1

Delay Aware Resource Management for GridEnergy Savings in Green Cellular Base stations

with Hybrid Power SuppliesVinay Chamola, Biplab Sikdar and Bhaskar Krishnamachari

Abstract—Base stations (BSs) equipped with resources to har-vest renewable energy are not only environment-friendly but canalso reduce the grid energy consumed, thus bringing cost savingsfor the cellular network operators. Intelligent management ofthe harvested energy can further increase the cost savings.Such management of energy savings has to be carefully coupledwith managing the quality of service so as to ensure customersatisfaction. In such a process, there is a trade-off between theenergy drawn from grid and the quality of service. Unlike priorstudies which mainly focus on network energy minimization,this paper proposes a framework for jointly managing thegrid energy savings and the quality of service (in terms ofthe network latency) which is achieved by downlink powercontrol and user association reconfiguration. We use a real BSdeployment scenario from London, UK to show the performanceof our proposed framework and compare it against existingbenchmarks. We show that the proposed framework can leadto around 60% grid energy savings as well as better networklatency performance than the traditionally used scheme.

Index Terms—Green communications, resource management,solar energy, base stations, cellular networks.

I. INTRODUCTION

To cater to the increasing cellular traffic demands, therehave been increasing number of cellular BSs deployments bytelecom operators across the globe. This has not only increasedthe operational expenditure of the operators, but has also ledto an increase in the contribution of cellular networks to theglobal carbon emissions. This has led to a number of initiativesfrom not only telecom operators but also government agenciesand researchers to bring down the power consumption in thesenetworks. Base stations contribute to around 60% of the powerconsumption in cellular networks. Thus powering base stationsby renewable energy is one of the promising solutions foraddressing this problem and such a solution has been alreadyadopted by many telecom operators across the world [1].According to a survery by Global System Mobile Association(GSMA) these deployments grew from just 9000 in the year

Manuscript received Apr. 14, 2016; revised Aug. 10, 2016 and Oct. 9, 2016;accepted Oct. 21, 2016. Date of publication XX XX, 2016; date of currentversion XX XX, 2016. The associate editor coordinating the review of thispaper and approving it for publication was K. Tourki. This work was supportedby the Ministry of Education, Singapore under grant R263-000-A81-133.

Vinay Chamola and Biplab Sikdar are with the Department of Electrical andComputer Engineering, National University of Singapore, Singapore 11907(e-mail:vinay.chamola.nus@gmail.com, bsikdar@nus.edu.sg).

B. Krishnamachri is with the Department of Electrical Engineering, Uni-versity of Southern California, Los Angeles, CA 90089, USA (e-mail:bkrishna@usc.edu).

Digital Object Identifier: 10.1109/TCOMM.2016.2629502

2010 to 43,000 in year 2014, showing 5 fold increase in aspan of 4 years [2].

Locations that are very rich in solar resources can havebase stations completely powered by solar energy. However,for locations with occasional bad weather periods, the size ofharvesters and storage devices (e.g. PV (photo-voltaic) panelsand batteries) required becomes very large which leads tovery high CAPEX (capital expenditure), thus discouragingoperators from adopting such a solution [3]. In such scenariosand in scenarios where the BSs are already connected to thegrid, using renewable energy in conjunction with grid energy isa more viable approach. Powering the BSs by solar energy canreduce the grid energy consumption. Intelligent managementof the harvested solar energy by such BSs and cooperationamong them can lead to further reduction in the grid energyconsumption in the network. Note that while doing so, theoperators also have to take into account the quality of service(QoS) offered to the users in terms of the network latency,and have to consider the trade-off between cost savings andthe network latency. Existing literature on joint managementof grid energy consumption and the network latency usesonly user-association reconfiguration to achieve the same.Additionally, some works propose dynamic BS operation (i.e.BS on/off strategies) which is also a means of bringing aboutgrid energy savings through network energy minimization. Incontrast to these approaches, we propose the use of intelligentgreen energy allocation and the use of down-link power controland user-association reconfiguration to address the problem.The efficacy of the proposed methodology has been shownby simulations using real BS deployment and solar energytraces for London, UK and by comparison against existingbenchmarks. The major contributions of this paper can besummarized as follows:

• We consider a network of BSs powered by grid andsolar energy, and formulate the problem of managing thegrid energy savings and its trade-off with the networklatency. We define a trade-off factor which captures thecontribution of the grid energy consumed and the systemlatency in the objective function.

• Unlike existing literature which has used only user-association reconfiguration as a means to manage thegrid energy savings while accounting for the networkdelay performance, we use BS downlink transmit powercontrol in addition to user-association reconfiguration andshow its performance gains. As the problem of downlink

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power control is non-convex with respect to the problemof managing the grid energy savings and network delay,we propose a greedy heuristic algorithm to achieve thepower control operations. We also provide an optimaluser-association policy which minimizes the objectivefunction value given the BSs operating at power levelsdecided by the power control algorithm.

• Majority of existing literature dealing with green cellularnetworks considers a time snapshot problem where theconsumption of resources is minimized for an instant oftime. However, such schemes do not address the problemof green energy allocation over time. In this paper, wepropose a simple algorithm which guides the temporalallocation of green energy over time so as to maximizethe benefit derived from it.

• We provide numerical results showing the trade-off be-tween the grid energy consumption and the networklatency for the proposed scheme. We also show thesuperiority of the proposed scheme over existing state-of-the-art benchmarks.

The rest of this paper is organized as follows. Section IIpresents a brief overview of related works. Section III de-scribes the system considered in the paper. Section IV presentsthe problem formulation. Section V presents the solutionmethodology. Section VI presents the numerical results andSection VII concludes the paper.

II. RELATED WORK

One of the possible ways of bringing grid energy savings ina network of grid-connected solar-powered BSs is to reducethe energy consumption in the network. In related work,authors in [4] propose dynamic BS switching to minimize thenetwork energy consumption. The energy savings in dynamicBS switching is brought by switching off some of the BSsduring low traffic periods. The authors in [5] present a practicalscheme (named SWES) for the implementation of dynamicBS switching for a network of BSs. The scheme is a greedyheuristic which seeks to determine the minimum number ofBSs to be switched on in order to serve the given area witha desired quality of coverage. BS switching for renewableenergy powered cellular networks is considered in [6]. Theproblem of grid energy minimization is formulated and theBS on/off strategy to solve the problem is derived through atwo-stage dynamic programming algorithm. In [7] the authorsconsider the problem of resource allocation and admissioncontrol in an OFDMA network and propose an algorithmfor dynamic power adaptation of femtocells to minimize theoverall power consumption of the network. An energy-efficientscheme for resource allocation in OFDMA systems withhybrid energy harvesting BSs is proposed in [8]. The schemeuses a stochastic dynamic programming approach for powerallocation to minimize the network energy consumption. Theauthors in [9] propose an algorithm for green energy awareload balancing. The approach is based on tuning the beaconpower levels (and not the actual transmit power levels) ofthe various BSs. By doing so, users are discouraged fromjoining BSs running low on green energy. In [10], the authors

propose a Lyapunov optimization approach for bringing gridenergy savings in a network of BSs where some of theBSs are connected to the grid whereas some are not. Notethat all of the above studies primarily focus on minimizingthe overall network energy consumption and most of themneglect the effect of doing so on the delay experienced by theusers in the network. Some of the recent studies addressingnetwork delay include [11] which proposes a distributed userassociation scheme using primal-dual formulation for trafficload balancing. The authors of [12] propose an α-optimaluser association for the flow level cell load balancing withthe objective of maximising the throughput or minimizingthe system delay. However the above-mentioned schemes([11],[12]) do not account for the green energy availabilityat the BSs.

Methodologies which consider the green energy availabilityin addition to the delay performance of the system include[13], [14], [15] and [16]. These studies address the issue ofbringing grid energy savings while managing the quality ofservice (in terms of the network latency) [17]. The authorsin [13]-[14] propose the GALA scheme which accounts forthe green energy availability at the BS while making user-association decisions. The authors formulate the problem ofminimizing the sum of weighted latency ratios of the BSswhere the weights are chosen to account for the green energyavailability at the BSs. The authors of [15] consider BSspowered by hybrid supplies and formulate the problem ofminimizing the weighted sum of the cost of average systemlatency and the cost of on-grid power consumption. Theauthors of [16] also consider BSs powered by hybrid suppliesbut formulates the problem of lexicographic minimization ofthe on-grid energy consumption so as to reduce both total andpeak on-grid energy consumption. The framework proposed in[16] introduces a penalty function to account for the networklatency. The approach in [13], [15] and [16] to manage theavailable energy and network latency is by reconfiguring theBS-MT (mobile terminal) user-association. In contrast to suchan approach, this paper presents a methodology for energy andlatency management based on BS downlink transmit powercontrol in addition to user association reconfiguration, anddemonstrates its performance gains over existing approaches.The use of intelligent temporal energy allocation has beenshown to have a superior performance in terms of managingthe green energy and delay for an off-grid scenario in ourprevious work [18] [19]. In this paper we use insights from[18] and propose a temporal energy allocation scheme for grid-connected solar powered BSs. The works in [18], [19] focus onan off-grid scenario where the BSs are solely powered by solarenergy, and consider the problem of minimizing the networklatency. However this paper considers the scenario where theBSs not only harvest solar energy but can also draw energyfrom the grid. Thus BSs may draw energy from the grid toimprove the network latency. The work in [18], [19] haveonly one parameter (i.e. the network latency) to be optimized.In contrast, the scenario of this paper requires both networklatency and grid energy drawn to be optimized, which makesthe problem more challenging.

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III. SYSTEM MODEL

In this section we describe the traffic model considered inthe paper. We also describe the formulation of the BS loadand the network latency.

A. Traffic Model, BS Load and Network Latency

Let us consider a region X served by a set, B, of BSs.We use x ∈ X to denote the user location. For simplicitywe primarily focus only on downlink communication (i.e.BSs to mobile terminals (MTs)). We denote the downlinktransmit power levels of the BSs by a vector P where thetransmit power levels can take discrete values i.e. P (j) ∈{0, ξ, 2ξ, · · · , Pmax}, where j is the index of the BS, ξ is thegranularity of power control and Pmax is the maximum trans-mit power level allowed. File transfer requests are assumedto arrive following a Poisson point process with an arrivalrate λ(x) per unit area at location x, with average file sizeof τ(x) bytes. We define the traffic load density at locationx as γ(x)=λ(x)τ(x), where γ(x) captures the spatial trafficvariability. The rate offered at location x served by a BS j canbe generally given using the Shannon-Heartley theorem [12]as

rj(x) = BWj log2(1 + SINRj(x)) (1)

where BWj is the total bandwidth offered by the j-th BS andSINRj(x) is given by

SINRj(x) =gj(x)P (j)

σ2 +∑k∈Ij gk(x)P (k)

(2)

where gj(x) denotes the channel gain between the j-th BS andthe user at location x which accounts for the path loss and theshadowing loss, σ2 denotes the noise power level and Ij is theset of interfering BSs for BS j. This paper assumes perfectinformation of the channel gain which may be estimated giventhe topological details of the terrain, and drive-through sitesurveys. We introduce a user association indicator functionqj(x) which indicates if the user at location x is served byBS j. If that is true then this variable has the value 1, and 0otherwise. The BS load ρj , which denotes the fraction of timethe BS j is busy serving its traffic requests can thus be givenas [13]

ρj =

∫X

γ(x)

rj(x)qj(x)dx. (3)

Definition 1: We denote the feasible set of the BS loads ρ =(ρ1, · · · , ρ|B|) by F which can be defined as

F ={ρ | ρj=

∫X

γ(x)

rj(x)qj(x)dx, 0 ≤ ρj ≤ ρth, ∀j ∈ B,

qj(x) ∈ {0, 1},∑j∈B

qj(x) = 1, ∀j ∈ B, ∀x ∈ X},

where ρth is a threshold on the permitted BS load to avoidcongestion at a given BS.

Note that as traffic requests follow a Poisson processes, thesum of such requests at a given BS is also a Poisson process.Further, as the BS’s service time follows a general distribution,its operation can be modeled as a M/G/1 processor sharing

queue. The average number of flows at BS j can thus be givenby ρj

1−ρj [15]. According to Little’s law, the delay experiencedby a traffic flow is directly proportional to the average numberof flows in the system [20]. Thus we take the total sum of theflows in the network as the network latency indicator, D, whichis given by [15]

D =∑j∈B

ρj1− ρj

. (4)

Note that this indicator has been widely used in existingliterature (e.g. in [5], [12], [13], [21]) to quantify the networklatency performance.

B. BS power consumption

The base station power consumption consists of a fixed partand a traffic dependant part. This paper considers macro BSswhere the power consumption for BS j, denoted by L(j), canbe modeled as [22]

L(j) = P0 + ∆P (j)ρj , 0 ≤ ρj ≤ 1, 0 ≤ P (j) ≤ Pmax (5)

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

We consider solar irradiation data provided by NationalRenewable Energy Laboratory (NREL) for London, UK [23].This data is fed to NREL’s System Advisor Model (SAM),to obtain the hourly energy generated by a PV panel of agiven rating. We assume that the BSs use lead acid batteriesto store the excess energy harvested by the PV panels. Theseare a popular choice in storage applications on account of theirlower cost and being more time tested than other alternatives.

IV. PROBLEM FORMULATION

This section describes the problem formulation. We beginby describing the mechanism for green energy allocation overtime. This mechanism is an important pre-requisite beforeformulating the optimization problem which jointly managesthe grid energy savings and the quality of service. Afterdescribing the green energy allocation scheme, we formulatethe optimization problem.

A. Green Energy Allocation

The green energy available to the BSs is in the form ofenergy stored in the batteries and the energy harvested duringthe day. This budget of green energy available to a BS needs tobe intelligently allocated during the different hours of the dayso as to optimize the use of the green energy, and in turn tominimize the grid energy usage. The green energy allocationfor a given hour is done based on the energy available inthe BS’s battery at that time and the energy expected to beharvested in future hours during the day. Additionally, to avoidbattery degradation, we dis-allow the battery from dischargingbelow a certain state of charge, νBcap where Bcap denotes thebattery capacity and ν is a value which decides the lower limitbelow which batteries are dis-allowed to discharge. The green

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energy budget Mt at the beginning of a hour t is the greenenergy available for allocation from that hour to the last hourof the day (i.e. t = 24). Please note that we use the subscriptt to denote the value of the variable during the t-th hourthroughout this paper. Considering the t-th hour of operationfor the j-th BS, the green energy budget at the beginning ofhour t, which is the overall green energy that can be used overa period begining from time t to the last hour of the day, canbe given as

Mt(j) = Bt−1(j)−Bcr(j) +

24∑h=t

Hh(j) (6)

where Bt−1 denotes the battery level at the end of theprevious hour, and

∑24h=tHh(j) denotes the green energy to

be harvested during the given hour and the coming hours ofthe day. The battery levels are dis-allowed to go below stateof charge νBcap at any point of time. Because the energyallocation is done based on the expected energy to be harvestedduring the day which is a random process, we add a marginof safety to reduce the likelihood that the battery level goesbelow νBcap. Thus we take Bcr = (1 + β)νBcap where βis the safety margin. Based on the information of the energybudget available, we allocate green energy to the given hourin proportion to the traffic load in the given hour. Thus thegreen energy allocated by the BS j to the hour t is given by

Gt(j) = Mt(j)Lt(j)

Lt(j) +∑24m=t+1Lm(j)

= Mt(j)P0 + ∆Pt(j)ρ

tj

P0 + ∆Pt(j)ρtj +∑24m=t+1Lm(j)

(7)

where ρtj denotes the load of BS j in the t-th hour. For sakeof clarity we use the following notation

At(j) = ∆Pt(j) (8)

Bt(j) = P0 +

24∑m=t+1

Lm(j). (9)

Thus the green energy allocated for the hour t is given by

Gt(j) = Mt(j)At(j)ρ

tj + P0

At(j)ρtj +Bt(j). (10)

Note that the green energy allocated for a given hour cannotexceed the green energy available to the BS at that time. Thuswe limit the value of Gt(j) to be always below Bt−1(j) −νBcap(j)+Ht(j) (i.e. the total green energy available for hourt.) The overall green energy allocated for hour t is thereforegiven by

Gt(j) = Λt(j)Mt(j)At(j)ρ

tj + P0

At(j)ρtj +Bt(j)

+(1−Λt(j)) (Bt−1(j)−νBcap(j)+Ht(j)) (11)

where Λt(j) is an indicator variable defined below. IfMt(j)

At(j)ρtj+P0

At(j)ρtj+Bt(j)< Bt−1(j) − νBcap(j) + Ht(j), then

the BS has sufficient energy to satisfy the proportional energyallocation in (10) and the variable Λt(j) is set to 1, and to0 otherwise. For ease of notation, we denote (Bt−1(j) −

Algorithm 1 The LPEA Algorithm1: for j = 1 : B do2: Mt(j)= Bt−1(j)−Bcr(j) +

∑24h=tHh(j);

3: if ρtj <Bt(j)Gthresh−Mt(j)P0

Mt(j)−Gthresh then4: Λt(j) = 15: else6: Λt(j) = 07: end if8: Gt(j) = Λt(j)Mt(j)

At(j)ρtj+P0

At(j)ρtj+Bt(j)

9: +(1−Λt(j)) (Bt−1(j)−νBcap(j)+Ht(j))10: end for

νBcap(j) + Ht(j)) by Gthresh. Then, Λt(j) = 1 when

Mt(j)At(j)ρ

tj + P0

At(j)ρtj +Bt(j)< Gthresh

⇒ ρtj <Bt(j)Gthresh −Mt(j)P0

Mt(j)−Gthresh(12)

and if the above inequality is not satisfied, Λt(j) = 0.The methodology for assigning the green energy described

above has been summarized in Algorithm 1 as the loadproportional energy allocation (LPEA) algorithm.

This paper assumes that all energy allocation operationsare done by a central server. The central server is assumedto have perfect information of the renewable energy that isharvested during the day which can be implemented in reallife using weather forecasts. In existing literature there aremany methodologies which predict the solar energy generation(e.g. [24], [25]). Integrating them with weather forecasts cangive a more accurate prediction. The proposed algorithm needsonly an hourly estimate of the solar energy generation for theday (i.e. an estimate of solar energy generation for the wholeday with time granulaity of one hour), making the task evensimpler. Also, for the initial green energy allocation (usingthe LPEA algorithm), any arbitrary load profile (like the onein [3] or [26]) can be used. Note that this energy allocationis just an initialization step and the green energy allocationis later iteratively updated after the downlink power controloperations as discussed in Section V-B.

The green energy allocated to the BS in a given hour, Gt,is used to power the BS. If it not sufficient, then additionalenergy is drawn from the grid. Thus the grid energy consumedby the network during hour t, denoted by Et, is given by

Et=∑j∈B

max (0,Lt(j)−Gt(j)) . (13)

Lemma 1: Grid energy is drawn by BS j in the t-th houronly if its load value is greater than a certain value given asfollows

ρtj >

{ Mt(j)−Bt(j)At(j)

Λt(j) = 1Bt−1(j)−νBcap(j)+Ht(j)−P0

At(j)Λt(j) = 0.

(14)

Proof. Considering BS j, the grid energy drawn by the BScan be written as

Et(j)=max (0,Lt(j)−Gt(j)) . (15)

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For energy to be drawn from the grid we need

Lt(j)−Gt(j) > 0. (16)

Note that for clarity, we omit the subscript t in the later part ofthe proof. First we consider the case when the BS has sufficientgreen energy for the load proportional allocation in (10) (i.e.Λ(j) = 1). From (5) and (11), substituting the values of L,G and Λ(j) in 16 we have

P0 + ∆P (j)ρj −M(j)A(j)ρj + P0

A(j)ρj +B(j)> 0

⇒ (A(j)ρj + P0)

(1− M(j)

A(j)ρ+B(j)

)> 0. (17)

Note that as ρj , A(j) and P0 are all positive, for the aboveinequality to be true we require the following

1− M(j)

A(j)ρj +B(j)> 0

⇒ ρj >M(j)−B(j)

A(j). (18)

Next for the case when Λ(j) = 0, (16) can be written as

P0 + ∆P (j)ρj − (Bt−1(j)− νBcap(j) + Ht(j)) > 0

⇒ ρj >Bt−1(j)− νBcap(j) + Ht(j)− P0

A(j). (19)

This completes the proof of the lemma. �

B. Problem Formulation

We consider the following problem of minimizing the gridenergy drawn and its trade-off with the network latency whichis formulated as problem [P1] and given by

[P1] minimizePt, ρt

24∑t=1

(Dt(Pt,ρt) + ηEt(Pt,ρt))

subject to: ρt ∈ F

where η is a parameter which controls the trade-off betweengrid energy savings and the delay performance. Note that forη = 0, the problem reduces to minimizing the network latency,whereas for η →∞ the problem becomes minimizing the gridenergy consumed without considering the delay performance.We propose to solve the above problem by using BS downlinktransmission power control and user-association reconfigura-tion which involves suitably tuning the BS transmit powerlevels (Pt) and managing the BS loads (ρt).

V. SOLUTION METHODOLOGY

This section presents the proposed methodology for ad-dressing the problem [P1]. We address the problem using BSdownlink power control and user association reconfiguration.The proposed framework for addressing the problem is namedGreen energy and Delay aware - Renewable Asset and re-source Management (GD-RAM).

The problem [P1] is very challenging on account of thecomplexity arising from the coupling between BS power levels

Algorithm 2 Sequence of operations1: for t = 1 : 24 do2: while power control convergence do3: while user association convergence do4: Perform green energy allocation for given hour

using the LPEA algorithm.5: Solve user association problem for the given

hour using the allocated green energy and the predictedtraffic.

6: end while7: Solve power control problem for the underlying

user-association determined in the inner loop.8: end while9: end for

and the resulting user-association. Thus to make our analysistractable, we make the assumption of time scale separationbetween the user association process and the period over whichthe power level control decisions are made. The user associa-tion process happens at a much faster time-scale than the timescale at which the green energy availability and the networktraffic load vary. Studies have shown that the green energyavailability and traffic pattern is nearly constant during a givenhour of the day [5]. Further, as the time scale for determiningthe power levels of the BSs is of the order of that of trafficpattern and green energy availability variation (i.e. hours), it ismuch greater than that of the user-association process. Hence,with this assumption we decompose our problem into two sub-problems, in which the BS power control problem is solvedat a slower time scale than the user association problem. TheBS power level decisions are made on an hourly scale whereasthe user-association scheme is periodically updated on a fastertime scale. These sub-problems are given as follows:

1) User association problem: For BSs operating withpower levels specified by a vector P , the user associationproblem aims at load balancing (balancing the BS loads) soas to find the optimal BS load vector ρ that minimizes theobjective function. This problem is denoted as [P-UA] andcan be expressed as

[P-UA] minimizeρt∈F

Dt(Pt,ρt) + ηEt(Pt,ρt). (20)

2) BS power control problem: The BSs try to adjust theirpower levels so as to minimize the objective function and theproblem is denoted by [P-PC] which can be given as

[P-PC] minimizePt⊂P̃

{Qt(Pt) = Dt(Pt) + ηEt(Pt)} .

(21)where P̃ is the set of all possible power level vectors andQt(Pt) is defined as the solution to the user association prob-lem in (20). Next, Section V-A describes the solution method-ology for addressing the user association problem whereasSection V-B describes the solution methodology for addressingthe BS power control problem. Algorithm 2 summarizes thesequence of the various operations inovolved in solving theproblem P1.

Remark: Note that problem P-UA does not have a sum-

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mation over time because user-association is a continuousprocess where the set of active users changes with time.However the active users associate with the BSs accordingto the proposed user-association policy so as to minimizethe objective function at a given time instant. Further theproblem P-PC does not have summation because it is solvedindividually for every hour of the day, with user-associationdetermined using the average traffic profile for that given hour.

A. Optimal User Association Policy

In this section we propose the user association policy whichachieves the global optimal of value of the objective function(with BSs operating at a given set of power levels).

Since qj(x) ∈ {0, 1}, the set F is not convex. Thus,to formulate the problem [P-UA] as a convex optimizationproblem, we relax the constraint to 0 ≤ qj(x) ≤ 1. Here qjcan be interpreted as the probability that the user at locationx associates with BS j. The relaxed set of BS loads, F̃ , canbe given as

F̃ ={ρ | ρj =

∫X

γ(x)

rj(x)qj(x)dx, 0 ≤ ρj ≤ ρth, ∀j ∈ B,

0 ≤ qj(x) ≤ 1,

|B|∑j=1

qj(x) = 1, ∀j ∈ B, ∀x ∈ X}.

The feasible set F̃ is convex. The convexity of F̃ has beenproved by the authors in [12]. The problem [P-UA] with therelaxation condition is denoted as [P-UAR] and can be givenas

[P-UAR] minimizeρ∈F̃

U(ρ) = D(ρ) + ηE(ρ).

Remark: We drop the subscript t throughout this sectionas user association is an continuous process where the setof active users in the network keeps changing, but at alltimes they associate with the BSs according to the proposeduser-association policy. Additionally, we drop P , as the time-scale of user-association problem is faster than that of thepower control operations, and thus power levels of the BSsare assumed to be fixed during the user-association operations.Further for notational simplicity we denote the optimizationfunction value in the problem [P-UAR] by U(ρ). Note thatalthough we formulate the optimization problem [P-UAR]using F̃ , the user association algorithm which we proposein this paper determines the deterministic user association(belonging to F). This is shown in Theorems 1 and 2.

The working of the proposed user association algorithm isdescribed as follows. The proposed user association algorithmoperates in an iterative way. The BSs periodically measuretheir traffic loads and use it to determine an operational vari-able (called coalition factors in this section) and advertise it tothe MTs. The mobile terminals choose which BS to associatewith based on these coalition factors in order to minimize theobjective function. The association between the MTs and theBSs is updated until convergence. To ensure convergence ofthe scheme, we assume that the traffic arrival and departureprocesses occur at a faster time scale as compared to that at

which the BSs broadcast their coalition factors. This ensuresthat the users are able to make their association decisions forthe broadcasted coalition factors before the next broadcast ofcoalition factors by the BSs. We assume BSs to be synchro-nized, thus broadcasting their coalition factors at the sametime. The proposed user-association scheme can be easilyimplemented in a distributed way where the BSs periodicallybroadcast their coalition factor that can be embedded in thethe beacon signals of the BSs [32] and users can use them tochoose which BSs to associate with as described above.

Next, we begin with describing the user side and the BSside algorithms for carrying out the proposed user associationmechanism.

1) User Side Algorithm: We define the time between twosuccessive BS-MT association updates as a time slot in ouralgorithm. At the start of k-th time slot, the BSs send theircoalition factors to the users using a broadcast signal. Theusers at location x in turn choose the BSs they associate withbased on the coalition factors. In this section, superscript kis used to denote the value of a particular variable at thebeginning of the k-th time slot. The coalition factor broadcastby BS j is given as

φkj =∂Uk(ρ)

∂ρkj

=1

(1−ρkj )2+ηζjA(j)

(1−Λ(j)M(j)

B(j)− P0

(Mρkj +B(j))2

)(22)

where ζj is a variable which captures whether BS j is drawingpower from the grid. If the BS is drawing power from the gridthen this variable is 1, else it is set to zero. The MTs updatetheir user association functions as

qkj (x) =

{1 if j = arg max

j∈B

rj(x)

φkj

0 otherwise.(23)

Note that the association functions (qj(x)) are indicator ofwhich BS the MTs at location x associate with as discussedin Section III-A. The computational complexity of the userside algorithm for an individual user is O(|B|).

2) BS side algorithm: At the end of the k-th time slot, theBSs measure their load levels which we denote by Tj(ρ

kj ),

and is given as

Tj(ρkj ) = min

(∫X

γ(x)

rj(x)qj(x)dx, ρth

). (24)

After measuring Tj(ρkj ), the BS updates its traffic load whichis used to evaluate the next coalition factor to be broadcast fortime slot k + 1 as [12]

ρk+1j = αρkj + (1− α)Tj(ρ

kj ) (25)

with 0 < α < 1 being an averaging exponential factor.Next, the proof of convergence and optimality and conver-

gence of the proposed user association algorithm is presented.We begin by showing that the objective function U is convex inρ ∈ F̃ in Lemma 2 which leads to Lemma 3 which shows thatthere is an unique optimal user association which minimizes

7

the objective function.Lemma 2: The objective function U(ρ) = D(ρ) + ηE(ρ) is

convex in ρ when ρ is defined on F̃ .

Proof. This can be proven by showing that O2Ui(ρ) > 0. Theobjective function can be written in terms of ρ as

U(ρ) = D(ρ) + ηE(ρ)

=∑j∈B

(ρj

1− ρj+ ηζj (L(j)−G(j))

)=∑j∈B

(ρj

1− ρj

)+∑j∈B

(ηζj

(A(j)ρj+P0−

(Λ(j)M(j)

A(j)ρj + P0

A(j)ρj+B(j)

+(1−Λ(j)) (Bt−1(j)−νBcap(j)+Ht(j)))))

(26)

We evaluate the first and second order derivatives of theobjective function with respect to ρ which are given as

OU(ρ) =∑j∈B

(1

(1− ρj)2

+ηζjA(j)

((1−Λ(j))M(j)

B(j)− P0

(A(j)ρj+B(j))2

))(27)

O2U(ρ) =∑j∈B

(2

(1− ρj)3

+2ηζjA(j)2Λ(j))M(j)B(j)− P0

(A(j)ρj +B(j))3

).(28)

Note that all the addition terms in the function above arenon-negative, and 2

(1−ρj)3 is always positive for all the BSs.Thus, the above term is always positive which proves that thefunction is convex. Also for the case when grid energy is notdrawn, the component in the objective function for a particularBS just consists of the first term which is always positive. Thuseven for the case when energy is not drawn from the grid, theobjective function is convex in ρ. �

Remark: Note that as we consider the steady state analysisof the system, the proof above assumes that ∂f(ρj)

∂ρg= 0 , j 6=

g ([9], [12], [15]) where f(ρj) is purely a function of ρj anddoes not depend on ρg (g 6= j).

Lemma 3: A unique optimal user association ρ∗ ∈ F̃ existswhich minimizes U(ρ) = D(ρ) + ηE(ρ).

Proof. It has been shown in Lemma 1 that the objectivefunction U(ρ) is a convex function of ρ ∈ F̃ . Thus thereexists a unique optimal ρ = ρ∗ which minimizes U(ρ). �

Next we prove the convergence of the proposed user-association algorithm. We begin with proving that Tj(ρk)gives a descent direction for U(ρk) at ρk (shown in Lemma4). Thus after some iterations the traffic load converges whichis proved in Theorem 1. Further, in Theorem 2 we prove thatthe trafic load thus obtained minimizes the objective functionU(ρ).

Lemma 4: For ρk 6= ρ∗, Tj(ρk) gives a descent directionfor U(ρk) at ρk.

Proof. U(ρ) is a convex function of ρ ∈ F̃ . Thus the factthat T (ρk) gives a descent direction to U(ρk) at ρk can beeasily proved by showing < OU(ρk), T (ρk)) − ρk > ≤ 0(where < a, b > denotes the inner product of vectors a and b)[33]. Let qj(x) and qTj (x) be user association indicators whichresult in BS traffic ρkj and T (ρkj ), respectively. Then the innerproduct can be written as

< OU(ρk), T (ρk)−ρk >

=∑j∈B

(1

(1−ρkj )2+ηζjA(j)

(1−Λ(j)M(j)

B(j)− P0

(A(j)ρkj +B(j))2

))×(Tj(ρ

kj )− ρkj

)=∑j∈B

(1

(1−ρkj )2+ ηζjA(j)

(1−Λ(j)M(j)

B(j)− P0

(A(j)ρkj +B(j))2

))

×

(∫X

γ(x)(qTj (x)− qj(x))

rj(x)dx

)

=

∫Xγ(x)

∑j∈B

(( 1(1−ρkj )2

+ηζjA(j)(1−Λ(j)M(j) B(j)−P0

(A(j)ρkj+B(j))2

))rj(x)

×(qTj (x)− qj(x))

)dx.

Note that

∑j∈B

(1

(1−ρkj )2+ηζjA(j)

(1−Λ(j)M(j) B(j)−P0

(A(j)ρkj+B(j))2

))(qTj (x)−qj(x))

rj(x)

≤ 0 holds because qTj evaluated based on (23) maximizes thevalue of rj(x)(

1

(1−ρkj)2

+ηζjA(j)

(1−Λ(j)M(j)

B(j)−P0(A(j)ρk

j+B(j))2

)) . Thus we

have < OU(ρk), T (ρk)− ρk >≤ 0. �

Theorem 1: The traffic load ρ converges to the traffic loadρ∗ ∈ F .

Proof. We prove this by showing that ρk+1 − ρk is also adescent direction of U(ρk). To show this we consider thefollowing expression

ρk+1j − ρkj = αρkj + (1− α)Tj(ρ

kj )− ρkj

= (1− α)(T (ρkj )− ρkj ). (29)

In Lemma 3, it has been shown that (T (ρk) − ρk) is adescent direction of U(ρk). Further we have (1 − α) > 0as 0 < α < 1, thus ρk+1−ρk also gives the descent directionof U(ρk). Additionally, as U(ρk) is a convex function it canbe easily concluded that U(ρk) converges to ρ∗. If U(ρk)converges to any other point than U(ρ∗), then ρk+1 againgives a descent direction so as to decrease U(ρk), whichcontradicts the assumption of convergence. Further, becauseρk is derived based on (23) where qj(x) ∈ {0, 1}, ρ∗ is inthe feasible set F . �

Theorem 2: If the set F is non-empty and the traffic loadρ converges to ρ∗, the user association corresponding to ρ∗

minimizes U(ρ).

8

Proof. Let q∗ ={q∗j (x)|q∗j (x) ∈ {0, 1},∀j ∈ B,∀x ∈ X }and u = {qj(x)|qj(x) ∈ {0, 1},∀j ∈ B,∀x ∈ X } be theuser association corresponding to ρ∗ and ρ, where ρ is sometraffic load vector satisfying ρ ∈ F . As U(ρ) is a convexfunction over ρ, the theorem can be proved by showing <OU(ρ∗),∆ρ − ρ∗ > ≥ 0. In the proof below, we substitute∂U(ρ∗)∂ρ∗j

as φj(ρ∗j ) for notational clarity (these expressions areidentical as shown in the derivation leading to (22). We have

< OU(ρ∗),ρ− ρ∗ > =∑j∈B

φj(ρ∗j ) (ρ− ρ∗)

=∑j∈B

(∫X

γ(x)(qj(x)− q∗j (x))

rj(x)φ−1j (ρ∗j )

dx

)

=

∫Xγ(x)

∑j∈B

(qj(x)− q∗j (x))

rj(x)φ−1j (ρ∗j )

dx.

But because the optimal user association is determined basedon the following rule

q∗j (x) =

{1, if j = arg max

j∈Brj(x)φj(ρ∗j ) ,

0, otherwise.,

we can say that,∑j∈B

q∗j (x)

rj(x)φ−1j (ρ∗j )

≤∑j∈B

qj(x)

rj(x)φ−1j (ρ∗j )

. (30)

Therefore, < OU(ρ∗),ρ − ρ∗ > ≥ 0 which completes theproof. �

B. Base Station Transmission Power Control

We assume that the power control operations are decidedby the central server before a day begins and that guides thepower levels of the BSs during the day. Further as the powerlevel decisions are made on a time-scale of an hour, the powercontrol operations just require the average traffic profile ata given location for each hour. We assume that the centralserver has this average traffic profile information which is usedto evaluate the underlying user association for facilitating thepower control decisions. There are a number of existing papersin literature which study, model and predict cellular networktraffic like [27], [29] and [28] . The information/ideas fromthese models could be used in real time implementation of ourwork. Additionally, such information could be also predictedby the operators using the traffic pattern during past fewweeks/months. Note that the above-mentioned assumptionshave been considered in several contemporary works (e.g.[30], [31]). Next, we show an important observation aboutthe downlink power control.

Proposition 1: The objective function Qt(Pt) = Dt(Pt) +ηEt(Pt) is a non-convex function of the BS power levels.

To verify this proposition using simulations, we consider anetwork of BSs as shown in Figure 2. The simulation settingsare as described in Section VI. We consider BSs operating at 3p.m (t = 15) on January 1st with BSs 2, 4, 5 and 6 operating attransmit power level 20 W. Next, we vary the power levels ofBSs 1 and 3 and study the effect of the same on the objective

010

2030

40

0

10

20

30

4014.5

15

15.5

16

16.5

17

P1 (W)P3 (W)

Q15

Fig. 1. Objective function (Qt) value variation with power control operationson BS 1 and BS 3 (η = 2, t =15).

function. Figure 1 shows the objective function (for η = 2)and from the figure we can easily conclude that the objectivefunction is a non-convex function of the BS power levels.

As shown above, the power level control problem to min-imize the objective function is a non-convex optimizationproblem. Finding the optimal solution for such a problemrequires a search over the entire state space and has a very highcomputational complexity. The order of such computationsincreases exponentially with the number of BSs (B) and thehours under consideration (denoted by T ) and is given byO(N |B|T ) where N denotes the number of possible powerlevels the BSs can operate at. To make the power controlapproach feasible, we resort to developing a greedy heuristicfor addressing the problem of power control and the proposeddownlink transmit power control algorithm is presented inAlgorithm 3.

The proposed algorithm is carried out sequentially for eachhour of the day. The working of the downlink transmit powercontrol algorithm can be explained as follows. For every hour,all the BSs start with a transmit power level of Pmax. Nextwe check for which BS the decrement of power level bringsthe largest improvement in the objective function (Qt). TheBS with the largest reduction in the objective function whilesatisfying the system constraints (which is tracked in thealgorithm by the variable con) is chosen for transmit powerreduction. This is done until no further improvement in theobjective function can be realized. The improvement in thedelay component of the objective function in the power controloperations is due to its interference management and loadbalancing effect. The reduction in the grid energy consumptionis due to the transmit power level of a BS low on green energygoing down, and further, some users being offloaded (whichreduces ρ), thus decrementing the BS power consumption.The worst case computational complexity of this algorithmis O(N|B|2). Note that the load levels of the BSs changeafter every iteration of power control operations. Thus afterthis algorithm is carried out for all the hours of the day, wehave different traffic load profiles for the different hours as

9

Algorithm 3 Downlink Transmit Power Control Algorithm1: Initialization2: Set Pt(j) = Pmax for all j ∈ B3: Compute Qt(P ); Set δQ = 14: while δQ > 0 do5: Qold= Qt(Pt)6: for j = 1 : |B| do7: Pcurr = Pt8: Pcurr(j) = max(0,Pt(j)− ξ)9: Q′(j) = Qt(Pcurr)

10: if max(ρ) > ρth then11: con(j)= 012: else con(j)= 113: end if14: end for15: a. z : index of BS having con = 1 for which power

control leads to minimum objective function value (Q′)16: b. Set Qnew = Q′(z)17: δQ = Qold −Qnew18: if δQ > 0 then19: Pt(z) = max(0,Pt(z)− ξ) ;20: end if21: end while

compared to that used for initial energy allocation during theday (using Algorithm 1). Consequently, we repeat the energyallocation followed by another application of the downlinktransmit power control algorithm for the day. After someiterations of doing this (typically 3-4 iterations) the solution forthe downlink power levels converges. Note that the proposedpower control approach does not guarantee an optimal solutionbut gives an local optimal solution. It follows the intution ofgreedy descent approach to minimize the objective function.At a given iteration, the BS for which the power leveldecrement leads to maximum delay reduction is chosen to bepowered down. Thus the power levels for the next iterationgives a delay performance better than that at the previousiteration. Additionally as the number of power levels a BScan take are limited and lower-bounded by 0, the algorithm isguaranteed to converge.

VI. NUMERICAL RESULTS

For performance analysis of the proposed scheme, weconsider a 3G BS deployment (shown in Figure 2) deployedby network provider Vodafone near Southwark, London, UKwith 6 BSs providing coverage to an area of 1 km2. The BSsare assumed to be equipped with PV panel with DC rating 6kW and 10 batteries. We consider that the BSs use 12 V, 205Ah flooded lead acid batteries. The carrier frequency is 2.5GHz and we assume 10 MHz bandwidth with full frequencyreuse. Log normal shadowing with standard deviation 8 dBwith the correlation distance for shadowing taken as 50m hasbeen considered [35]. We model the path loss, PL, as [34]

PL(dB) = 40(1− 4× 10−3hBS)log10(R)− 18log10(hBS)

+21log10(f) + 80 (31)

Fig. 2. 3G BS deployment near Southwark (London).

where R denotes the distance between the MT and the BS,hBS is the base station antenna height above rooftop and f isthe carrier frequency in MHz. We take hBS as 15 meters andthe carrier frequency is 2.5 GHz, based on the suggestionsfrom the baseline test scenario mentioned in IEEE 802.16evaluation methodology document [35]. Thus, the path lossis calculated as PL(dB) = 130.19 + 37.6 log(R). We takethe noise power to be -174 dBm/Hz [35]. A homogeneousPoisson point process is used to generate the file transferrequest. The rate of the Poisson process depends on the hourof the day, with the smallest number of file transfer requestsduring early morning hours (2-5 am) with an average of 20requests per unit area (km2) and the largest number of requestsin the evening (5-7 pm) with an average of 200 requests perunit area. For weekends a lower traffic level with minimumand maximum number of file transfer requests (per unit area)of 10 and 150 respectively, in the corresponding hours havebeen considered. For simplicity, we assume that each filetransfer request requires 50 KB of data traffic to be served.The entire area (of 1 km2) is divided into 1600 locations witheach location representing a 25 m x 25 m area. To modeltemporal traffic dynamics, a new spatial profile of file transferrequests is generated after every 2 minutes. The location basedtraffic load density is calculated based on the traffic model.For simulations we consider solar energy data obtained fromNREL [23] for the month of January of typical meteorologicalyear (TMY) data for London. Figure 3 shows the solar energyharvested by the PV panels during the different days of thismonth by the BSs (with PV panels having DC rating 6 kW).Additionally we assume that 1st January is Monday (i.e.weekday load profile). The values of P0, Pmax and ∆ usedfor the results were 412.4 W, 40 W and 22.6 respectively [22].The granularity of the power control, ξ, was 5 W and ρth usedfor the results was 0.85. The value of ν, the limiting state ofcharge was taken as 0.3, and the safety margin β was takenas 0.1. The initial battery levels were randomly chosen for thedifferent BSs for 1st January. We take the averaging factor αfor the BS side algorithm to be 0.95, and with this value theproposed user-association algorithm was observed to converge

10

1 4 7 10 13 16 19 22 25 28 310

2

4

6

8

10

12

14

Day of the month

En

erg

y h

arve

sted

du

rin

g t

he

day

(kW

h)

Fig. 3. Solar energy harvested during the day by the BSs for the month ofJanuary of Typical meterological year (TMY) for London (PV panel rating:6 kW).

1 4 7 10 13 16 19 22 25 28 310

20

40

60

80

100

120

Day of the month

Grid

ene

rgy

cons

umpt

ion

(kW

h)

GD−RAM, η = 0GD−RAM, η = 1GD−RAM, η = 10Best−EffortSWESGALA

Fig. 4. Grid energy consumption for the different schemes.

to the optimal solution within 20 iterations.As a benchmark for comparison, we consider a Best-Effort

scheme where all BSs operate with transmit power 20 Wand the MTs associate with the BS with the strongest signalstrength at that location. BSs use green energy as long asit is available and after that draw energy form the grid. Wealso consider the GALA [13] scheme with BSs operating attransmit power 20 W, and the SWES [5] scheme which is aBS on-off scheme with BSs operating at 40 W when they areswitched on. The GALA and the SWES scheme have beenbriefly described in Section II.

A. Grid Energy Savings

Figure 4 shows the grid energy consumption for the differentschemes for the month of January. It can be seen that theBest-Effort scheme leads to very high values of grid energyconsumption. The GALA scheme shows significant grid en-ergy savings as compared to the Best-Effort scheme. Note thatthe SWES scheme has lower grid energy consumption thanthe Best-Effort and the GALA scheme. This is because inthis scheme some of the BSs switch off to reduce the overall

1 4 7 10 13 16 19 22 25 28 311

2

3

4

5

6

7

8

9

10

Day of the month

Ave

rage

net

wor

k la

tenc

y in

dica

tor

GD−RAM, η = 0GD−RAM, η = 1GD−RAM, η = 10Best−EffortSWESGALA

Fig. 5. Average network latency performance for the different schemes.

1 4 7 10 13 16 19 22 25 28 310

5

10

15

20

25

30

Day of the month

Pea

k ne

twor

k la

tenc

y in

dica

tor

GD−RAM, η = 0GD−RAM, η = 1GD−RAM, η = 10Best−EffortSWESGALA

Fig. 6. Peak network latency performance for the different schemes.

network power consumption. The BSs which are switched offsave energy and the energy harvested during this period isstored in the batteries to be used for future hours, thus reducingthe need to draw energy from the grid. The proposed GD-RAM scheme allows a wide range of control over the gridenergy consumption. Note that with η = 0, the grid energyconsumption is the highest which is comparable to the Best-Effort scheme. This is because for this case, the power controland user association operations are done solely considering thenetwork delay. For η = 1, we observe that the grid energyconsumed is smaller as compared to the other benchmarkschemes. Further, for η = 10 the energy drawn from the gridis even smaller. Note that the grid energy savings in the SWESscheme and our scheme for η = 10 is at the expense of anincrease in the network latency (Figure 5) which is discussedin the next subsection.

B. Delay Performance

Figures 5 and 6 show the average network latency andthe peak network latency for the benchmark schemes and forthe proposed scheme for three different values of the trade-off factor η for the days under consideration. Note that the

11

1 3 5 7 9 11 13 15 17 19 21 230

2

4

6

8

10

12

14

16

18

20

Hour of the day

Net

wor

k la

tenc

y in

dica

tor

(D)

GD−RAM, η = 0

GD−RAM, η = 1

GD−RAM, η = 10

Best Effort

SWES

GALA

Fig. 7. Hourly network latency for the different schemes (25th January).

proposed algorithm shows delay performance better than theBest-Effort and the SWES scheme for all three η values. Thenetwork latency performance of the GALA scheme is betterthan the Best-Effort and the SWES scheme. Note that for mostof the days, the average latency for η = 1 is smaller thanthat for η = 0. This is because of the non-convexity of theobjective function with respect to power control operations.Note that for η = 1, the BS power levels reduce to muchlower values as compared to the case for η = 0, so asto bring grid energy savings. Our experiments show that atlower BS power levels, there is better interference managementthrough the power control operations, thus also bringing downthe network latency. However, for η = 10, on certain dayswhich have very bad weather, the proposed scheme trades thenetwork latency performance for bringing about grid energysavings. For example, the values of the average delay andpeak delay on 25th January (which is a bad weather day)for η = 10 are significantly higher than that for η = 0 andη = 1. However on good weather days, like 12th January,the delay performance for η = 10 is comparable to that forη = 0 and η = 1. Additionally, the results show that thenetwork latency is lower on weekends as compared to theweekdays. This is because the traffic to be served on these daysis lower than that on weekdays. Note that the SWES schemeleads to a lower average delay on weekends as compared toall other schemes. This is because the traffic to be servedduring weekends is smaller and therefore most of the BSsturn off, thus reducing the interference to the BSs that areturned on. This contributes to reducing the system delay forthe SWES scheme on these days. However on weekdays, asthe traffic to be served is higher, turning off BSs has the effectof increasing the network latency as can be seen from theresults. Figure 7 shows the hourly network latency for 25th

January. The network latency is low for all the schemes duringthe early morning hours due to the low traffic during thosehours. However, during the daytime, the SWES scheme andthe proposed scheme for η = 10 lead to a higher delay thanthe Best-Effort scheme. The GALA scheme and our proposedscheme (for η = 0 and η = 1) have better delay performancethan the other benchmarks. Figure 8 shows the transmit power

levels of the BSs on 25th January for the GDRAM scheme forthree different η values. Note that the power levels for η = 0are relatively higher than for the cases when η = 1, 10. Thisis because for η = 0 the power control operations are aimedsolely on delay reduction. As η = 1 also accounts even forthe grid energy consumption, the power levels for this caseare lower as compared to those with η = 0. For the case ofη = 10, the power levels are still lower as compared to thecase of η = 1.

C. Grid Energy Consumption and Delay Trade-off

Figures 9 and 10 show the grid energy consumption anddelay trade-off for the proposed GD-RAM scheme for differenttrade-off parameter values and for the benchmark schemes(averaged for the month of January). Note that for GALAscheme, θ is the trade-off parameter and its value varies from0 to 1. Figure 9 considers the trade-off between the gridenergy consumption and the average (over 31 days) of thehourly network latency whereas Figure 10 considers the trade-off between the grid energy consumption and the average(over 31 days) of the daily peak network latency. We canobserve that for the proposed scheme, as we start increasing ηfrom 0, the average grid energy consumption reduces sharplywhile there is no degradation in the latency, rather there isa slight improvement in the network latency. The reason forthis phenomenon is the non-convexity of the objective functionwith respect to power control operations. Note that as the ηvalue increases from 0, the BS power levels become smallerin order to reduce the grid energy consumption. However, thepower level adjustments are made while accounting for thenetwork latency, in addition to accounting for the grid energysavings (as our objective function accounts for both). Figure8 shows the transmit power levels for three different η values(η = 0, 1 and 10). For η = 1, the transmit power levels forall the BSs are lower as compared to those for η = 0. Areduction in the transmit power level of a BS reduces the signalpower received by the MTs served by it. However, becausethe transmit power levels of the other BSs also reduce, theinterference term in (2) also reduces. Thus, the reduction inpower levels does not necessarily decrease the SINR (and thusthe rate offered by the BSs and in turn the network latency)at the MTs. Rather, slightly better latency performance isrealized due to better interference management when BSs areoperating at lower transmit power levels. However, for largevalues of η (say η = 10), as can be seen from Figure 8, tosave grid energy, the transmit power levels of the BSs arevery low and additionally some of the BSs are switched offeven during the peak traffic hours of the day (e.g. hour 16(4 p.m.) to hour 20 (8 p.m.)). This increases the traffic thatis handled by the BSs which are switched on and degradesthe network latency performance. Additionally, as the transmitpowers of the BSs decreases to very low levels, the impactof the reduced interference power on improving the SINRbecome marginal, and in many cases, the SINR degradesdue to lower signal power. These two factors contribute thedegradation of network latency at higher η values. Therefore,for higher values of η (e.g. η = 10), when η is increased,

12

1 3 5 7 9 11 13 15 17 19 21 230

5

10

15

20

25

30

35

40

45

50

55

60

65η=0

Hour of the day

Tra

nsm

it p

ow

er le

vel (

W)

BS1BS2BS3BS4BS5BS6

1 3 5 7 9 11 13 15 17 19 21 230

5

10

15

20

25

30

35

40

45

50

55

60

65η=1

Hour of the day

Tra

nsm

it p

ow

er le

vel (

W)

BS1BS2BS3BS4BS5BS6

1 3 5 7 9 11 13 15 17 19 21 230

5

10

15

20

25

30

35

40

45

50

55

60

65η=10

Hour of the day

Tra

nsm

it p

ow

er le

vel (

W)

BS1BS2BS3BS4BS5BS6

Fig. 8. Transmit power levels for the GD-RAM scheme for different η values (25th January).

3 3.5 4 4.5 5 5.5 6 6.5 70

10

20

30

40

50

60

Average network latency indicator

Ave

rage

grid

ene

rgy

cons

umpt

ion

(kW

h)

GD−RAMBest−EffortSWESGALAη = 0.1

η = 0

η = 0.5

η = 1

η = 2

η = 4

η = 10

η = 7η = 20

η = 40

η = 0.25

θ = 0

θ = 1

θ = 0.75

θ = 0.5

θ = 0. 25

Fig. 9. Tradeoff between grid energy savings and average network latency.

8 10 12 14 16 180

10

20

30

40

50

60

Average peak network latency indicator

Ave

rage

grid

ene

rgy

cons

umpt

ion

(kW

h)

GD−RAMBest EffortSWESGALA

η = 10

η = 0.1

η = 0

η = 1

η = 0.5

η = 0.25

η = 2

η = 7

η = 4

η = 20 η = 40

θ = 0.75 θ = 1

θ = 0.5

θ = 0. 25

θ = 0

Fig. 10. Tradeoff between grid energy savings and peak network latency.

the energy savings are less significant whereas the increase inthe delay for the marginal savings in the grid energy is veryhigh. For a η value of 1 we observe that there is around 60%grid energy savings as compared to the traditional Best-Effortscheme while ensuring a better network latency performance.Additionally, in Figure 11 we present results showing the

3.5 4 4.5 5 5.5 6 6.5 7 7.5 80

10

20

30

40

50

60

Average network latency indicator

Ave

rage

grid

ene

rgy

cons

umpt

ion

(kW

h)

GD−RAM− both power control and user association

GD−RAM− only power control

No power control,no user association

GD−RAM− only user association

η = 0

η = 0

η = 0.5

η = 4

η = 10η = 20

η = 40

η = 40

η = 1

η = 0.5

η = 1η = 4 η = 10

η = 20

η = 10

η = 0

η = 1η = 40

Fig. 11. Tradeoff between grid energy savings and average network latencyfor GD-RAM with and without power control and user-association.

energy-delay trade-off for the GD-RAM scheme with andwithout power control and user-association. It is note-worthythat the power control operation is much more effective inreducing the energy consumption as compared to the use ofuser-association reconfiguration.

VII. CONCLUSION

In this paper we considered a network of grid connectedsolar powered BSs. We proposed a methodology for reducingthe grid energy consumption while ensuring good quality ofservice. The methodology also gives the operator the freedomto mange the trade-off between the grid energy savings and thequality of service. The objective of reducing the grid energyconsumption while maintaining the QoS was achieved byintelligent temporal energy allocation, BS downlink transmitpower control and user association. A real BS deploymentscenario and real solar energy traces were used to test theperformance of the proposed methodology and to show itssuperiority over existing benchmark schemes. Compared toexisting schemes, the proposed GD-RAM scheme providescontrol over trading energy for delay, and for a good choice ofthe trade-off factor (η), it can outperform all other benchmark

13

schemes in terms of minimizing the grid energy required whilemaintaining good quality of service.

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Vinay Chamola received his B.E. degree in elec-trical & electronics engineeerig and Master’s degreein communication engineering from Birla Instituteof Technology & Science (BITS), Pilani, India in2010 and 2013 respectively. He received his Ph.D.degree in electrical and computer engineering fromthe National University of Singapore, Singapore, in2016. From June to Aug. 2015, he was a visitingresearcher at the Autonomous Networks ResearchGroup (ANRG) at the University of Southern Cal-ifornia (USC), USA. Currently he is a Research

Fellow at the National University of Singapore. His research interests includesolar powered cellular networks, energy efficiency in cellular networks,internet of things, and networking issues in cyberphysical systems.

Biplab Sikdar [S’98, M’02, SM’09] received theB.Tech. degree in electronics and communicationengineering from North Eastern Hill University,Shillong, India, in 1996, the M.Tech. degree inelectrical engineering from the Indian Institute ofTechnology, Kanpur, India, in 1998, and the Ph.D.degree in electrical engineering from the RensselaerPolytechnic Institute, Troy, NY, USA, in 2001. Heis currently an Associate Professor with the De-partment of Electrical and Computer Engineering,National University of Singapore, Singapore. His re-

search interests include wireless MAC protocols, transport protocols, networksecurity, and queuing theory.

Bhaskar Krishnamachari received his B.E. inElectrical Engineering at The Cooper Union, NewYork, in 1998, and his M.S. and Ph.D. degrees fromCornell University in 1999 and 2002 respectively.He is a Professor in the Department of Electrical En-gineering at the University of Southern CaliforniasViterbi School of Engineering. His primary researchinterest is in the design and analysis of algorithmsand protocols for next generation wireless networks.