Network utility optimizationbased joint user association and content placement in heterogeneous networks
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Abstract
The rapid growth of traffic demands has posed challenges and difficulties on both the radio access networks (RANs) and the backhaul links. While heterogeneous networks (HetNets) are expected to offer diverse radio access capabilities and improve the transmission performance of user equipments (UEs) significantly through integrating various RANs efficiently, the backhaul links may still experience challenges in offering quality of service (QoS) guaranteed services to UEs. To tackle these problems, caching technology, more specifically, caching user contents at the infrastructures of different RANs is proposed as an effective approach. In this paper, we consider the joint user association and cache content placement problem in cacheenabled HetNets. Stressing the tradeoff between user download delay and caching cost, we introduce the concept of utility function which characterizes the joint network performance as the weighted sum of user download delay and the caching cost and formulate the joint user association and cache content placement problem as a network utility optimization problem. As the formulated optimization problem is a nonlinear integer optimization problem which cannot be solved conveniently using traditional optimization tools, we transform the original optimization problem equivalently into three convex subproblems by applying Lagrange partial relaxation and McCormick envelopes, and then propose an iterative algorithm. Within each iteration, for a given set of Lagrange multipliers, the three subproblems are solved respectively by means of the modified KuhnMunkres (KM) algorithm and the locally optimal solutions can be obtained, based on which the Lagrange multipliers can be updated through applying subgradient method. Simulation results demonstrate the effectiveness of the proposed algorithm.
Keywords
Heterogeneous networks User association Cache content placement User download delay Caching cost1 Introduction
The rapidly growing requirements for highspeed mobile broadband applications, such as video streaming and online games, have posed great challenges on both radio access networks (RANs) and core networks. By integrating different RANs in an efficient and coordinated manner, heterogeneous networks (HetNets) are expected to improve the transmission performance of user equipments (UEs) significantly [1]. In HetNets, UEs should associate with the infrastructures of the RANs, such as base stations (BSs) of cellular networks or the access points (APs) of wireless local area networks (WLANs) before conducting information transmissions. Different user association or cell selection strategies may result in different network transmission performance and quality of service (QoS) to users due to the heterogeneity of RANs.
While various user association schemes have been proposed for HetNets [2, 3, 4, 5, 6, 7] and effectively enhanced the transmission performance of the RANs, the backhaul links may still cause challenges and difficulties in offering QoS guaranteed services to UEs. In particular, the demanding requirements of user services, such as multimedia streaming, web browsing applications, and socially interconnected networks, may cause network congestion and long transmission delay in backhaul links [8]. One promising approach for achieving backhaul offloading and reducing user download latency is to deploy cache storages at the mobile edge networks, e.g., the BSs or APs of the HetNets [9, 10].
It has been shown in previous research works that the transmission performance of UEs can be enhanced significantly by caching contents at the infrastructures of the RANs [11, 12, 13, 14, 15, 16]; hence, designing reasonable cache content placement schemes by taking into account both caching constraints and possible performance enhancement is of particular importance. However, while most of previous research works study user association problem or cache content placement problem independently, these two problems are indeed closely related. For further enhancing the network performance and user QoS, it is highly desirable to jointly design user association and content placement scheme in HetNets, which has been demonstrated in some recent research works [17, 18, 19].
Besides, it should be noted that the cost of storing contents at the BSs or APs can be relatively high. More specifically, caching a large number of files at the BSs or APs requires a large memory size, which may be expensive. Furthermore, accessing the requested contents from the caches of BSs or APs also results in content fetching delay, which may vary depending on the accessing BSs or APs.
In this paper, we consider the joint user association and content placement problem in cacheenabled HetNets and define a utility function as the weighted sum of user download delay and caching cost; the joint user association and cache content placement problem is then formulated as a network utility minimization problem. The original optimization problem is then decomposed into three subproblems based on McCormick envelopes and Lagrange partial relaxation, an iterative algorithm is designed to obtain the optimal strategy for joint user association and content placement.

We study the joint user association and content placement problem of cacheenabled HetNets which consists multiple RANs. To achieve joint resource management and performance enhancement of various access networks, we propose a joint resource management architecture, based on which a joint user association and content placement algorithm is designed.

The problem of user association or content placement in HetNets has been studied separately in previous works [2, 3, 4, 5, 6, 7] and [11, 12, 13, 14, 15, 16]. In this paper, we jointly consider the user association and content placement problem in cacheenabled HetNets and design jointly optimal strategies so that the overall performance of the networks can be maximized.

Stressing the tradeoff between user download delay and caching cost, we characterize the joint network performance as the weighted sum of user download delay and the caching cost via applying the concept of utility function and formulate the joint user association and content placement problem as a network utility minimization problem.

Since the formulated optimization problem is a nonlinear integer optimization problem which cannot be solved conveniently using traditional optimization tools, we apply Lagrange partial relaxation and McCormick envelopes method and transform the original optimization problem equivalently into three convex subproblems, which can then be solved by a proposed iterative algorithm. Within each iteration, for a given set of Lagrange multipliers, the three subproblems are solved respectively by means of the modified KuhnMunkres (KM) algorithm and the locally optimal solutions can be obtained, based on which the Lagrange multipliers can be updated through applying subgradient method.
The rest of the paper is organized as follows. Section 2 presents an overview of related works. The system model considered in this paper and the proposed joint resource management architecture are described in Section 3. The proposed optimization problem is formulated in Section 4. In Section 5, the solution to the formulated optimization problem is presented. Simulation results are discussed in Section 6. Finally, the conclusions are drawn in Section 7.
2 Related works
In this section, we present an overview of related works, including user association schemes and content placement schemes of HetNets.
2.1 User association schemes of HetNets
In HetNets, UEs with multiple interfaces are allowed to associate with the BSs or APs of different RANs. The design of user association schemes in HetNets is of particular importance which should account for both the wireless channel and interference characteristics between UEs and the infrastructures of RANs as well as the heterogeneity of RANs.
In the past few years, user association or cell selection have been studied for HetNets [2, 3, 4, 5, 6, 7]. In [2], the authors address the user association problem in the downlink transmissions of a multitier HetNet and propose a unified distributed algorithm, which aims at maximizing the sum utility of longterm rate and minimizing global outage probability at the same time. In [3], the authors examine the latency and reliability issues of fiberwireless (FiWi)enhanced LTEA HetNets and propose a backhaulaware user association algorithm to achieve intercell load balancing and network performance improvement. The authors in [4] investigate the user association and resource allocation problem in HetNets and propose an optimal user association and resource allocation algorithm which minimizes the average packet delay of user traffic across the network.
The authors in [5] study user association and resource allocation problem in multiantenna HetNets and propose a jointly optimal scheme aiming at maximizing the network utility which is defined as a function of user data rate and associate probability. In [6], the authors consider the joint optimization problem of user association, subchannel allocation, and power allocation for downlink transmission in multicell multiassociation orthogonal frequency division multiple access (OFDMA) HetNets with the objective of maximizing the weighted sumrate and propose an alternating optimization method to solve the joint optimization problem. The authors in [7] deal with the problem of user association in HetNets and propose a novel collaborative filtering (CF)based wireless network recommendation system, which involves social interactions among UEs. A satisfaction game is formulated to deal with this problem, and a utility function is defined to measure a UE’s satisfaction.
2.2 Content placement schemes of HetNets
Content placement is fairly critical in reaping the benefit brought by caching. In cacheenabled HetNets, a UE can fetch contents from multiple infrastructures of RANs as the coverage of several BSs and APs overlaps and hence different cache content placement strategies can affect user QoS as well as network transmission performance.
In recent years, content deployment strategies with different optimization objectives in HetNets have been studied [11, 12, 13, 14, 15, 16]. The authors in [11, 12] aim to maximize the cache hit probability, defined as the probability that a file requested by the typical user is delivered successfully to the user, to achieve the optimal cache content placement strategies. In [11], the authors address the content placement problem in cacheenabled multitier HetNet and the optimal tierlevel placement policies are yielded which achieve the maximal hit probability over content placement probabilities. The authors in [12] study the effect of retransmissions on the optimal cache placement policy for both static and mobile user scenarios in cacheenabled small cell networks and determine the optimal caching probability of the files that maximizes the hit probability. In [13], the authors consider a caching system consisting of a video retailer (VR) and a number of network service providers (NSPs) aiming to achieve the maximal network profit. The caching strategy is obtained by modeling the system within the framework of a Stackelberg game and establishing the profit models for both the VR and the NSPs.
The authors in [14] consider the joint content placement and service scheduling problem in femtocell caching networks. To maximize the traffic volume served from the cache, the authors formulate the femto BSs’ decisionmaking process as an Markov decision process (MDP) and develop an efficient online randomized algorithm to achieve the optimal content placement and service scheduling strategy. In [15], the authors investigate the content placement problem in a HetNet where a tier of multiantenna macro BSs (MBSs) is overlaid with a tier of helpers with caches and propose an optimal content placement strategy which maximizes the successful offloading probability of the MBSs. The authors in [16] study the cache content placement problem in caching enabled small cell networks to minimize the average backhaul load subject to the cache capacity constraints. The optimization problem is formulated and solved to obtain the optimal cache content placement strategy.
Most of the previous works focus on either user association scheme or content placement scheme design in HetNets. Since user association strategy over the network may affect the content placement design significantly, it is highly desirable to jointly design user association and content placement strategy in HetNets in order to further enhance the network performance and user QoS. This has been demonstrated in some recent research works [17, 18, 19]. The authors in [17] study the problem of joint user association and caching placement in multicastaided HetNets and propose a joint cooperative caching and multicast scheduling scheme to minimize the system power consumption. The formulated joint optimization problem is then solved by a distributed algorithm to reduce the signaling and computation complexity. In [18], the authors consider the caching and user association problem in a HetNet with wireless backhaul and formulate the problem as a mixed discretecontinuous optimization to minimize the total time that the HetNet must be active in order to satisfy the average requests for given bandwidth and cache resources. They show that the optimal caching is to store the most popular files at each pico BS and the optimal user association strategy is of a threshold form. The authors in [19] consider the joint design of caching and user association policy in a cacheenabled HetNet. Taking into account the characteristics of wireless channels and backhaul links, the authors propose an average download delay minimizationbased joint caching and user association strategy.
Meanwhile, we should note that the cost of caching contents at the BSs or APs can be high, which may affect the user association and content placement decisions. More specifically, the more contents stored in the caches of the RANs, the more cost is required to cache the files, which may weaken the benefits achieved from caching severely. Furthermore, fetching contents from caches of different BSs or APs may result in different content fetching delay. Therefore, different from previous works, the joint user association and cache content placement problem for cacheenabled HetNets is studied in this paper by emphasizing the tradeoff between user download delay and caching cost. We define the network utility of the HetNet as a weighted sum of file downloading delay and caching cost and find the optimum user association and content placement solution to optimize the utility.
3 System model and proposed joint resource management architecture
In this section, we describe the system model considered in this paper and propose a joint resource management architecture.
3.1 System model
We consider the downlink transmission in a HetNet consisting of M_{1} cellular BSs, M_{2} WLAN APs, and N UEs, where UEs in the network may access a BS or an AP for information interactions. For convenience, we introduce the concept of general AP (GAP) which can be either a BS or an AP and indexed by i, where i=1:M_{1} is a BS and i=M_{1}+1:M is an AP, where M=M_{1}+M_{2}.
To allow resource sharing among multiple UEs accessing one GAP, we assume that the bandwidth resource of one GAP is divided into a number of subchannels with equal bandwidth and each UE can only be allocated one subchannel. Let \({W_{i}^{\max }}\) denote the available bandwidth of GAP i and W_{ i } denote the bandwidth of each subchannel of GAP i, the maximum number of users associated to GAP i can be calculated as \(A_{i}=\left \lfloor \frac {W_{i}^{\max }}{W_{i}}\right \rfloor \).
In this paper, we assume the received signal of UE j from GAP i denoted by y_{ ij } can be expressed as \({y_{ij}} = \sqrt {{p_{i}}{g_{ij}}} {s_{ij}} + {z_{ij}}\), where s_{ ij } represents the transmitted data symbol of GAP i when transmitting to UE j and p_{ i } denotes the transmission power of GAP i, g_{ ij } represents the channel gain of the link from GAP i to UE j, \({g_{ij}} = {l_{ij}}g_{ij}^{0}\), where l_{ ij } denotes the path loss of the link between GAP i and UE j and \(g_{ij}^{0}\) denotes the slow fading channel coefficient of the link from GAP i to UE j, which is modeled as a Rayleigh distributed random variable, z_{ ij } is the additive white Gaussian noise (AWGN) with zero mean and variance \({\sigma _{ij}^{2}}\).
3.2 Proposed joint resource management architecture
URME is a functional module embedded in each UE. It is responsible for collecting and storing user status information, including channel state information (CSI) and service requirements, and sending the collected information to the associated LRME, which is a functional module deployed in each RAN. LRME is responsible for monitoring and storing network status information, collecting user status information from the associated URMEs, and then sending the network and user status information to the GRME. In practice, an LRME can be integrated to a GAP. GRME is a functional module deployed on top of all the RANs. It receives network and user state information from different LRMEs and conducts the proposed user association and content placement algorithm and sends the strategies to the LRMEs. Upon receiving association and resource allocation strategies from the GRME, the LRMEs conduct the corresponding operations and forward the strategies to the associated URMEs.
It should be mentioned that the information interactions between GRME, LRMEs, and URMEs can be performed over a common control channel. In this paper, we assume that efficient information interactions between GRME, LRMEs, and URMEs can be achieved, and design joint user association and content placement algorithm accordingly.
4 Utility function optimization formulation
In this section, we formulate the joint user association and cache content placement problem in HetNet as a utility optimization problem.
4.1 Objective function
We first consider the download delay for UE j when acquiring file k through GAP i. The main components of the download delay are the wireless transmission delay from the GAPs, the content fetching delay from the caches, and the backhaul delay through the core network, the formulations of which are described in following subsections.
4.1.1 Wireless transmission delay
where \({\sigma _{ij}^{2}}\) denotes the noise power of the link between UE j and GAP i.
4.1.2 Content fetching delay
To access the contents stored at local caches, the content fetching delay, i.e., the time duration required for searching the contents in the cache should be considered. In general, content fetching delay may vary depending on the types of storage devices, the underlying file searching mechanisms, and the amount of caching contents. Referring to [20], we model the content fetching delay as an exponentially distributed random variable and denote \(D_{ijk}^{\text {ca}}\) as the average content fetching delay required when UE j fetching file k from GAP i.
4.1.3 Backhaul transmission delay
When the contents users request cannot be fetched from local caches, the users should download the requested contents from the core network through backhaul links, thus resulting in backhaul transmission delay.
where H_{ il } denotes the distance between the lth hop node and the (l+1)th hop node of the backhaul link between GAP i and the gateway and v is the propagation speed of the wired link.
where κ_{ il }, a_{ il }, and ϖ_{ il } are constants, representing the processing capability of the lth hop node in the backhaul link of GAP i.
where ρ_{ i } denotes the unit price of caching contents at GAP i.
where λ is a weighting factor.
4.2 Optimization constraints
To minimize the network utility in terms of joint user association and cache content placement strategies, a number of optimization constraints have to be considered. In this subsection, we discuss the optimization constraints.
4.2.1 Transmission rate constraint
4.2.2 Maximum cache capacity constraint
4.2.3 User association constraints
4.3 Optimization problem
Through solving above optimization problem, we can obtain the optimal joint user association and cache content placement strategies.
5 Solution of the optimization problem
The optimization problem formulated in (18) is a nonlinear integer optimization which cannot be solved conveniently using traditional optimization tools. In this section, we apply Lagrange partial relaxation and McCormick envelopes to obtain the Lagrangian dual problem. Benefited from the McCormick envelopes, the coupling among optimization variables in the optimization problem is removed; hence, we will be able to equivalently transform the optimization problem into of three subproblems. To jointly calculate the optimization variables and the Lagrange multipliers contained in the three subproblems, we propose an iterative algorithm in which given a set of Lagrange multipliers, the three subproblems are solved respectively by means of the modified KM algorithm and the locally optimal optimization variables can be obtained, based on which the Lagrange multipliers can be updated through applying subgradient method. The detail process will be described in this section.
5.1 Equivalent transformation of original optimization problem
The tight coupling of the user association variables and the content placement variables in the objective function in (18) causes the difficulties in solving the problem. In this subsection, by introducing new variables and applying Lagrange partial relaxation and McCormick envelopes, the original optimization problem is equivalently transformed into three subproblems.
5.1.1 Introduction of new variable
5.1.2 Lagrangian dual problem formulation
5.1.3 Subproblem formulation
5.2 Proposed iterative method
To obtain the optimal solution of the subproblems SP1, SP2, and SP3, the Lagrange multipliers should be jointly solved together with the optimization variables. To this end, we propose an iterative method, which compute the optimal solution and the Lagrange multipliers of the subproblems iteratively.
5.2.1 KM algorithmbased optimal solutions to the subproblems
It can be shown that for a given set of Lagrange multipliers, the subproblems SP1, SP2, and SP3 are constrained integer optimization problem, which is equivalent to the optimal matching problem in the bipartite graph theory, thus can be solved by applying the classical algorithms such as modified KM algorithm [24]. In this subsection, we assume that the Lagrange multipliers are given and seek for the locally optimal solution to the subproblems based on the modified KM algorithm.
The following are some definitions and a theorem related to modified KM algorithm.
Complete bipartite graph: Given a graph G=(V;E) where V denotes a set of vertices and E denotes a set of edges connecting pairs of vertices. If the set V can be divided into two disjoint and nonempty sets, X and Y, i.e., V=X∪Y and X∩Y=Φ, where Φ denotes the empty set, every edge in E connects one vertex in X to another vertex in Y and no edge connects two vertices of the same set, we call G a complete bipartite graph.
Weighted complete bipartite graph: A complete bipartite graph G=(V;E) is a weighted complete bipartite graph if any edge e_{x,y}∈E connecting x∈X and y∈Y is assigned a nonnegative weight w(x,y).
Maximum matching: A matching H of graph G=(V;E) is defined as a subset H⊆E which meets the condition that for \(\phantom {\dot {i}\!}\forall {e_{x,y}},{e_{x',y'}} \in H \), e_{x,y} and \({e_{x',y'}}\phantom {\dot {i}\!}\) are not adjacent in G. The size of a matching H, denoted by H is defined as the number of edges contained in H. A matching H is called a maximum matching if for any other matching H^{′} of G, the condition H^{′}≤H holds.
Feasible vertex labeling: A real valued function l is called a feasible vertex labeling if for any x∈X and y∈Y, l(x)+l(y)≤w(x,y) holds.
Equality subgraph: If l is a feasible vertex labeling, let G_{ l } denote a subgraph of G, if the condition l(x)+l(y)=w(x,y) holds, then G_{ l } is called the equality subgraph of G with respect to l.
TheoremIf l is a feasible vertex labeling of G and H is an optimal matching of X to Y with H⊆G_{ l }, then H is an optimal assignment from X to Y. Thus, the problem of finding an optimal matching in a complete bipartite graph reduces to the problem of finding a feasible vertex labeling of which the equality subgraph contains an optimal assignment from X to Y.
 1.
Define an initial feasible vertex labeling l(u).
 2.
Given l(u), obtain G_{ l } from G^{0} and determine a maximum matching H of G^{0}.
 3.
If H is an optimal matching of G^{0}, the optimization problem is solved and the optimal user association strategy can be obtained correspondingly.
 4.
If H is not an optimal matching of G^{0}, a vertex x∈V_{1} having not being allocated is selected in G_{ l }, set S={x} and T=Φ.
 5.Let \(N_{G_{l}}(S)\) denote the collection of vertices which connect with S in G_{ l }. If \(N_{G_{l}}(S)\neq T\), go to step 4. Otherwise, \(N_{G_{l}}(S)= T\). Find$$ \Delta=\min_{u,v}\{l(u)l(u)+l(v)w(u,v), u\in S, v\in V_{2}T\} \ $$(32)and define a new labeling \(l^{'}(u)\phantom {\dot {i}\!}\) by$$ l^{'}(u)= \left\{\begin{array}{ll} l(u)\Delta,~\textrm{\(u\in S\)}\\ l(u)+\Delta,~\textrm{\(u\in T\)}\\ l(u), ~\textrm{others.} \end{array} \right. $$(33)
 6.
Replace l(u) by \(\phantom {\dot {i}\!}l^{'}(u)\), go to step 2.
Through conducting above process iteratively, an optimal matching of G^{0} can be obtained corresponding to the optimal user association strategy. Similar methods can be applied to solve the optimization problem SP2 and SP3 and obtain the optimal content placement variable \(\delta _{ik}^{*}\) and the optimal joint variable \(\varphi _{ijk}^{*}\). Both subproblems are constrained integer optimization problem, which can be transformed as an optimal matching problem in the bipartite graph and solved based on the modified KM algorithm.
5.2.2 Updating Lagrange multipliers
where [z]^{+}= max{0,z}, and ε_{1}, ε_{2}, and ε_{3} are the step sizes with respect of μ_{ ijk }(t),υ_{ ijk }(t), and θ_{ ijk }(t), respectively.
Conducting the above process iteratively, we will be able to achieve the convergence of the algorithm [25]. Once the convergence condition meets, we can obtain the globally optimal user association and content placement strategy.
The proposed method is summarized in Algorithm 1.
6 Simulation results
System parameters. The system parameters considered in the simulation
Parameters  Value 

Maximum cache capacity of BS  20 Mbits 
Maximum cache capacity of AP  10 Mbits 
File sizes  9, 8, 10, 9, 8, and 10 Mbits 
Content fetching delay at BS  0.2 s 
Content fetching delay at AP  0.3 s 
Maximum numbers of active users of BS and AP  3 
Minimum data rate requirements of users  1, 2, 0.5, 0.5, 1, and 2 Mbps 
Small scale fading distribution  Rayleigh fading with zero mean and unit variance 
Channel path loss model  128.1+27 log(d) dB, d denotes the distance 
7 Conclusions
In this paper, we study the joint user association and cache content placement problem in cacheenabled HetNets. By introducing a utility function defined as a weighted sum of user download delay and the caching cost, the joint user association and content placement problem is formulated as a utility function optimization problem which is transformed equivalently into three convex subproblems by applying McCormick envelopes and Lagrange partial relaxation. We then propose an iterative algorithm which compute the Lagrange multipliers and the optimal solution of the subproblems iteratively. Numerical results demonstrate the effectiveness of the proposed algorithm.
Notes
Acknowledgements
This work is supported by the National Science and Technology Specific Project of China (2016ZX03001010004), National Natural Science Foundation of China (No. 61571073), the Joint Scientific Research Fund of Ministry of Education and China Mobile (MCM20160105), Wenfeng Talent Program of CQUPT (W201519), the special fund of Chongqing Key Laboratory (CSTC), and the project of Chongqing Municipal Education Commission (Kjzh11206).
Authors’ contributions
The authors have equal contributions. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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