Downlink Power Control for Latency Aware Grid Energy Savings in. Green Cellular Networks. Vinay Chamola, Pratik Narang and Biplab Sikdar. Department of ...
Downlink Power Control for Latency Aware Grid Energy Savings in Green Cellular Networks Vinay Chamola, Pratik Narang and Biplab Sikdar Department of Electrical and Computer Engineering, National University of Singapore, Singapore Abstract—Mobile service providers can achieve cost savings by deploying Base Stations (BSs) which harvest renewable energy as they reduce the energy drawn from the grid and its associated cost. The cost savings can be further enhanced by careful management of the system resources. Furthermore, mobile operators require that such resource management be carefully coupled with managing the quality of service (QoS) to ensure customer satisfaction. This process involves trade-off between energy drawn from the grid and the QoS performance. In contrast to prior research which has addressed the problem of joint management of grid energy savings and the QoS performance using user-association reconfiguration or BS on/off schemes, we present a framework for doing so using BS downlink power control. Our proposed framework is evaluated through simulations using a real BS deployment from London, UK, and we show its superior performance over existing benchmarks. We demonstrate that our framework can lead to around 40% grid energy savings with better network latency performance as compared to the traditionally used scheme.
I. I NTRODUCTION With increasing cellular traffic demands worldwide, the number of cellular base station deployments around the globe have been consistently increasing. More BS deployments not only lead to increased operating expenditure for network operators due to higher energy consumption, but also lead to increased contribution of cellular networks to global carbon emissions. Such factors have garnered the attention of telecom operators, government agencies and researchers alike, and motivated them towards greening of cellular networks. Base stations alone contribute to nearly 60% of power consumption in cellular networks [1]. Utilizing renewable sources of energy to power BSs is therefore an attractive proposal for greening cellular networks. Several network operators have successfully deployed such BSs in different parts of the world [2]. Running BSs completely on solar power is possible only at locations which are very rich in solar resources. For most other locations, adopting such an approach is not very feasible. At locations with occasional bad weather periods, the size of storage devices and the harvesters becomes very large. This leads to higher capital costs for the operator, and is thus not an attractive solution from a business perspective [3], [4]. In such scenarios, and in scenarios where the BSs already have a grid supply in place, using renewable energy in conjunction with grid energy is a better approach from technical as well as business perspectives. Coordinating between the two sources of energy and intelligent management of the system resources like the harvested solar energy can lead to further reduction in grid energy and thus lower the costs involved. However, while doing so, the operators must also ensure reliable quality
of service in terms of the network latency to their users by intelligently considering the trade-off between cost savings and network latency performance. Prior research on joint management of grid energy consumption and network latency has seen the use of userassociation reconfiguration or BS on/off approaches. In contrast, this work proposes a joint framework for the management of grid energy savings along with the network latency performance, achieved through downlink power control. We also present a methodology for intelligently allocating the green energy during the day to maximize the benefit derived from it. For performance evaluation, we perform simulations using a real BS deployment from London, UK, and compare the performance of the proposed methodology against existing benchmarks (e.g. the GALA scheme [5] and the SWES scheme [6]). The rest of this paper is organized as follows. Section II discusses a brief overview of related work. In section III, we describe the system considered in the paper. Section IV presents the problem formulation and our solution methodology, and Section V presents the simulation results. We conclude in Section VI. II. L ITERATURE R EVIEW One of the ways of achieving grid energy savings in a network of grid-connected solar-powered BSs is by reducing the energy consumption in the network. Authors in [1] leverage this fact and utilize a dynamic BS switching approach to minimize the energy consumption in the network. A dynamic BS switching approach switches off some of the BSs during low traffic periods. In [6], the authors present their approach named SWES which implements dynamic BS switching for a network of BSs. They implement their scheme as a greedy heuristic which calculates the minimum number of BSs required to be switched on in order to provide desired quality of coverage to a given area. Authors in [7] propose an energy-efficient scheme for resource allocation in OFDMA networks involving hybrid energy harvesting BSs. Their scheme minimizes network energy consumption by using a stochastic dynamic programming approach. Authors in [8] propose an algorithm for green energy aware load balancing. The algorithm uses tuning of beacon power levels to discourage users from joining BSs running low on green energy so as to minimize the need to draw energy from the grid. All the above-mentioned studies focus on network energy minimization, but do not consider the network latency performance while doing so.
Work by authors in [9] is a recent study which addresses network latency by proposing an α-optimal user association for the flow level cell load balancing aimed at maximizing the throughput or minimizing the system delay. However, this approach does not account for the green energy. Approaches in [5] and [10] are some recent studies which account for green energy availability along with the network delay performance. Both these approaches address grid energy savings with management of the quality of service (in terms of the network latency). The approach of authors in [5], named GALA, considers green energy availability while making user-association decisions. The authors formulate it as a problem of minimizing the sum of weighted latency ratios of the BSs where the weights are chosen to consider the green energy availability at a BS. Authors in [10], on the other hand, formulate the problem of minimizing the sum of the cost of average system latency and the cost of on-grid power consumption. Both these approaches manage energy availability and network latency by reconfiguring BS-MT (mobile terminal) user-association. In contrast to such an approach, our work presents a methodology for energy and latency management based on BS downlink transmit power control and demonstrates its performance gains over existing approaches. In our past research [11], we have presented the use of intelligent temporal energy allocation and demonstrated its superior performance in terms of managing the green energy and delay jointly for an off-grid scenario. In this paper, we use insights from [11] and propose a temporal energy allocation scheme for BSs connected to grid. III. S YSTEM D ESCRIPTION A. Traffic model, BS load and Network latency We consider a network of cellular BSs providing coverage to a region X . Let B denote the set of BSs providing coverage to X . We denote the user location by x ∈ X . For simplicity, our model focuses only on downlink communication, i.e., from BSs to the mobile terminals (MTs). The downlink transmit power level of the BSs is denoted by P, where the transmit power levels take discrete values, i.e. P(k) ∈ {0, µ, 2µ, · · · , Pmax }, where k is the index of the BS, µ is the granularity of power control and Pmax is the maximum transmit power level allowed. We assume file transfer requests arrive following a Poisson point process. The arrival rate of requests is given by λ(x) per unit area, and the amount of traffic request generated by each arrival follows a general distribution with average size of τ (x) bytes. The rate offered at location x served by a BS k can be given as [9] rk (x) = BWk log2 (1 + SIN Rk (x))
(1)
where BWk is the total bandwidth offered by the k-th BS and SIN Rk (x) is given as SIN Rk (x) =
σ2
gk (x)P(k) P + m∈Ik Im
(2)
where gk (x) denotes the channel gain between the k-th BS and the user at location x and takes into account the log-normal
shadowing and the path loss, σ 2 is the noise power and P(k) is the downlink transmit power of the k-th BS. Ik is the set of interfering BSs for BS k whereas Im denotes the interference power from the m-th interfering BS. The average traffic load density at location x served by BS k can be expressed as [5] %k (x) =
λ(x)τ (x) uk (x) rk (x)
(3)
where uk (x) indicates if the user at location x is served by BS k. If that is true then this variable has the value 1, and 0 otherwise. The BS load, which denotes the fraction of time the BS is busy serving its traffic requests is thus given as [5] Z ρk = %k (x)dx. (4) X
Definition 1: The feasible set of the BS loads ρ (ρ1 , · · · , ρ|B| ) is denoted by F and can be defined as Z n F = ρ | ρk = %k (x)dx,
=
X
0 ≤ ρk ≤ ρth , ∀k ∈ B, uk (x) ∈ {0, 1}, ∀k ∈ B, ∀x ∈ X , |B| X
o uk (x) = 1, ∀k ∈ B, ∀x ∈ X ,
k=1
where ρth is a threshold on the permitted BS load to avoid congestion at a given BS. The MT-BS association is decided based on the strongest signal rule. Since traffic requests are assumed to follow a Poisson process, the sum of such requests at a BS will also be a Poisson process. Note that the BS’s service time follows a general distribution. Thus, its operation can be modeled as a M/G/1 processor sharing queue with latency indicator ρk [10]. In a cellular network with multiple given by 1−ρ k BSs, the network level latency can be evaluated by adding up the latencies of the BSs in proportion to the normalized traffic being served by them. Thus, network latency indicator, denoted by N , is given by [5] N =
|B| X k=1
ρk 1 − ρk
(5)
The above-mentioned indicator has been widely used in existing literature (e.g. in [6], [10] and [11]) to quantify the network latency performance. B. BS Power Consumption This work considers a network of macro BSs. The power consumption of each BS consists of a fixed part and a variable part (traffic-dependent). The power consumption of BS k is denoted by L(k) and is given as [11]: L(k) = P0 + ∆P(k)ρk , 0 ≤ ρk ≤ 1, 0 ≤ P(k) ≤ Pmax (6) where P0 is the power consumption at no load (zero traffic) and ∆ is the slope of the load-dependent power consumption.
C. Solar Energy Resource and Batteries This work uses solar irradiation data provided by National Renewable Energy Laboratory (NREL) for London, UK [12]. Hourly energy generated by a Photo-voltaic (PV) panel of a given rating is obtained by feeding this data to NREL’s System Advisor Model (SAM). The BSs are assumed to utilize lead acid batteries to store excess energy harvested by the PV panels. Lead acid batteries are a low-cost and time-tested storage application, and are thus a popular choice for such use. IV. P ROBLEM F ORMULATION AND S OLUTION M ETHODOLOGY In this section, we discuss the problem formulation and our solution methodology. We begin by describing the mechanism of green energy allocation over time which is a pre-requisite for optimization of joint management of grid energy savings and the quality of service. After discussing the allocation of green energy, we formulate the optimization problem. To solve this problem, we use BS downlink transmit power control. We assume that a centralized server performs the energy allocation and downlink power control decisions at the beginning of the day. The energy allocation and downlink power decisions are made for a time-scale of an hour and the decisions made by the central server guide the energy allocation and power control during the day. We assume that the central server has perfect knowledge of the renewable energy to be harvested during the day. This may be implemented in a real-world scenario using weather forecasts. There are also existing methodologies for predicting solar energy generation for hours and days in advance (such as [13]). Coupled with weather forecast predictions, these can help achieve a robust prediction of renewable energy to be harvested. Further, our approach requires that the central server has the information of average hourly traffic profile, which is used to evaluate the underlying user association for facilitating power control decisions. A number of existing papers in literature have studied the modeling and prediction of cellular traffic (e.g. [14]). Ideas from these models may be leveraged for a realworld implementation of our work. It could also be possible for the operators to predict this information based on the traffic pattern seen in the past few weeks or months. Note that the above-mentioned assumptions are in line with the assumptions considered in recent research (e.g. [5], [10]). A. Temporal Energy Allocation Solar energy harvested during the day and the energy stored in the batteries forms the sum total of green energy at the disposal of a BS. Intelligent allocation of the available green energy is required to optimize its usage and minimize the burden on the grid. This allocation needs to be done for the different hours of the day. To this end, we propose a Load Proportional Energy Provisioning (LPEP) algorithm (Algorithm 1). The green energy budget (given by Z) is dependent on the initial battery level (Sini ) and the green energy to be harvested during the day (H). Note that k denotes the BS index whereas t denotes the hour of the day in the
Algorithm 1 The LPEP Algorithm 1: for k = 1 : B do P24 2: Z(k)= Sini (k) − ψScap (k) + t=1 Ht (k); 3: for t = 1 : 24 do ; 4: Et (k) = Z(k) P24Lt (k) h=1 Lh (k) 5: end for 6: end for algorithm. To prevent battery degradation, we use a threshold state-of-charge ψ and forbid the discharge of battery below ψScap , where Scap denotes the maximum storage capacity of the batteries. The LPEP algorithm allocates green energy in a given hour t denoted by Et , in proportion to the estimated BS power consumption in that hour. Throughout this work, the subscript t is used to denote a particular variable’s value in the given hour t. LPEP requires a load profile for the initial green energy allocation. For this purpose, any arbitrary load profile (as in [3] or [6]) can be used. This is, however, just an initialization step. Green energy allocation is later iteratively updated after the downlink power control operations as discussed in section IV-C. B. Problem Formulation A BS k is powered by the green energy allocated to it in a given hour (Et (k)). If this energy is not sufficient (i.e. if Lt (k) > Et (k)), additional energy is drawn from the grid. The estimated battery level after doing so, S¯t , can be expressed as S¯t (k) = St−1 (k) − min(Lt (k), Et (k)) + Ht (k)
(7)
where St−1 denotes the battery level in the previous hour. Energy from the grid is also drawn to avoid the event where the battery level goes below the threshold ψScap . Thus, we can give the grid energy consumed by the network during hour t in the following manner Gt =
B X
max (0, Lt (k)−Et (k))+
k=1
B X
max(0, ψScap (k)−S¯t (k)).
k=1
(8) The problem of minimizing energy drawn from the grid and its trade-off with network latency is formulated in the following manner: 24 X minimize (Nt + βGt ) P
t=1
subject to: ρ ∈ F, where the trade-off between grid energy savings and network delay is controlled by the parameter β. This equation reduces to the problem of minimizing the network latency if β = 0. On the other hand, for β → ∞, it is a problem of minimizing the grid energy consumed without any consideration of the delay related to network latency. We approach the above problem using downlink transmission power control through suitable tuning of the BS transmit power levels. The power level control problem is, however, a non-convex optimization problem. An optimal solution to this problem would require
Algorithm 2 The GTPC Algorithm 1: Initialization 2: Set P(k) = Pmax for all k ∈ B 3: Compute M(P); Set δM = 1 4: while δM > 0 do 5: Mold = M(P) 6: for k = 1 : B do 7: Pcurr = P 8: Pcurr (k) = max(0, P(k) − µ) 9: M0 (k) = M(Pcurr ) 10: if max(ρ) > ρth then 11: con(k)= 0 12: else con(k)= 1 13: end if 14: end for 15: a. z : index of BS having con = 1 for which power control leads to minimum objective function value (M0 ) 16: b. Set Mnew = M0 (z) 17: δM = Mold − Mnew 18: if δM > 0 then 19: P(z) = max(0, P(z) − µ) ; 20: end if 21: end while 22: for k = 1 : B do 23: Lt (k) = P0 (k) + ∆P(k)ρ(k) 24: S¯t (k) = St−1 (k) − min(Et (k), Lt (k)) + Ht (k) 25: W(k) = max(0, Et (k) − Lt (k)) 26: for h = t + 1 : 24 do 27: Eh (k) = Eh (k) + W(k) P24 Lh (k) m=t+1 Lm (k) 28: end for 29: end for P|B| 30: Gt = max(0, Lt (k) − Et (k)) k=1 P B 31: + k=1 max(0, ψScap (k) − S¯t (k))
exhaustive search over the entire solution space, and will have high computational complexity. The computational complexity varies exponentially with the number of BSs (B) and the hours under consideration (T ), and can be given by O(Q|B|T ), where Q denotes the number of possible power levels at which a BS can operate. To solve the power level control problem in a meaningful amount of time, we propose a greedy transmit power control algorithm. The greedy heuristic based approach allows us to achieve very low computational complexity in comparison to exhaustive search over the entire solution space. To facilitate our task, we define a utility function Mt (Pt ), which corresponds to value of the objective function for a given power allocation Pt during the t-th hour, and is given as Mt (Pt ) = Nt + βGt . (9) C. Greedy Transmission Power Control In this section, we discuss our proposed solution named Greedy Transmit Power Control (GTPC) Algorithm (Algorithm 2). The algorithm is carried out sequentially for each
Fig. 1. 3G BS Deployment near Southwark (London).
hour of the day. For each hour, every BS starts with the transmit power level of Pmax . Next, power level decrement is applied to all BSs, one at a time, and the resulting objective function value is noted (and stored in M0 ). The BS resulting in the lowest value of the objective function, while satisfying the system constraints (tracked in the algorithm by the variable con), is selected for power level reduction. This process is repeated until no further improvement in Mt can be achieved by reducing the power level of any BS. Note that the improvement in the latency component of the utility function in the power control operations is due to its load balancing effect and interference management. The reduction in the grid energy consumption is due to the transmit power level of a BS low on green energy going down, and further, some users being offloaded (which reduces ρ), thus decrementing the BS power consumption. Given the above calculation of transmit power levels, a BS might not utilize all of the energy allocated to it for a particular hour. The leftover energy (denoted by W in the algorithm) is distributed among the subsequent hours in proportion to the power consumption in those hours. After performing the power control operations for the day using the GTPC algorithm, we shall have different BS load levels in contrast to the load profile used for the initial energy allocation (using Algorithm 1). Thus, after performing the power control operation for the day, we perform another set of energy allocation using the updated BS load values. After performing a few iterations (typically three to four) of Algorithm 1 followed by the GTPC algorithm, the solution of the downlink power level converge. Our algorithm achieves a worst case computational complexity of O(Q|B|2 ). V. S IMULATION R ESULTS To test our proposed methodology, we consider a real 3G BS deployment which consists of six BSs deployed in an area of 1 km2 near Southwark, London, UK, owned by network provider Vodafone (shown in Fig. 1). Our evaluation considers BSs to be equipped with PV panel with DC rating 6 kW and 10 batteries. Further, we consider that each BS uses 12 V, 205 Ah flooded lead-acid batteries. The carrier frequency is taken as 2.5 GHz with 10 MHz bandwidth and full frequency reuse is assumed. Log normal shadowing with standard deviation
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Fig. 2. Solar energy harvested during the day by the BSs (PV rating: 6 kW). Fig. 3. Grid energy consumption for the different schemes.
A. Grid energy savings A comparison of grid energy savings for the month of January, obtained with different approaches, is shown in Fig. 3. It is worth noting that the Best-effort scheme has a very high grid energy consumption. In contrast, GALA achieves significant savings in the grid energy consumption. Further, we observe that SWES scheme reported lower consumption of grid energy than the Best-effort scheme as well as GALA.
10
GTPC, β = 0 GTPC, β = 1 GTPC, β = 10 Best Effort SWES GALA
9
Average network latency indicator
8 dB with the correlation distance for shadowing taken as 50m has been considered [15]. Additionally, the path loss is calculated as P L(dB) = 130.19 + 37.6 log(R) [15], where R denotes the distance between the MT and the BS. We take the noise power to be -174 dBm/Hz. File transfer requests are generated using a homogeneous Poisson point process. The arrival rate is dependent on the time of the day, with the smallest number of file transfer requests with an average 20 requests per unit area (km2 ) during early morning hours (2–5 AM), and the largest with an average of 200 during the evening hours (5–7 PM). For weekends, a lower traffic level is considered. The corresponding values for the smallest and largest number of file transfer requests are taken as 10 and 150 for the weekend, respectively. Each file transfer request is assumed to request 50 KB of data traffic to be served. Solar energy data obtained from NREL [12] for the month of January of typical meteorological year (TMY) data for London is used for the purpose of our simulations. Fig. 2 shows the solar energy harvested by the PV panels during the different days of this month by the BSs (with PV panels having DC rating 6 kW). The values of P0 , Pmax and ∆ have been taken as 412.4 W, 40 W and 22.6 W respectively [11]. The granularity of transmit power control, µ, has been taken as 5 W. ψ, the threshold state of charge, has been taken as 0.3. Sini is randomly chosen for different BSs for 1st January and we assume that day to be Monday. To facilitate comparison with the proposed methodology, we consider the Best-Effort scheme which uses green energy as long as it is available, and then switches to the grid energy. All BSs are assumed to operate with a fixed transmit power of 20 W. We also consider the GALA scheme [5] with BSs operating at transmit power 20 W and the BS on-off scheme (SWES) proposed in [6] with BSs operating at transmit power 40 W when they are on.
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Fig. 4. Average network latency performance for the different schemes.
This can be attributed to the fact that SWES switches off some of the BSs to reduce the overall network consumption. The BSs which are off naturally save grid energy. Solar energy harvested during this period is stored in the batteries for their use in the future hours, thus reducing the dependency on grid energy. From the figure, it can be seen that our proposed approach allows a wider control over the consumption of grid energy by tuning the parameter β. With β = 0, our approach gives high grid energy consumption which is comparable to the Best-effort scheme. This is attributed to the fact that, for β = 0, power control operations are performed only accounting the network delay performance and not the grid energy consumption. With the value of β = 1, it is noted that consumption of grid energy quickly reduces. We achieve a smaller value of grid energy consumption and it is comparable to that achieved using the SWES scheme. With β = 10, the energy drawn from the grid is further lower. Note that the grid energy savings achieved in our approach with β = 10 as well as in SWES scheme are at the expense of higher network latency (Fig. 4), which is discussed in the next subsection. From Fig. 3, we also note that for very bad weather days (e.g. those after 25th January), the SWES scheme as well as the proposed scheme for β = 1 and β = 10 has much lower grid energy consumption than the GALA scheme.
TABLE I C OMPARISON OF AVERAGED M ETRICS FOR D IFFERENT S CHEMES
18 GTPC, β = 0 GTPC, β = 1 GTPC, β = 10 Best Effort SWES GALA
Scheme Best-Effot GALA SWES
Gavg 50.1 34.5 26.3
Davg 5.15 4.71 5.27
Scheme GTPC (β = 0) GTPC (β =1) GTPC (β =10)
Gavg 61.9 28.9 11.4
Gavg 4.78 4.57 5.29
B. Delay performance In Fig. 4, we depict the average network latency for various schemes and compare them with our proposed approach. For β = 0 and β = 1, our approach achieves a better delay performance than the Best-effort scheme as well as SWES scheme. GALA scheme shows a better network latency performance than Best-effort scheme and SWES scheme. For most of the days, the average latency for β = 1 is smaller as compared to the value for β = 0. This is observed because of the non-convex nature of the underlying objective function with respect to the power control operations. For β = 1, power levels of BSs reduce to much lower values in comparison to the case when β = 0 so as to give more grid energy savings. Our experiments show that, at lower power levels of BSs, power control operations provide better interference management which also brings down the network latency. However, for the days which have bad weather, our proposed scheme trades the network latency performance in favor of grid energy savings (see the corresponding values for β = 10). It can also be seen from the figure that the network latency is lower on weekends than on weekdays. This is because the traffic to be served on weekends is usually lower than the traffic on weekdays. With SWES, it is noted that the average delay is lower on weekends in comparison to all other schemes. This is because SWES switches off most of the BSs when the traffic is low (as on weekends) which reduces the interference to the BSs that are turned on, in turn reducing the delay achieved. But turning off the BSs on weekdays has the effect of increasing network latency since the traffic to be served is higher. Fig. 5 depicts the hourly delay for 18th January. For all schemes, the latency is low during the early morning hours since the traffic to be served is low. In the day time, SWES and our proposed scheme with β = 10 lead to higher values of delay in comparison to the Best-effort scheme. Our proposed approach (for β = 0 and β = 1) along with GALA have better delay performance than the other benchmarks. Table I summarizes some key parameters for the various benchmark schemes as well as the proposed GTPC scheme for three different β values. Gavg represents the average value of daily grid energy consumption (in kiloWatthour(kWh)) whereas Davg represents the average network latency indicator averaged for the month of January. Note that for β = 1 the proposed GTPC scheme exhibits around 40% grid energy savings as compared to the traditionally used BestEffort scheme while ensuring a better latency performance. VI. C ONCLUSION This paper proposed a novel approach which achieves reduction in the grid energy consumption while ensuring
Network latency indicator
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Fig. 5. Hourly network latency for the different schemes (18th January).
good QoS for green BSs with hybrid supplies. Our approach provides a wide control over grid-energy savings by managing the trade-off between grid-energy savings and the network latency. This was achieved by intelligent green energy allocation and BS downlink transmit power control. The proposed framework was evaluated using simulations with a real BS deployment, and its superiority over existing benchmarks was demonstrated. R EFERENCES [1] M. A. Marsan, L. Chiaraviglio, D. Ciullo, and M. Meo, “Optimal energy savings in cellular access networks”, Proc. IEEE ICC, Dresden, Germany, Jun. 2009. [2] V. Chamola and B. Sikdar, “Solar Powered Base Stations: Current Scenario, Issues and proposed Solutions,” IEEE Communications Magazine, vol. 54, no. 5, May 2016. [3] V. Chamola and B. Sikdar, “Resource Provisioning and Dimensioning for Solar Powered Cellular Base Stations”, Proc. IEEE GLOBECOM, Austin, USA, 2014. [4] V. Chamola and B. Sikdar, “Power Outage Estimation and Resource Dimensioning for Solar Powered Cellular Base Stations,” IEEE Transactions on Communications, (DoI: 10.1109/TCOMM.2016.2587285). [5] T. Han et. al., “Green-energy aware and latency aware user associations in heterogeneous cellular networks,” Proc. IEEE GLOBECOM,, 2013. [6] E. Oh, K. Son and B. Krishnamachari, “Dynamic base station switchingon/off strategies for green cellular networks,” IEEE Transactions on Wireless Communications, vol 12, no. 5, pp. 2126-2136, 2013. [7] D. Ng, E. Lo and R. Schober, “Energy-efficient resource allocation in OFDMA systems with hybrid energy harvesting base station,” IEEE Transactions on Wireless Communications, vol. 12.7, 2013. [8] T. Han and N. Ansari, “ICE: Intelligent Cell BrEathing to Optimize the Utilization of Green Energy,” IEEE Communications Letters, vol. 16, no. 6, pp. 866-869, June 2012. [9] H. Kim, D. G. Veciana G, X. Yang and M. Venkatachalam, “Distributedoptimal user association and cell load balancing in wireless networks.,” IEEE/ACM Transactions on Networking, pp. 177-90, Feb. 2012. [10] D Liu et. al., “Distributed delay-energy aware user association in 3tier HetNets with hybrid energy sources,” Proc. IEEE GLOBECOM Workshops, Austin, TX, 2014. [11] V. Chamola, B. Krishnamachari and B. Sikdar, “An Energy and Delay Aware Downlink Power Control Strategy for Solar Powered Base Stations”, IEEE Communications Letters, vol. 20.5, pp. 954-957, 2016. [12] http://www.nrel.gov/rredc/solar_data.html, Last accessed: 10 March, 2016. [13] T. Khatib , A. Mohamed and K. Sopian, “A review of solar energy modeling techniques,” Renewable and Sustainable Energy Reviews., vol. 16, iss. 5, pp. 2864-2869, 2012. [14] X. Chen, Y. Jin, S. Qiang, W. Hu and K. Jiang, “Analyzing and modeling spatio-temporal dependence of cellular traffic at city scale,” Proc. IEEE ICC, London, UK, 2015. [15] IEEE 802.16m-08/004r5: IEEE 802.16m Evaluation Methodology Document (EMD), 2009
