Towards User QoE-Centric Elastic CellularNetworks: A Game Theoretic Framework forOptimizing Throughput and Energy Efficiency

Umair Sajid Hashmi∗, Amann Islam†, Karim M. Nasr‡§ and Ali Imran∗∗School of Electrical and Computer Engineering, University of Oklahoma, Tulsa, OK, USA

†Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, IL, USA‡Institute for Communication Systems, 5G Innovation Centre, University of Surrey, United Kingdom§Faculty of Engineering & Science, University of Greenwich, Kent ME4 4TB, United Kingdom

Abstract—User-centric network architectures are a keyproponent to enable the uniform Quality of Experience(QoE) requirement for future dense heterogeneous net-work (HetNet) deployments. However, catering to spatio-temporally varying user service demands arising from theplethora of diverse mobile applications remains a challengein such network architectures. In this paper, we proposea QoE-centric elastic framework for a dense multi-tiercellular network deployment. The framework leverages thecontrol and data plane separation architecture (CDSA) forenabling selective data base station (DBS) activation withinuser equipment (UE)-centric virtual cells (also referredto as service zones). The allocation of these virtuallyelastic service zones around selected UEs is conductedvia a central control base station (CBS) and modeledthrough two game techniques, namely evolutionary andauction games. Both the games are based on a utility min-imization problem which is a function of weighted meanUE throughput and usage based UE service demands. Toillustrate the trade-offs between the game models, networklevel performance is compared in terms of aggregatethroughput, energy efficiency, algorithm convergence speedand mean UE scheduling probabilities.

Index Terms—User-centric architectures, Control andData Plane separation, evolutionary game, auction game

I. INTRODUCTION

Network densification through the use of small cellsis considered a viable solution for meeting the capacitytargets in future cellular networks (i.e. 5G). Whiledensification is inevitable, it has a couple of majorassociated problems that persist as a bottle neck innetwork planning: i) high inter-cell interference andii) low energy efficiency [1]. Though upcoming 5Gtechnologies such as massive multiple input multipleoutput (MIMO) and millimeter wave (mmWave) of-fer promising prospects for increased system capacity[2], they may not address the aforementioned issues.Redesigning the network orchestration in cell planningfrom the traditional base station (BS)-centric to a userequipment (UE)-centric approach [3] has been recentlyenvisioned as a first step to address these challenges [4].This user-centric (UEC) architecture guarantees a higherenergy efficiency (EE) along with location-independent

uniform Quality of Experience (QoE). Analysis in [5]has shown that the cell density that yields optimal EEis different than that which yields maximum outagecapacity. In [6], we leverage this analysis to proposea UEC network deployment solution where an ultra-dense network is deployed, and is then orchestratedbetween EE and area spectral efficiency (ASE) optimalmodes by intelligently switching OFF/ON small cells.This switching ON and OFF is done by creating non-overlapping exclusion zones around high priority UEswithin which only one small cell is turned ON duringeach scheduling instant. The size of the exclusion zoneis then used as a control parameter to realize the desiredcompromise between EE and ASE. However, due todiversity in mobile data usage trends, a static networkwide optimal exclusion zone size does not offer theelasticity to optimize individual user’s QoE in differentspatio-temporal zones.

In this paper, we present and introduce a secondtier of elasticity within UEC systems that integratesnon-uniform exclusion zones centered around users.These non-uniform exclusion zones, which we call asservice zones (S-Zones), cater for data demand disparitybetween spatio-temporal zones as well as the diversityof data requirements from user applications (for instanceHD video streaming v/s whatsapp messaging) within asingle spatio-temporal zone. The basic premise behinddeploying virtual flexible service zones around mobileusers is to control the interference limit that a user canexperience while still getting the throughput sufficientfor its data needs. For instance, high definition real-time gaming applications will require a high throughputand low latency communication link, which can beguaranteed if the signal to interference ratio (SINR)is sufficiently high. To ensure that, the controller willassign this user a large service zone to not only assignit larger number of resources, but also to reduce in-terference from concurrent downlink transmissions forother users. The same is true other way round for

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IoT based sensor devices that require low throughputtransmission, and hence a relatively moderate SINR.Consequently, a smaller service zone would suffice fortheir data requirements.

This demand based UEC scheme is an ideal can-didate for implementation in a control-data separationarchitecture (CDSA) [7] where small cells referred to asdata base stations (DBSs) provide data services to UEswhile macro base stations also referred to as control basestations (CBSs) provide necessary control and signaling.While CBSs provide the essential coverage, intelligentactivation/de-activation of the DBSs enables potentialfor significant energy savings in CDSA. In addition tothis, CDSA can offer better spectral efficiency mainlybecause of selection diversity that stems from largenumber of DBSs in dense deployments. Centralized co-ordination at the CBS solves the cell discovery problemfor DBSs in a conventional BS-centric architecture. Inthe proposed UEC framework, this allows for turningDBSs ON/OFF, depending upon an individual UE’s S-Zone size and the propagation link quality between thatUE and the DBSs within its S-Zone.

The analysis of strategies UEs may adapt whilecompeting for downlink (DL) resources to meet theirdata requirements in a UEC CDSA is the focus of thispaper. To this end, we investigate the application ofgame theoretic techniques which have been well knownfor resource management and interference mitigation indense small cell networks [8] [9]. In particular, we applyauction and evolutionary game techniques (referred to asAGT and EGT respectively), with users as game playersadapting strategies to secure DL scheduling within vir-tually interference free S-Zones. While there has beensignificant research in user-centric networks in recenttimes [10],[11], to the best of our knowledge, analysisof second tier elasticity in user-centric CDSA that catersto non-uniform user demands remains a terra incognita.This work is a first attempt to analyze the tradeoff ofgame theoretic techniques for UE level demand basedCDSA architecture. The contributions and findings ofthis work are summarized as follows:A. Contributions• The analysis of UE-centric systems with a CDSA

architecture requires incorporating the idiosyn-crasies of the dynamic activation/de-activation ofDBSs within a two-tier network. We present a sys-tem model that links the activation of DBSs to userrequirements as well as the level of interference inthe environment surrounding the scheduled users(Section II-A,B,C,D).

• Contrary to our previous UEC models in [4], [5]and [6] that were based on static first tier exclusionzone modelling, this work takes a step furtherand incorporates the effect of non-uniform userdemands across and within spatio-temporal zones(Section II-E).

Fig. 1. S-Zones concept illustration in UE-centric CDSA architectures.

• In order to evaluate mechanisms for integratingthroughput demand disparity in S-Zone assignment,we perform a detailed comparative analysis usingtwo game theoretic techniques, namely evolution-ary game and auction theory (Section III). Both thegames are based on a distributed utility minimiza-tion problem. The evolutionary game involves itera-tive action strategy adjustment by the UEs, whereasthe auction game comprises of UEs bidding theirtrue valuation with the aim of winning the auctionand securing virtual S-Zones for DL scheduling.

• Simulation results are presented for performanceevaluation of the algorithms in terms of aggregatesystem throughput, energy efficiency, user schedul-ing ratio and mean algorithm convergence time(Section IV). We show that the proposed QoEbased user-centric service zone provisioning yieldsbetter performance as compared to a UE-centricnetwork with static system-wide service zone area.Our analysis advocates integration of an intelligentself-organizing network (SON) engine [12] withinthe proposed UEC CDSA network architecture. TheSON engine would optimize a network efficiencymetric by dynamically shifting game strategies withrespect to network dynamics and spatio-temporallyvarying operator’s business model.

II. SYSTEM MODELA. UE-Centric CDSA Network

Fig. 1 shows a UE-centric based CDSA networkmodel where users having a high payoff (used inter-changeably with utility) and scheduling priority areserved by a single DBS providing best channel quality(e.g. CQI (channel quality indicator) measure) withintheir virtual service zones respectively. Each scheduledUE is the center of an S-Zone with an active DBS.The remaining DBSs within and outside the S-Zones areturned OFF to reduce inter-cell interference as well aslower overall power consumption. The area of S-Zonesaround scheduled UEs is adjustable based on individualUE’s throughput requirements. This two-tier CDSA withelastic service zone model consists of a central CBSproviding essential control and signaling functionalities

to the UEs while the DBSs serve the UEs with DLdata transmissions. Based on the channel feedback bythe UEs, the CBS allocates S-Zones to scheduled usersbased on outcome of game models (Section III) duringeach transmission time interval (or TTI).B. Network Model

Borrowing from well established tools in stochasticgeometry [13], we model the spatial distributions ofDBSs and UEs using two independent stationary Poissonpoint processes (SPPPs): ΠDBS ∈ R2 and ΠUE ∈ R2

with intensities λDBS and λUE respectively. Specifically,at an arbitrary time instant, the probability of findingni ∈ N, i ∈ {DBS,UE} DBSs/UEs inside a typicalmacro-cell with area foot-print A ⊆ R2 follows thePoisson law with mean measure Λi(A) = λiv2(A)[4]. The mean measure is characterized by the averagenumber of DBSs/UEs per unit area (i.e., λDBS\λUE )and the Lebesgue measure [13] v2(A) =

∫A dx on R2,

where if A is a disc of radius r then v2(A) = πr2 isthe area of the disc.C. Channel Model

The channel between a DBS x ∈ ΠDBS and anarbitrary UE y ∈ ΠUE is modeled by hxyl(||x − y||).Here hxy ∼ E(1) is a unit mean exponential ran-dom variable which captures the impact of a Rayleighblock-fading channel between x and y. The small-scaleRayleigh fading is complemented by a large-scale path-loss modeled by l(||x−y||) = K||x−y||−α power-lawfunction. ||x− y|| is the Euclidean distance between xand y, K is a frequency dependent constant and α ≥ 2is an environment/terrain dependent path-loss exponent.The fading channel gains are assumed to be mutuallyindependent and identically distributed (i.i.d.). Withoutany loss of generality, we assume K = 1 for the rest ofthis discussion. Furthermore, we assume that all DBSsemploy the same transmit power.D. UE-Centric DBS Scheduling

The first step in DBS scheduling is identification ofhigh priority users to be scheduled in a given TTI. Thesecond step is creation of non-overlapping circular S-Zones centered around each UE selected to be servedin that TTI. The size of the S-Zone is the parameterof optimization and will be discussed later. Each UE isthen served by a DBS within its S-Zone that providesstrongest received signal power. The remaining DBSsare switched off. The size of circular S-Zone around ascheduled UE x is characterized by a variable radiusRSZ,x which is a function of x’s data requirements andthe interference from nearby active DBSs. The CBS isresponsible for control signaling to all the UEs within itsfootprints. In addition, the CBS also assigns schedulingpriorities in the form of a mark/tag pUE ∼ U(0, 1) toeach UE. The marked PPP [13] formed as a result ofuser-centric scheduling impacts the downlink schedulingpriority of the UEs. More specifically, the lower the

value of the mark, the higher is the priority of the UEto be scheduled. Effectively, these marks can be thoughtof as the timers corresponding to each UE that aredecremented in each time slot where DL service to thisUE is deferred. Based on the channel quality measurebetween the DBSs and the UEs, the CBS decidesand activates the relevant DBSs for DL transmissionto the scheduled UEs. The advantages of such UECscheduling is two-fold: firstly, due to non-overlappingS-Zones, the interference experienced by a scheduledUE is considerably reduced and secondly, on-demandactivation of DBSs provides the network self-organizingcapabilities to cope with spatio-temporal variations inuser demography.

One might argue that such a one-to-one UE-DBSassociation within a non overlapping user-centric S-Zone scheme may result in service holes, i.e. there mayexist UEs that are not associated with any DBSs dueto empty UE-centric S-Zones. Since we are consideringdense small cell deployments with λDBS and λUE ofthe same order, UE-centric S-Zones with realistic areaswill hardly be void. In the unlikely scenario of a voidS-zone though, user clustering strategies [14] may beemployed where nearby UEs are grouped together andoptimization is performed on the UE clusters ratherthan individual UEs. Furthermore, it is known that bestDBS activation with a proximity constraint providesdual benefits of low outage probability and high powerefficiency in dense deployment scenarios [15].E. UE’s payoff function and S-Zone size for Gameformulation

Payoff function: We model the payoff of a UE xas ux = δ(τ̄ − τx(RSZ,x)) + (1 − δ)(τd,x − τx(RSZ,x));where τx(RSZ,x) is the achievable data throughput for x,τ̄ = 1

N

∑Nn=1 τn is the mean achievable user throughput

(considering N active UEs) of the spatio-temporal zoneestimated through a central entity (such as the CBS) andτd,x is x’s variable throughput demand based on theapplication usage. 0 ≤ δ ≤ 1 is a weight priority index,controllable via CBS, with factor δ enforcing uniformthroughput regardless of service demand disparity while1 − δ allows users with high scheduling priority toselfishly meet their data demands at the expense of non-priority users.

The first component of the payoff measures the utilityof a UE in terms of the penalty (positive / negative)depending upon how much lesser / greater the UE’sachievable throughput is to the mean achievable through-put of all UEs. Similarly, the second component ofthe payoff determines the penalty associated with howdeviant the achievable throughput is to the UE’s actualservice based throughput demand at a given S-Zoneradius. Using this novel characterization of payoff, wecan formulate the optimization problem to be solved bythe game models for a UE x’s payoff as a function ofRSZ,x and given as

minRSZ,x

|δ(τ̄ − τx(RSZ,x)) + (1− δ)(τd,x− τx(RSZ,x))|. (1)

S-Zone radius: The achievable throughput for a UE xis expressed using Shannon’s theorem as

τx(RSZ,x) = log2(1 + SINR(RSZ,x)), (2)

where the S-Zone size dependent received SINR at xwhen served by DBS y can be written as follows:

SINR(RSZ,x) =maxy∈ΠDBS∩(x,RSZ,x)hxyl(||x− y||)

No +∑

z∈ΠIhxzl(||x− z||) . (3)

ΠDBS ∩ (x, RSZ,x) is the thinned PPP representing theDBSs within the UE-centric virtual circular cell ofarea πR2

SZ,x around x, ΠI denotes the thinned PPP ofinterfering DBSs, i.e. the active DBSs in S-Zones otherthan that centered around x, and No is the variance ofthe additive white Gaussian noise at x.

To ensure that the UE-centric S-Zones are withinpractical dimensions, we tried several mathematical for-mulations of RSZ,x as a function of λDBS, λUE andγx. Drawing insights from extensive simulation basedexperiments with different DBS and UE densities, wepropose the following model to characterize the S-Zonearea around a UE x served by a DBS y1:

RSZ,x =||x− y|| ln(λDBS)

(1− γx) ln(λUE), (4)

where 0.1 ≤ γx ≤ 0.9 is the application based variableUE demand with normal distribution N(0.5, 0.1). Thelimits on the UE demand ensures avoiding circumstanceswhen UEs with extremely high/low service demandsrequest impractically high/low S-Zone radii.

III. GAME FORMULATIONS FOR UE-CENTRICSERVICE ZONE SCHEDULING

We leverage both evolutionary (EG) and auction (AG)games to determine optimal S-Zone sizes by solving theoptimization problem in (1). Let N={1,2,...,N} denotethe set of UEs participating in each game iteration.Each UE x demands a certain throughput τd,x, whichis a function of the variable demand variable γx, suchthat τd,x ∝ γx. For this work, we consider a linearrelationship, τd,x = Kγx+ε, where ε is the UE specificnoise in the throughput demand. The throughput demandτd,x in turn determines the S-Zone radius RSZ,x throughiterative update in γx until convergence is achieved forthe utility in (1). The CBS calculates and communicatesτ̄ to every UE within its coverage so that they may adjustγx with the objective of solving (1).

A. Evolutionary Game

In the context of an evolutionary game for S-Zonesize optimization, each UE adapts its demand strategyaccording to the received payoff in (1). This evolutionof the game allows the population states to evolve overtime. For this work, we are considering two UE popu-lation states: over-served and under-served expressed as

1Note that the formulation for RSZ,x is done for the parametersconsidered in Section IV. A different formulation may be required forsuburban and sparsely deployed DBS regions.

UEOS and UEUS respectively. An over-served UE is char-acterized by a negative utility in (1) indicating surplusresources in terms of higher achievable throughput ascompared to the mean throughput and/or the applicationbased throughput demand. The action strategy for over-served UEs is an adjustment in their S-Zone size througha prefixed step reduction in γx. Similarly, the under-served UEs with positive utilities increase their S-Zoneareas through a prefixed step increase in γx, within thedemand constraints (Step 1, Algorithm 1).

The evolutionary game in Algorithm 1 is governedby principles of replicator dynamics [9], according towhich the number of UEs selecting a particular strategywill increase if that action yields close to zero payoff.The frequency for a particular action strategy is given byXs = Ns

N . Ns is the number of UEs selecting strategys where s ∈ S = {increase γx, reduce γx}.

Algorithm 1 EG algorithm1: Each UE chooses a throughput demand τd,x based onthe application usage. The disparity in τd,x is modeledby assuming that the UE demand γx has a normaldistribution, i.e. γx ∼ N(0.5, 0.1), and constraints 0.1 ≤γx ≤ 0.9. Iteration counter is set to i = 1.2: Based on the channel gains and γx values, the CBScalculates RSZ,x, creates virtual S-Zones around highpriority UEs and turns ON a single DBS per S-Zone.Elaborating mathematically, a UE x is scheduled iffp{x}UE < p

{x′}UE ;∀x ∈ ΠUE,x

′ ∈ ΠUE ∩ (x, RSZ,x),x′ 6=x.3: The scheduled UEs observe SINR(RSZ,x) and sub-sequently the achievable throughput τx(RSZ,x) which issent to the CBS.4: The CBS calculates τ̄ and broadcasts it to all UEs.5: Each scheduled UE computes its utility ux and adjustsγx. If ux > 0, then γx = min(γx+0.05, 0.9); if ux < 0,then γx = max(γx − 0.05, 0.1); and left unchangedotherwise.6: Update p{x}UE , increment i and go to step 2 while i <imax.

imax is the maximum number of simulation itera-tions for a given network configuration. The EG basedstrategy adaptation algorithm functions in a distributivemanner where each UE adapts its individual strategyto optimize (1). Additionally, the algorithm relieves theCBS from centralized optimization computation, makingits implementation scalable throughout the network.

B. Auction GameAuction theory allows players to intelligently select

their strategies in order to gain maximum resources. Forour work, we adapt the Vickrey Clark Groves (VCG)auction mechanism which is known for ensuring assur-ance of truthfulness from the players as well as max-imization of fairness [16]. Also called the "sealed-bid

second-price auction", this auctioning scheme awardsthe bid to the highest bidder who pays an amountequivalent to the second highest bid. Contrary to thefirst price auctions, VCG auctions prevent selfish playersfrom cheating because bidding the true valuation isthe weakly dominant strategy in this model [17]. Thisguarantees that under most general circumstances, VCGwill yield bid winners as players with highest valuations.

In contrast to EG where S-Zone assignment wasdependent upon p

{x}UE alone, in AG (Algorithm 2), we

integrate the utility ux within the bidders’ (or UEs’)valuation structure as

bx =1

p{x}UE [δ(τ̄ − τx(RSZ,x)) + (1− δ)(τd,x − τx(RSZ,x))]

.

(5)

As seen from (5), the UEs with optimal utilities arerewarded with higher bid values. Each iteration in theAG is a new game as the winners of the conductedauctions are assigned S-Zones by the CBS and barredfrom further bidding. Because we analyze system levelperformance metrics, the cost paid by UEs after winningthe bids is irrelevant for this work. However, we employa VCG auction due to its relevance to wireless networks[18]. Moreover, the existing framework can be analyzedin extensions of this work and include the effect of UEcost when modeling the network over large number ofTTIs.

Algorithm 2 AG algorithmSteps 1-4 same as EG algorithm.5: Each UE participating in the auction calculates its bidvalue bx and sends it to the CBS.6: The CBS chooses a player as the winner of the auctionif its bid is not lower than any other player that can forma non-overlapping S-Zone with the existing S-Zones, i.e.a UE x is the auction winner iff bx > bx′ ;∀x,x′ ∈ Π

′

UE,where Π

′

UE refers to the UEs whose RSZ,x (and RSZ,x′ )allow non-overlapping S-Zones with past auction win-ners.7: The CBS removes the auction winner in currentiteration from future bidding. New bidding round (step5) continues until there is no new winner.8: CBS schedules auction winners, updates p{x}UE and i.Go to step 3 and re-evaluate the metrics for existingplayers. Continue until i < imax.

IV. SIMULATION RESULTS AND DISCUSSION

In this section, we discuss the simulation results fora range of efficiency parameters to evaluate the perfor-mance of the game theoretic techniques in question, i.e.EGT and AGT within the elastic CDSA framework. Thebasic simulation parameters are given in Table 1.

A. Aggregate Throughput performance

The aggregate throughput is calculated numericallyas the sum of the achievable throughput of the served

TABLE ISIMULATION PARAMETERS

Parameter ValueSimulation area dimensions (|A|) 100 m x 100 m

λUE|A| 400λDBS|A| 50, 100, 150

α 4δ 0, 0.25, 0.5, 0.75, 1

Power consumption parametersPo, Pu, ∆u and Pou 6.8, 1, 4 and 4.3 W

θ 0.5imax 100

No. of Monte Carlo realizations 1000

UEs within a TTI, i.e. λDBS,Act|A|∑λDBS,Act|A|

1 τx whereλDBS,Act|A| denotes the number of activated DBSs (orserved UEs) in the network. The results in fig. 2 revealcontrasting trends with varying δ and DBS densitiesunder considered game theoretic algorithms. While theEGT demonstrates reduction in throughput for the rangeof DBS densities considered as δ increases, the AGTshows increasing throughput trends for denser DBSdeployments with an increase in δ. The trends aredisruptive for δ = 1 which is the pure fairness centricscheduling scheme and takes no consideration of users’QoE requirements.

As far the deployment density is concerned, EGTis the superior scheme for λUE/8 DBS density. Fordenser networks with mean DBS deployment densityof 3λUE/8, AGT is clearly the preferred game model.The findings highlight the necessity of a SON imple-mentation within the CBS for intelligent and dynamicadaptation of game model as a function of both λDBSand δ to maximize the system throughput.

Fig. 2. System throughput comparison of EGT and AGT.

B. Energy Efficiency of the UEC CDSATo estimate the EE of an elastic CDSA under UE-

centric architecture, we take inspiration from the work ofaward winning European project EARTH [19] and applyrelevant modifications to construct a power consumptionmodel for a UE-centric CDSA given as

PCDSA = λDBS,Act|A|(θPo + ∆uPu + Pou), (6)

where Po, Pu and Pou denote fixed power consumptionof an active DBS, transmit power of a UE terminal andcircuit power consumed at UE terminal during discoveryrespectively [20]. 0 ≤ θ ≤ 1 is a system deploymentefficiency parameter with θ = 1 capturing least energyefficient deployment. The power consumption of theCDSA as seen from (6) is an increasing function of theDBS density and a decreasing function of the averageUE S-Zone area.

Fig. 3. Energy Efficiency comparison of EGT and AGT.

Although AGT (fig. 3) demonstrates comparable EEperformance for λDBS = λUE/4 and δ ≤ 0.5; for mostof the simulated scenarios, EGT is a clear winner. Thiscan be attributed to a larger average S-Zone area for theEGT implementation which reduces the average numberof concurrent DL transmissions and hence more DBSsare deactivated.

C. Convergence analysis

To analyze the convergence of the algorithms, weplot the average payoff received by UEs using EGT andAGT (fig. 4). It can be seen that the system convergesto equilibrium relatively faster with AGT. Particularlyat low DBS densities, for instance at λDBS = λUE/8in fig. 4b, the mean UE utility converges to 0 almostinstantly. Not only does the AGT outperform EGT inconvergence speed, but also in achieving optimal UEutility, i.e. by minimizing |ux|. Negative utilities forEGT indicate UEs receiving sufficiently high SINRto attain achievable throughputs exceeding the desiredlevels needed to optimize (1). The root cause for thenon-ideal UE utility distribution with EGT can be tracedback to UE demand constraints (0.1 ≤ γx ≤ 0.9) whichbars the UEs with high negative utilities to further reducethe S-Zone size and increase their utility.

D. UE Scheduling success

The expected delay for a UE waiting to be sched-uled is analyzed by plotting the mean served UE ratio(λDBS,ActλUE

) under variable DBS densities and δ values(fig. 5). The served UE ratio represents the expectednumber of scheduled UEs after equilibrium is achievedfor the EGT and AGT games. The smallest wait time

Fig. 4. Convergence of (a) EGT and (b) AGT algorithms for an elasticUEC CDSA network.

is observed for AGT scheme with λDBS = 3λUE/8where an arbitrary UE is expected to be re-scheduledafter every 5th or 6th TTI. For λDBS = λUE/8, EGTmarginally outperforms AGT while AGT exhibits higherscheduling success for δ ≥ 0.5 when λDBS = λUE/4.The simulation results in fig. 5 once again reiterate thepracticality of a SON engine capable of adjusting δand alternating between game models to yield desiredservice delay times within UE-centric CDSA.

Fig. 5. UE Scheduling Success probabilities with EGT and AGTalgorithms.

E. Performance Comparison with first tier user-centricelasticity

Fig. 6 shows the performance gains in terms of aggre-gate system throughput (fig. 6(a)) and energy efficiency(fig. 6(b)) for the proposed UE-centric elastic CDSA incomparison to the uniform user-centric service regionsproposed in earlier works [21]. The network models withfixed user-centric regions in [21] to maximize ASE andEE are referred to as FS(ASE) and FS(EE) respectively.The variable-sized QoE-centric service zones proposedin this work with EGT and AGT implementations arereferred to as VS(EGT) and VS(AGT) respectively.Clearly, the proposed model outperforms "one-size fitsall" strategy both in terms of system throughout andEE by virtue of assigning flexible user-centric servicezones that are appropriately sized to meet an arbitraryUE’s data requirements. While AGT yields higher datathroughput, particularly at high λDBS, the EGT is moreenergy efficient. Once again, this result reiterates the

need for an intelligent SON enabled CBS that can switchthe game models to support a higher data throughout (orenergy efficiency).

0.005 0.01 0.015λ

DBS

0

100

200

300

400

Aggre

gate

Thro

ughput

FS(ASE)

FS(EE)

VS(EGT)

VS(AGT)

0.005 0.01 0.015λ

DBS

0

0.5

1

1.5

2

2.5

EE

(bits/s

/J)

FS(ASE)

FS(EE)

VS(EGT)

VS(AGT)

(b)(a)

Fig. 6. (a) System throughput and (b) EE comparison of uniform user-centric [21] and QoE-centric service zone approaches with differentDBS densities.

V. CONCLUSION

In this paper, we presented an elastic cellular networkframework capable of catering to individual UE QoErequirements. The QoE flexibility is realized throughvirtual interference free service zones centered aroundscheduled UEs. We proposed a distributed utility mini-mization problem to model appropriate S-Zone forma-tions around the UEs. To evaluate the optimization of S-Zone allotment to UEs, we conducted a detailed compar-ative analysis using evolutionary and auction based gameimplementations at a centralized CBS. We investigateddifferent key performance indicators including aggre-gate network throughput, energy efficiency, mean UEscheduling probability and algorithm convergence speed.Results indicated that for each efficiency metric, withvariations in DBS density and the priority distributionbetween a fair UE throughput network versus a ser-vice requirement driven throughput network, the gamescheme exhibiting superior performance fluctuates. Tofully optimize a network efficiency parameter, we ad-vocate a SON enabled CBS that is capable of dynamicadaptation of game modes to offer higher throughputor energy savings, whichever is desired by the net-work operator. Future works include evaluation of theproposed model at mmWave frequencies and includingthe associated signaling costs within the optimizationframework.

ACKNOWLEDGEMENT

This material is based upon work supported by theNational Science Foundation under Grant 1619346,Grant 1559483, Grant 1718956, and Grant 1730650.

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