A refunding strategy: opportunistic user association with congestion-based pricing in macro-femto hybrid network
- Yanjia Qi^{1},
- Hongyu Wang^{1}Email author,
- Baoming Li^{2} and
- Fuliang Chen^{2}
https://doi.org/10.1186/s13638-016-0791-1
© The Author(s) 2017
Received: 9 May 2016
Accepted: 11 December 2016
Published: 3 January 2017
Abstract
Femtocell technology addresses the severe problems of poor network capacity and indoor coverage. Meanwhile, the emergence of high-capacity air interfaces and dense deployment of small cells result in increasingly high backhaul cost in cellular wireless networks. Purchasing on leased lines can guarantee the service provision during busy hours, however, purchased capacity goes to waste in off-peak time. Hybrid mode is the most promising one among all femtocell access modes which allows macro users to associate with adjacent femtocells with idle bandwidth resources. Femto holder (FH) is egoistic and unwilling to share bandwidth with transferred users from macrocells without any compensation, thus the successful implementation of hybrid access becomes a challenging problem. In this paper, we present an economic refunding framework to motivate hybrid access in femtocells. Macro users can opportunistically associate with adjacent femtocells with excess backhaul capacity. FH can receive certain refunding from wireless service provider (WSP) in exchange for traffic offloading. FH employs congestion pricing policy so as to control the cell load in the femtocell. Within this framework, we design a general utility maximization problem for user association that enables macro users to associate with femtocells based on traffic status, cell load, and access price. Dual decomposition is used to obtain an approximate solution. The impact of congestion pricing on the aggregate throughput and load balancing is also analyzed. Extensive simulations show the proposed scheme achieves a remarkable throughput gain compared with that with no compensation and compensation with usage-based pricing policy. Load balancing is substantially improved as well.
Keywords
1 Introduction
Fortunately, various network access modes provide the possibility to relieve the pressure of backhaul cost. Indeed, how to make each user access the appropriate network substantially affects the network performance [5]. Femtocell hybrid access is a promising choice to control user association between macrocells and femtocells [6, 7], rather than the closed access and open access mode which render femtocells fully closed and open to macro users. Hybrid access permits macro users to exploit remaining femtocell resources after each femto user reserves its own capacity. Usually, macrocells and femtocells are controlled by wireless service providers (WSPs) and femto holders (FHs), respectively. FHs are egoistic to share bandwidth with transferred macro users. Incentive mechanisms should be designed from the perspective of economic compensation. Otherwise, FHs do not accept hybrid access mode if they have no benefit from offering own resources to transferred macro users. With the compensation, FHs are willing to share the remaining resources with macro users. Meanwhile, macro users should pay for the used bandwidth from FHs.
Several refunding mechanisms between WSP and FHs are investigated in the past few years. Chen et al. early propose a framework of utility-aware refunding [8], where WSP provides the certain refunding to motivate FHs to open their resource for macro users then FHs decide the resource allocation among femto and macro users. A Stackelberg game is formulated to maximize the utilities for both WSP and FHs. Shih et al. present an economic framework based on the game theoretical analysis [9], where the FHs determine the proportion of femtocell resources they will share with public users, while WSP maximizes its benefit by setting the ratio of the revenue distributed to FHs. Yang et al. show the refunding mechanism for small cell networks with limited-capacity backhaul [10], in which small cell holders receive refunding as incentives to serve guest users with their remaining backhaul capacity. WSP decides individualized refunding and interference constraints to different small cell holders; meanwhile, each small cell holder serves guest users in a best-effort manner while maximizing its own utility. Li et al. show a rate-based pricing framework within which the macro BS provides profit to motivate femto BSs to adopt hybrid access policy and guarantee transmission rates of associated users [11]. Ford et al. study a model where third parties provide backhaul connections and lease out excess capacity to WSP when available [12], presumably at significantly lower costs than guaranteed connections. Multi-leader multi-follower data offloading game is investigated in [13], where macro BSs propose market prices and accordingly small cells determine the traffic volumes they are willing to offload. Shen et al. propose an auction mechanism to establish the hybrid access [14], where femto access points (FAPs) decide their bids independently by maximizing their own utilities. After receiving the bids, the macro BS searches the winner FAP and optimizes the number of offloaded macro users. The compensation is paid by the macro BS to the winner FAP for serving the additional macro users. A price discount strategy for WSP to promote the hybrid access mode of femtocell is developed in which WSP provides a price discount in exchange for the FHs to share part of their resource with macro users [15]. An interference management scheme for the two-tier femtocell networks is studied [16], where the macro BS protects itself by pricing the interference from the femtocell users. Price bargaining between femtocell users and macrocell exists so as to maximize the revenues and protect the QoS requirements. Zhu et al. design an incentive mechanism in which WSP pays the small cell service providers for the shared radio resource [17]. A hierarchical dynamic game framework is proposed in which an evolutionary game is used to model and analyze the service selection of users in the lower lever while a Stackelberg differential game is formulated where WSP and small cell service providers act as the leader and followers, respectively. A utility gain framework where each femtocell reserves a fraction of resource to macro users and gets a gain from WSP is proposed [18]. A learning mechanism allows both WSP and FH to choose the best strategy to reach a win-win situation. Iosifidis et al. present a market where WSPs lease multiple FAPs and each FAP can concurrently serve traffic from multiple WSPs [19]. An iterative double-auction mechanism is designed to ensure the maximization of differences between offloading benefits of operators and offloading costs of FAPs. Zhang et al. propose an incentive method where macro BS allocates a portion of subchannels to FAP for spurring the FAP to serve macro users [20]. The FAP allocates the subchannels and power to maximize the femtocell network utility and the throughput of the served macro users. Yang et al. propose a bargaining cooperative game where spectrum leasing is used as the incentive mechanism to motivate small cell working as the relays [21]. Macrocell leases some of its dedicated spectrum to the selected relay small cell, and then cooperative bargaining strategy between the relay small cell and the macrocell is formulated to enhance the system spectral efficiency and balance the capacity. In [22], Liu et al. propose an opportunistic user association in multi-service HetNets, where the opportunistic user association is formulated as an optimization problem which can be solved by Nash bargaining solution (NBS).
However, cell load congestion problem in networks will also affect the achieved network performance. Congestion can severely degrade the QoS performance, user’s satisfaction, and obtained revenues. Congestion pricing, early proposed in [23], is a promising solution that can help alleviate the problem of congestion. Al-Manthari et al. survey recent congestion pricing techniques for wireless cellular networks [24], which verifies that congestion pricing can reduce congestion and generate higher revenues for network operators. Niu et al. present a congestion pricing model to charge media streaming operators based on the bandwidth-delay product on each overlay link [25]. Khabazian et al. study a mechanism by which the femto and macro capacity resources are jointly priced according to a dynamic pricing-based call admission mechanism [26]. Cheung et al. consider the network selection and data offloading problem in an integrated cellular WiFi system by incorporating the practical considerations [27]. Interactions of the users’ congestion-aware network selection decisions across multiple time slots as a non-cooperative network selection game is formulated. When the players repeatedly perform better response updates, the system is guaranteed to converge to a pure Nash equilibrium. Wang et al. solve the optimization problem under the stochastic decision framework and propose a distributed heuristic algorithm to independently and dynamically associate each user with the best BS [28]. By posing a price factor to the BS evaluation update, users dynamically associate the best BS based on the congestion state.
- 1)
We formulate an optimal opportunistic user association problem, in which macro users associate with macrocells or adjacent femtocells with limited backhaul capacity, cell load, and access price. We present a general net utility maximization problem, where the utility is represented by logarithmic utility of throughput minus cost. Cost is measured by price per unit bit rate. Then, we show a dual decomposition method that enables fast computation of global optimal solution in an efficient, distributed manner via augmented Lagrangian techniques.
- 2)
We adopt congestion pricing policy to control each cell load. When macro users intend to associate with femtocells, each user will get its own bandwidth to maximize the aggregate utility. Here, the price is not fixed but changes according to the number of users associated with the same femtocell. The more macro users associate with the same femtocell, the higher price per unit bandwidth is. Then, users in congested cells will be impelled to associate with uncrowded femtocells.
- 3)
We conduct numerical simulations to evaluate this framework and verify the influence of dynamic price for user association. Results show that when FHs adopt congestion pricing policy, the remarkable throughput gain can be achieved under different congestion levels. Due to dynamic cell load control, the effect of load balancing can also be substantially improved.
The remainder of this paper is organized as follows. We describe the system model in Section 2. The optimal user association problem and the dual decomposition to solve a net utility maximization problem are proposed in Section 3. In Section 4, extensive simulations are presented along with related discussions, and finally, our work and the outlook are summarized in Section 5.
2 System model
In this section, we describe the system model including the system architecture, interference model, and necessary network constraints. Then, we propose a cell load-based congestion pricing policy where price per bit rate can be adjusted as the cell load changes.
2.1 System architecture
where P _{ i } is transmission power from BS i, Γ _{BS} is the set of BSs, H _{ ij } is the channel attenuation coefficient between BS i and MU j, and σ ^{2} is the thermal noise power. \(\sum _{s\in \Gamma _{\text {BS}}, s\neq {i}}P_{s}H_{sj}\) is the received aggregate interference from all the BSs except the serving BS. In this model, the intra-cell interference can be avoided since there are no overlapped subcarriers for all users served by one cell. Before the bandwidth allocation process, the amount of the subcarriers allocated to one user is uncertain, thus the inter-cell interference is approximately evaluated by the worst case that all BSs generate aggregate interference to the users. Here, we rewrite se _{ ij } for short instead of log(1+γ _{ ij }). Assume that the attenuation model is slow fading so the channel conditions are fixed through frames.
2.2 Congestion pricing model
- 1)
The wasted backhaul resource is null regardless of whether the cell is congested or not, which means that bandwidth resource should be fully utilized
- 2)
When no congestion occurs, the change of price should be as small as possible to ensure user’s fair association
- 3)
In case of congestion, the change rate of price should increase faster than that during no congestion period. This faster increasing rate of price can be used to discourage users in associating with heavy-load cell.
where the p _{ i }(k) is the price at time k in cell i, p _{0} is the initial access price, and l _{ i }(k) is cell load at time k for cell i. Here, l _{ i }(k) is the ratio of actual cell load to cell tolerable maximal load L _{max}. We use parameter n to control the steepness of this function and n≥1.
3 User association optimization
As mentioned above, an important issue is that how MUs associate with macrocells controlled by WSP or femtocells deployed by FHs when they acquire services within the cellular coverage. We generalize this issue into a net utility maximization problem including network constraints, interference condition, access price, and cell load.
3.1 Optimization formulation
where C(r _{ i }) is the cost that WSP should pay. Once macro users associate with the adjacent femtocells, a positive cost is generated since backhaul resources in femtocell are utilized. Suppose that if macro users associate with macrocells, C(r _{ i })=0, while \(C(r_{i})=p_{i}\sum _{j\in \Psi _{\text {BS}}(i)}w_{ij}{se}_{ij}\) when macro users associate with adjacent femtocells, where p _{ i } represents price per unit backhaul capacity of each femtocell and this price changes with cell load.
Then, we will provide the analysis and algorithms for solving optimization problem (8)–(11). We propose a low-complexity distributed algorithm for a large-scale network.
3.2 Dual decomposition algorithm
The optimization (8)–(11) is not convex due to constraint (11). It is unpractical to solve this problem by Karush-Kuhn-Tucker condition. An alternative algorithm is necessary, especially for a large scale network. Fortunately, following [30], we can obtain an approximate solution by dual decomposition method. Traditionally, centralized solution for this convex optimization problem is usually achieved on a central server in the core network. The long computational time and coordination requirement among different tiers result in excessive computational complexity and low reliability. The computational complexity exponentially increases when the network scale is large. An distributed algorithm based on dual decomposition method can overcome this difficulty. First, we neglect the constraint (11), thus the results are the allocated bandwidth from all BSs. Then, among these candidates, the one which offers the largest rate is retained. This truncation method is well-known in network theory and results in few errors [31].
3.2.1 Dual problem
This bound applies even when the objective function is non-convex. Moreover, \(D(\lambda _{i}^{\text {bw}},\lambda _{i}^{\text {rate}})\) is always convex in \(\lambda _{i}^{\text {bw}},\lambda _{i}^{\text {rate}}\). Strong duality holds that the maximum value of primal problem equals to the minimum value of its dual problem. Therefore, the primal problem can be solved by its dual problem. By solving the dual optimal \(\lambda _{i}^{\mathrm {bw*}}\) and \(\lambda _{i}^{\mathrm {rate*}}\), the optimal solution \(w_{ij}^{*}\) of the primal problem can be achieved.
3.2.2 Distributed algorithm implementation
where |Ψ _{BS}(i)|(k) is the number of MUs associated with BS i at the kth iteration. In each iteration, a MU may select the different optimal BS which provides maximal rate so cell load may change as the increase of iteration times. 2) BS’s side:
where α>0 is a step size and we assume that α remains constant in the process of iterations. After iterations following the above steps, the algorithm can be converged to a sub-optimal solution. In fact, \(\lambda _{i}^{\text {bw}}\) and \(\lambda _{i}^{\text {rate}}\) can be interpreted as the shadow price in economics. If the demand \(\sum _{j\in \Psi _{\text {BS}}(i)}w_{ij}(k)\) and \(\sum _{j\in \Psi _{\text {BS}}(i)}{se}_{ij}w_{ij}(k)\) for BS i exceeds the maximum value, the shadow price will go up. Otherwise, the shadow price will decrease. Thus, when BS i is the congested state, its price will increase and fewer MUs will associate with it, while other lightly load BSs attract more MUs to associate with due to the lower price. In addition, the complexity is reduced to \(\mathcal {O}(M+N)\). In comparison to the complexity \(\mathcal {O}(M*N)\) of the centralized method, the distributed method guarantees the convergence fast and effective, especially for a large-scale network.
Since the derivative of D(λ) is bounded and this property satisfies the condition of Proposition 6.3.6 in [32], we can confirm that the dual decomposition algorithm converges to a sub-optimal solution.
4 Performance analysis
As the adoption of congestion pricing policy, each cell will change its price according to the load at each iteration, thus MUs select the best serving BSs to associate with. When most MUs associate with the same cell, price will go up even more dramatically when cells are in highly congested state. Due to the lower price, MUs who originally reside in highly load cells are attracted to associate with other lightly load cells. Here, we show some benefits due to the introduction of dynamic pricing policy and related mathematical proofs.
Proposition 1
The scheme under congestion pricing policy achieves throughput gain in comparison to that under usage-based pricing policy, especially when actual cell load is less than the load threshold.
Proof
Here, we discuss two kinds of cases to prove the throughput gain due to the introduction of congestion pricing policy and then figure out approximate gain value.
Case 1: We consider the single cell case, where all MUs select the same BS to associate with. w _{ ij }, se _{ ij }, W _{ i }, C _{ i }, and p _{ i } can be rewritten as w _{ j }, se _{ j }, W, C, and p for short, respectively. Our goal is to explore the relation between bandwidth allocation for each MU and the price that MU is charged.
where \(p_{\text {con}}=p_{0}(\frac {1-l_{\text {shift}}}{1-|\Psi _{\text {BS}}|(k)})^{n}\) and p _{use}=p _{0}. All the formulas on the nominator are greater than zero when p _{con}<p _{use}, namely |Ψ _{BS}|<l _{shift} L _{max}, the throughput under congestion pricing policy is more than that under usage-based pricing policy. The lower the cell load is, the more the gain is achieved. However, when the optimal solution is reached, the summation of bandwidth or rate allocation approaches the bandwidth or backhaul limit. One MU will reassociate with other lightly load cells if sufficient bandwidth resources are provided for the sake of this throughput increment, which leads to multiple cells case analysis.
where \(p_{\text {con}}=p_{0}(\frac {1-l_{\text {shift}}}{1-|\Psi _{\text {BS}}(i)|(k)})^{n}\) and p _{use}=p _{0}. All formulas on the nominator are greater than zero when p _{con}<p _{use}, namely max(|Ψ _{BS}(1)|,|Ψ _{BS}(2)|,…,|Ψ _{BS}(M)|)<l _{shift} L _{max}. Therefore, the total throughput under congestion pricing policy is more than that under usage-based pricing policy. □
Proposition 2
The throughput increases monotonously as the parameter n increases (n ≥1).
Proof
As the same analysis method in the proof of Proposition 1, the throughput increment can be given in the form of difference under two different prices. As parameter n increases, the price decreases consequently under the same cell load. Following the proof of Proposition 1, lower price results in higher throughput, and thus the throughput under the congestion pricing policy is more than that under the usage-based pricing policy. □
Proposition 3
Under the congestion pricing policy, the cell load tends to be more balancing in comparison to that under the usage-based pricing policy.
Proof
JFI and JFI^{′} differ only in denominators, if and only if l _{ i }−l _{ k }>1, JFI^{′}> JFI. Since cell load l _{ i } exceeds l _{ k }, the Jain fairness increases which means cell load tends to be more balancing due to dynamic pricing control. □
5 Simulation results
Simulation parameters
Parameter | Value |
---|---|
Topology | Uniform with wrap around |
Total area | 1000 m×1000 m |
Antenna pattern | Omni antenna |
MU distribution | Uniform, 10, 30, and 50 per macrocell |
FBS ditribution | 8 per macrocell |
MBS Tx power | 46 dBm |
FBS Tx power | 20 dBm |
Macrocell pathloss | 15.3+37.6 log10(d) |
Femtocell pathloss | 35.3+37.6 log10(d) |
Bandwidth | 10 MHz |
Backhaul capacity | 50 Mbps |
Shadowing | 8-dB standard deviation |
Thermal noise power | −104 dBm |
Carrier frequency | 2.1 GHz |
Mobile model | Static |
Fading | None |
Access price | 8 |
l _{shift} | 0.8 |
The comparison of throughput under different number of MUs (n=2)
Scenario | Without compensation | Usage-based pricing compensation | Congestion pricing compensation |
---|---|---|---|
Cell-edge rate (Mbps) (MU density =10/macrocell) | 0.17 | 0.20 | 0.27 |
Cell-edge rate (Mbps) (MU density =30/macrocell) | 0.06 | 0.11 | 0.13 |
Cell-edge rate (Mbps) (MU density =50/macrocell) | 0.04 | 0.07 | 0.09 |
Medium rate (Mbps) (MU density =10/macrocell) | 0.76 | 0.82 | 1.10 |
Medium rate (Mbps) (MU density =30/macrocell) | 0.26 | 0.39 | 0.51 |
Medium rate (Mbps) (MU density =50/macrocell) | 0.17 | 0.31 | 0.38 |
The comparison of load balancing under different scenarios (n=2)
Scenario | Without compensation | Usage-based pricing compensation | Congestion pricing compensation |
---|---|---|---|
JFI (MU density = 10/macrocell) | 0.088 | 0.103 | 0.268 |
JFI (MU density = 30/macrocell) | 0.098 | 0.189 | 0.393 |
JFI (MU density = 50/macrocell) | 0.107 | 0.254 | 0.379 |
The comparison of throughput under different parameters n (MU density =10/macrocell)
Number | 0 | 1 | 2 | 3 |
---|---|---|---|---|
Cell-edge rate (Mbps) | 0.19 | 0.22 | 0.28 | 0.32 |
Medium rate (Mbps) | 0.78 | 0.94 | 1.14 | 1.25 |
6 Conclusions
In this paper, we present an economic compensation framework between WSP and FHs. Under this framework, WSP pays certain refunding to FHs to implement traffic offloading. Macro users can opportunistically associate with FBS for transmission when there are remaining backhaul resources. We generalize this user association as an utility maximization problem. In the consideration of congestion that occurred in femtocells, each FH adopts the congestion pricing policy to control cell load. To reduce the computation complexity in large-scale networks, a dual decomposition algorithm is presented which incorporates bandwidth, backhaul capacity, and access price. Simulation results show that as the number of MUs increases, our optimization achieves remarkable throughput gains. Load balancing measured by Jain fairness index is also improved drastically. Actually, there are further problems to be investigated. Our work focuses on the interrelation between only one WSP and one type of FH. As a matter of fact, the types of WSP and FH vary widely. Therefore, the interrelation between WSP and each FH becomes more complicated. Our future work is to research multi-WSP-multi-FH problem and design corresponding solutions.
Declarations
Authors’ contributions
All authors contributed to all aspects of the article. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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