm). The input with respect to each transmitter is assumed to be θ for the proposed distributed algorithm. In the first step (local variables update), since each transmitter is only responsible for solving its corresponding subproblem, the size of θ is 2I × 1 and the time complexity is O((2I)k ) with k > 0. In the second step (global variables update), let g be the the number of elementary steps needed for calculating global variables. The complexity for the second step is thus calculated as I(J + 1)g. In the third step (dual variables update), let d be the the number of elementary steps needed for updating dual variables, and the time complexity is Id. Accordingly, the sum complexity with respect to each iteration is O((2I)k ) + I(J + 1)g + Id = O((2I)k ); considering that



Tmax is the number of iterations that algorithm converges, the overall complexity reaches Tmax O((2I)k ).

8

TABLE I: Simulation Parameters Uplink bandwidth

5 MHz

Downlink bandwidth

10 MHz

VI. S IMULATION R ESULTS AND D ISCUSSIONS

Path loss

35.3 + 37.6log(d(m))

In this section, we show the performance of proposed ADMM-based distributed algorithm with caching and D2D via simulation results and study the impact of the following parameters: 1) the number of users, 2) the average required data rate per user, 3) the number of content types, and 4) the average size of all contents. We use the following two metrics to measure the performance of the proposed algorithm: (i) total utility of MVNOs and (ii) total reduced backhaul usage. Meanwhile, for performance comparison, three other algorithms are also evaluated. These algorithms are listed as follows: 1) Centralized algorithm with (w.) caching and D2D, which collects CSI and content distribution information from all slices (transmitters) and then executes virtual resource allocation in a centralized manner. 2) Distributed algorithm w. caching and D2D, which is the proposed algorithm in this paper. 3) Distributed algorithm without (w.o.) caching but w. D2D, which is also based on ADMM but cannot save backhaul bandwidth through caching popular contents. 4) Distributed algorithm w. caching but w.o. D2D, which is also based on ADMM but cannot support D2D communications in the proposed framework.

Multiple-path fading

Exponential distribution with unit mean

Shadowing

Log-normal distribution with standard deviation of 8dB

Noise spectral density

-174 dBm/Hz

BS Tx power

46 dBm

D2D Tx power

24 dBm

300000

Total utility of MVNOs (units)

250000

200000

150000

100000

Centralized algorithm w. caching and D2D Distributed algorithm w. caching and D2D Distributed algorithm w.o. caching but w. D2D Distributed algorithm w. caching but w.o. D2D

50000

0 0

5

10

15

20

25

30

35

Number of users

(a) 160

A. Simulation Parameters Consider a single cell, with a radius of 500m. We adopt the clustered-based distribution model in [29], where multiple users are located within one cluster with a radius of 50m. Moreover, the well-known Monte Carlo methods are employed, and all results are averaged over 500 random dropping. Assume that there exist 4 MVNOs in the infrastructure, and each user subscribe to any MVNO with a probability of 25%. In addition, each D2D transmitter has the equal probability of holding one of all C kinds of contents. For BS, since it has sufficient memory, it is assumed that each content is held by BS with a probability of 50%. The interval of each period is set to 1s. To estimate the net gain from caching contents, the Zipf popularity distribution is adopted, with ǫ = 1.5. In our simulations, we take 1) αi = 10 units/Mbps, ∀i ∈ I, 2) β0 = 30 units/MHz, βj = 1000 units/MHz, ∀j ∈ J , 3) γj = 10 units/Mbps, ∀j ∈ J0 , 4) φi = 100 units/Mbps, ∀i ∈ I and 5) ψi = 10 units/Mb, ∀i ∈ I. Other parameters are summarized in Table I. B. Simulation Results Fig. 3 shows the impact of the number of receivers on the performance of different algorithms. In this scenario, there are 30 D2D transmitters, the average data rate requirement is 2 Mbps, the average size per content is 2 Mb, and the number of content types is 2. As Fig. 3(a) shows, the total utility obtained by MVNOs increases with the increase of the number of users. That is due to the fact that a network incorporating

Total reduced backhual usage (Mbps)

140

120

100

80

60 Centralize algorithm w. caching and D2D Distributed algorithm w. caching and D2D Distributed algorithm w.o. cahing but w. D2D Distributed algorithm w. caching but w.o. D2D

40

20 0

5

10

15

20

25

30

35

Number of users

(b)

Fig. 3: (a) The total utility of MVNOs and (b) the total reduced backhaul usage with different numbers of users. (There are 30 D2D transmitters, the average data rate requirement per user is 2 Mbps, the average size per content is 2 Mb, and there are 2 types of contents.)

more receivers will introduce multi-user diversity gain. Note that, in the distributed algorithm w. caching but w.o. D2D (i.e., Algorithm 4), the caching functions are only available in the BS due to the non-existence of D2D communications. Thus, Algorithm 4 will result in the least utility compared to other three algorithms. Similarly, in Fig. 3(b), Algorithm 4 gets the least backhaul bandwidth savings compared to other three algorithms. In Fig. 4, we compare the behaviour of four algorithms at different average data rate requirements per user. In this scenario, there are 10 D2D transmitters and 20 requesting



9

600000

90000

80000 500000



70000 Centralized algorithm w. caching and D2D 60000

Distributed algorithm w. caching and D2D Distributed algorithm w. o. caching but w. D2D Distributed algorithm w. caching but w.o. D2D

50000

40000

30000

400000

300000 Centralized algorithm w. caching and D2D Distributed algorithm w. caching and D2D Distributed algorithm w.o. caching but w. D2D Distributed algorithm w. caching but w.o. D2D

200000

20000 100000 10000 0 0

0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

4.0

4.4

0

2

4

4.8 5.0

6

8

10

12

14

15

14

15

Number of content types

Average required data rate per user (Mbps)

(a)

(a) 100 140 80

Total reduced backhaul usage (Mbps)

Total reduced backchaul usage (Mbps)

120

100

80

60


20

0

0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

60

40


120

100

80

60

40 4.0

4.4

4.8 5.0

0

2

4

6

8

10

12

Number of content types

Average required data rate per user (Mbps)

(b) (b)

Fig. 4: (a) The total utility of MVNOs and (b) the total reduced backhaul usage with different average required data rates per user. (There are 10 D2D transmitters and 20 requesting users, the average size per content 2 Mb, and there are 5 types of contents.)

users, the average size per content is 2 Mb, and the number of content types is 5. Fig. 4(a) shows that the total utility obtained by MVNOs declines as the average required data rate increases. This is because a network with larger average data rate requirement tends to be more fair across users compared to that with smaller requirement, thus decreasing the total utility seen by MVNOs. Similarly, all four algorithms will save less backhaul bandwidth usage as the requirement increases. Fig. 5 shows the impact of the number of content types on the performance of different algorithms. In this scenario, there are 10 D2D transmitters and 10 requesting users, the average data rate requirement per user is 2 Mbps, and the average size per content is 2 Mb. From Fig. 5(a) and Fig. 5(b), we can see that both total utility and saved backhaul bandwidth decrease as the number of content types increases. This is because more content types will lead to the case that a requesting user is unlikely to exactly receive the specific content from neighboring transmitters. Note that, it is based on the assumption that the storage is limited. Meanwhile, more content types will result in reduced popularity of all contents according to Zipf popularity distribution, thus decreasing caching gain. In Fig. 6, we compare the performance of different algo-

Fig. 5: (a) The total utility of MVNOs and (b) total reduced backhaul usage with different numbers of content types. (There are 10 D2D transmitters and 10 requesting users, the average data rate requirement per user is 2 Mbps, and the average size per content is 2 Mb.)

rithms with different average sizes of contents. In this scenario, there are 10 D2D transmitters and 20 requesting users, the average data rate requirement is 2 Mbps, and the number of content types is 2. Fig. 6(a) and Fig. 6(b) show that both total utility and saved backhaul bandwidth are almost proportional to the average size of contents for Algorithm 1 and Algorithm 2. However, for Algorithm 3, both performance metrics almost remain constant, which can be interpreted as that the majority of saved backhaul bandwidth consumption comes from caching popular contents, rather than directly fetching existing contents from BS and D2D transmitters. Fig. 7 demonstrates the convergence of the proposed algorithm with ρ = 500, 550, 600. It is observed that the proposed algorithm with different values of ρ eventually converges to the same total utility. Meanwhile, all the curves converge to a stable solution monotonically within 20 iterations. The difference of values for ρ only takes effect on the speed of convergence but not on the value of stable solution. It can be seen that ρ = 600 is the fastest in converging to the stable solution, while ρ = 500 is the slowest. Nevertheless, the difference is not significant.



1000000 900000


800000 700000 600000 500000 400000 Centralized algorithm w. caching and D2D Distributed algorithm w. caching and D2D Distributed algorithm w.o. caching but w. D2D Distributed algorithm w. caching but w.o. D2D

300000 200000 100000 0 0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Average size per content (Mb)

10

to build a 15 × 1 vector, of which each element is 1 bit, to indicate which content is both cached in the transmitter and required by the receiver. Therefore, there are totally (20 × 21)channels × 15bits/channel = 6300bits to indicate the content distribution information. The amount of information is thus (3360 + 6300)bits = 9660bits. For the distributed algorithm, each transmitter needs to update a local 20×1 vector, of which each entry is 1bit, to VRM. The amount of information is thus equal to (20 × 21)bits = 420bits. The proposed algorithm typically converges at 15 iterations, reaching (420 × 15)bits = 6300bits information updating.

(a)

VII. C ONCLUSIONS

AND

F UTURE W ORK

100

Total reduced backhaul usage (Mbps)

80

60

40


120

100

80

60

40 0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Average size per content (Mb)

(b)

Fig. 6: (a) The total utility of MVNOs and (b) total reduced backhaul usage with different average sizes per content. (There are 10 D2D transmitters and 20 requesting users, the average data rate requirement per user is 2 Mbps, and there are 2 types of contents.) 120000

ACKNOWLEDGMENT

100000


In this paper, we proposed a novel framework with information-centric wireless virtualization and D2D communications. In this framework, we studied the virtual resource allocation and caching issues. Different from existing works, we considered the radio resource allocation and caching decisions not only in the BS but also in potential D2D users. Considering that the computing complexity and signaling overhead are prohibitively high in the centralized algorithm, we used ADMM algorithm to decouple the coupling variables and split the optimization problem into multiple subproblems. By this means, multiple separable subproblems can be solved in the corresponding transmitters in a distributed manner. Simulation results showed that the proposed framework is able to take the advantages of both information-centric wireless virtualization and D2D communications. The total utility of MVNOs can be improved and the backhaul usage can be reduced significantly in the proposed scheme. In addition, the convergence of proposed distributed algorithm was also demonstrated. Future work is in progress to consider imperfect CSI in our proposed framework.

We thank the reviewers for their detailed reviews and constructive comments, which have helped to improve the quality of this paper.

80000

60000

40000

R EFERENCES

Centralized algorithm w. caching and D2D Distributed algorithm w. caching and D2D, ρ = 500

20000

Distributed algorithm w. caching and D2D, ρ = 550 Distributed algorithm w. caching and D2D, ρ = 600 0

0

5

10

15

20

25

30

35

40

45

50

Number of iterations

Fig. 7: Convergence of the ADMM-based algorithm under different values of ρ. C. Signaling Overhead Assume that there are 20 D2D transmitters, 20 D2D receivers, 15 types of contents and one BS in the infrastructure. For each channel between user and transmitter, we use 8bits to represent its CSI. Thus, the amount of CSI across networks is 8bits/channel × 20 × (20 + 1)channels = 3360bits. Likewise, for each receiver and transmitter pair, we need

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11

Kan Wang received the B.S. degree in broadcasting and television engineering from Zhejiang University of Media and Communications, Hangzhou, China, in 2009. He is currently working toward the Ph.D. degree in military communications with the State Key Lab of ISN, Xidian University, Xi’an, China. From Oct. 2014 to Oct. 2015, he was also with Carleton University, Ottawa, ON, Canada, as a visiting scholar funded by CSC. His current research interests include 5G cellular networks, resource management, and interference alignment.

F. Richard Yu (S’00-M’04-SM’08) received the PhD degree in electrical engineering from the University of British Columbia (UBC) in 2003. From 2002 to 2006, he was with Ericsson (in Lund, Sweden) and a start-up in California, USA. He joined Carleton University in 2007, where he is currently an Associate Professor. He received the IEEE Outstanding Leadership Award in 2013, Carleton Research Achievement Award in 2012, the Ontario Early Researcher Award (formerly Premiers Research Excellence Award) in 2011, the Excellent Contribution Award at IEEE/IFIP TrustCom 2010, the Leadership Opportunity Fund Award from Canada Foundation of Innovation in 2009 and the Best Paper Awards at IEEE ICC 2014, Globecom 2012, IEEE/IFIP TrustCom 2009 and Int’l Conference on Networking 2005. His research interests include cross-layer/cross-system design, security, green IT and QoS provisioning in wireless-based systems. He serves on the editorial boards of several journals, including Co-Editorin-Chief for Ad Hoc & Sensor Wireless Networks, Lead Series Editor for IEEE Transactions on Vehicular Technology, IEEE Communications Surveys & Tutorials, EURASIP Journal on Wireless Communications Networking, Wiley Journal on Security and Communication Networks, and International Journal of Wireless Communications and Networking. He has served as the Technical Program Committee (TPC) Co-Chair of numerous conferences. Dr. Yu is a registered Professional Engineer in the province of Ontario, Canada.

Hongyan Li (M’08) received the M.S. degree in control engineering from Xi’an Jiaotong University, Xi’an, China, in 1991 and the Ph.D. degree in signal and information processing from Xidian University, Xi’an, in 2000. She is currently a Professor with the State Key Laboratory of Integrated Service Networks, Xidian University. Her research interests include wireless networking, cognitive networks, integration of heterogeneous network, and mobile ad hoc networks.


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Inflight Broadband Connectivity Using Cellular Networks - IEEE Xplore

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Software-defined and Virtualized Cellular

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Optical Networks [Book Reviews] - IEEE ... - IEEE Xplore

The IEEE Neural Networks Society - IEEE Xplore

Neural Networks, IEEE Transactions on - IEEE Xplore

mobile social networks - IEEE Xplore