1

Energy Prioritized Caching for Cellular D2DNetworks

S. Sinem Kafıloglu, Gurkan Gur† and Fatih AlagozDepartment of Computer Engineering, Bogazici University

Istanbul, Turkey†Zurich University of Applied Sciences (ZHAW)

Winterthur, SwitzerlandEmail: {sinem.kafiloglu, fatih.alagoz}@boun.edu.tr, gueu@zhaw.ch

Abstract—Multimedia content transmission heavily taxes net-work resources and puts a significant burden on wireless systemsin terms of capacity and energy consumption. In this context,device-to-device (D2D) paradigm has a utilitarian value to al-leviate the network burden by utilizing short-range transmis-sions with less energy cost. For the realization of proper D2Dnetworking, caching in devices is essential. Additionally, cachingneeds to operate efficiently with the aim of realizing network-wideenergy improvements. To this end, we study multimedia cachingin cellular D2D networks and propose an energy prioritized D2Dcaching (EPDC) algorithm in this work. We also investigatethe optimal caching policy in that system setting. The impactof device capacity and D2D transmission range on energyconsumption is studied by focusing on different operation modessuch as D2D and base station transmissions. According to thesimulation results, EPDC algorithm has substantial energy-efficiency gains over the commonly utilized Least Recently Used(LRU ) algorithm and content-based caching algorithms PDCand SXO. For larger D2D transmission ranges, this improvementbecomes more evident.

I. INTRODUCTION

The multimedia traffic in data networks has surged withthe exploding video consumption of users and substantiallyenriched services of multimedia providers. Based on the CiscoAnnual Internet Report forecasts, multimedia continues tobe of enormous demand today, and there will be escalatedburden with the application requirements of the future with8K and VR streaming, and cloud gaming even beyond theforecast period of 2023 in 5G networks [1]. In this context,the network operators have to meet certain QoS levels forprovisioning consumer-driven content-based services. Never-theless, the network resources are limited and burgeoningcontent consumption requests are observed leading to spikingenergy consumption. In that regard, the energy efficiency(EE) problem emerges in these content-flooded networks.This problem needs to be resolved by practical networkingparadigms in an efficient manner.

In-network caching is one of the techniques to alleviate theEE problem in future wireless networks. In this approach, thenetwork load is reduced while transmission latency is low-ered [2]. In [3], an energy-efficiency based in-network cachingalgorithm is proposed. It can perform better than the existing

This work was supported by the Scientific and Technical Research Councilof Turkey (TUBITAK) under grant number 116E245.

algorithms in term of both energy consumption and cache hitrate according to their simulation results. Fang et. al. alsoinvestigated in-network caching for achieving green contentcentric network paradigm [4]. Overall, in-network caching isa promising solution to tackle the EE challenges. In the samevein, Device-to-Device (D2D) communication technique isbeneficial in terms of various aspects such as delay reduction,improved data rates, boosted spectral efficiency in addition toreduced energy consumption [5]. D2D mechanism can be usedas a relaying factor to improve the power-efficiency of cellularnetworks [6]. It also improves the radio resource utilization toalleviate the communication coverage challenges in cellularsystems [7]. Therefore, it is posed as a crucial enabler forboosting system capacity for heavy multimedia workloads andimproving network-wide energy efficiency [8].

The simultaneous exploitation of edge caching and D2Dnetworking is broadly studied, e.g. [9]. The major part of theliterature focuses on the service improvement as a crucial ele-ment in cache-aided D2D networks [10], [11]. In that regard,some studied metrics are throughput [10], total service suc-cess probability [11], transmission delay [12] and offloadingrate [12], [13]. Furthermore, the energy consumption and effi-ciency pose as vital metrics to be examined in cache-enabledD2D networks. In [8], the energy efficiency in a D2D cachingHetNet is investigated in great detail without focusing on D2Dcaching optimization. On the contrary, in [14] a greedy cachingalgorithm is proposed and compared to the optimal case interms of energy efficiency. That latter work resides not on D2Dnetworks but Information-Centric Networks (ICNs). Lee et.al. propose caching policy and cooperation distance design inD2D caching networks for i) energy efficiency ii) throughputoptimization separately in [15]. However, their energy modelis limited to the device reception powers only.

In this work, we investigate the edge cache managementtechniques in D2D cellular networks owing to the fact thatin-network caching is regarded as an efficient facilitator forimproving system-wise energy consumption. We have a com-prehensive service-mode based energy model and define con-tent energy expenditures based on the prospective consumptionacross the network. We formulate the optimization for thecache replacement problem in D2D networks and solve itwith dynamic programming. Besides, we propose a heuristicalgorithm Energy Prioritized D2D Caching (EPDC) to im-

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prove the time complexity of the content services. Finally, arigorous performance analysis is performed while focusing onthe service rate and energy consumption in different operationmodes separately.

The key contributions of this work are as follows:• We introduce a new energy expenditure model based on

prospective energy consumption for content retrieval incellular D2D networks.

• We optimally manage caches for the replacement problemin our D2D network architecture with the aim of keepingcontents that would induce large energy cost.

• We propose an energy cost based heuristic, namely En-ergy Prioritized D2D Caching (EPDC) algorithm.

• We investigate the impact of cache capacity and D2Dtransmission range on the service capacity and energyconsumption of several operation modes.

II. RELATED WORK

There is a plethora of work in the literature on contentcaching in D2D networks. We start our investigation byelaborating on papers for content-based D2D cache man-agement. In [16], they have shown that Mandelbrot-Zipf(MZipf) distribution scale law in cache-aided D2D networksis the same with commonly utilized Zipf distribution andhence already existing studies utilizing the Zipf distributionbecome practically usable. Besides, they have shown thatD2D cache network has improvement over the alternativeBS unicast scenario. Congruently, we make use of the Zipfdistribution in our content popularity model. However, insteadof a comparison with no cache-aided D2D scenario, we specif-ically focus on the cache replacement for the energy aspectand make our comparison to conventional cache replacementtechniques. Chen et. al. learn user preferences and managecaching accordingly, and they achieve a remarkable cachinggain over the baseline that utilizes content popularity [17].They exhaustively study the offloading probability while wefocus on the energy consumption in great detail and inspectconsumption in modes separately. Li et. al. propose cachingin Fog Radio Access Network (f-RAN) enhanced with D2Dtechnology [18]. Based on social preferences, AP communitiesare constructed and within a community, cooperative cachingis utilized while communities are dynamically re-determined.For further improvement in transmission delay, D2D modetransmission is used and most appropriate device in everyAP and most requested contents are selected for the cachingscheme. They interrogate cache hit and delay metrics while inour study we deliberately focus on the network-wise energyconsumption. Besides, we have a more general network archi-tecture that can be tuned for custom network scenarios suchas fog architecture if needed. Overall, these studies are on thecontent-based caching in D2D networks.

Now, we specifically discuss energy focused caching stud-ies. The greening of computer networks becomes more chal-lenging with the advent of 5G networking due to high multi-media traffic and low latency requirements [19]. To overcomethe energy burden of 5G heterogeneous networks, in-networkcaching is broadly utilized in different segments. Yang et.

al. propose a self-optimizing in-network caching algorithmfor improving energy-efficiency in 5G networks [20]. How-ever, the D2D communication mechanism is not utilized intheir study. As D2D paradigm is a major component in oursystem, we particularly focus on the D2D network cachingstudies. Chen et. al. propose to place contents via mobility-awareness to optimize cache hit performance in [21]. Apartfrom that, they optimize content transmission powers of smallbase stations (SBSs) and devices to alleviate the energy cost.They demonstrate the improvement in terms of cache hit andenergy efficiency in contrast to random, popular and mobility-aware caching with fixed data amount (MCF). Similar to ourstudy, they interrogate the general 5G environment from theperspective of caching and EE. However, we restrain ourselvesto a more specific 5G domain that is the “edge D2D network”.Above all, they analyze the cache placement problem whilewe focus on the replacement. In [22], they define an energyratio metric and propose a sub-optimal caching scheme builtupon this metric to improve EE. According to their study, theirproposal performs better than the equal probability random,most popular random and cut-off random caching techniquesin terms of EE. They have restricting assumptions such as noenergy consumption in cache hits and the lack of universalsource concept. Besides, we define EE as the total energyconsumption over the successfully received data while theymeasure differently as the ratio of the energy in cachingnetwork over no-caching network.

Finally, we elaborate on some optimization studies in D2Dcaching networks. Chen et. al. optimize the caching andresource allocation for maximizing the offloading of servicesto local hits or from neighbouring devices in D2D opera-tion mode [23]. However, this study is limited to offloadingprobability inspection only whereas we focus both on theservice capacity and energy consumption of our entire D2Dcellular network. In [24], they study cache partitioning, contentplacement and user association problems in D2D HetNets.First, they propose a game-based cache partitioning schemeto achieve the optimal cache space allocation. Building uponthis, they formulate a service delay minimization problem forcontent placement and user association. Due to the mixedinteger nonlinear nature of this problem, Lagrangian partialrelaxation and partitioning into sub-problems is applied andsolved accordingly. Even though this is a holistic cachingoptimization study in D2D networks, it lacks the energyefficiency research that is a very fundamental premise of ourwork. Besides, our content model is more realistic with chunkand layer dimensions that are not available in [24]. Choi et.al. propose a cache placement algorithm to maximize theoverall content quality observed by users and also a resourceallocation algorithm with the objective of maximizing theexpected requested content quality of users constrained bytolerable delay [25]. They consider different content qualitiesin D2D caching networks and focus on the content qualitywhile our main objective is to improve the energy efficiency ofD2D network. In [26], Chen et. al. propose optimal proactivecaching for improving offloading to D2D and also optimizeD2D transmission power to maximize service percentage.Even though they consider overlaying in D2D communications

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and investigate the D2D offloading gain and device energyconsumption, their content model is limited. We utilize lay-ering and chunking in our content model yielding a morecomprehensive content structure.

In a nutshell, the core motivation of our study is to optimizethe cache replacement problem of popularity, partition andquality based multi-attributed multimedia contents for mini-mizing the energy burden of D2D edge networks.

III. SYSTEM MODEL

In this section we present the network architecture, contentmodel and content request management in our system. Thenetwork architecture is shown in Fig. 1. In our networkarchitecture, there is one cell with one base station (BS) andD2D enabled user devices are scattered across this cell. Asbroadly utilized in the literature [27], [28], devices are spreadacross the cell according to Point Poisson Process (PPP) withmean density λNHU . There exists the universal source to servethe contents that are not available in any system unit (e.g. BS,device) at the edge network. In our network architecture, thereare four main service operation modes: 1 local hit, 2 D2Dmode, 3 BS mode (direct), 4 BS mode (from the universalsource) as marked in Fig. 1.

Universal Source

4

4

3

2

1

 1) Local hit 2) D2D mode 3) BS mode 4) BS mode(from      universal)

Fig. 1: Network architecture.

In our content model, request probabilities are determinedby popularity that is based on the Zipf distribution. Theprobability of content requests are calculated via Zipf(s,Nc)where s determines the distribution skewness and Nc is thetotal number of contents in the system. Content chunkingis also used in communication systems with the aim ofperformance improvement [29], [30]. Accordingly, we utilizechunked contents in our model. Inter-chunk popularity differ-entiation is another approach used for improving transmissionand caching performance in content-driven networks. In thatregard, the request rate of content chunks are calculated bythe commonly used Weibull(λ, k) distribution with the scaleand shape parameter λ and k respectively.

Is requested contentunit available in

local cache?

Is it available in atleast one device atmost RD2D away?

Fetch from the closestdevice in D2D mode

Local Hit

Is it available in theBS cache?

The resource managementmodule assignes anavailable channel for

transmission in BS mode

Fetch from theuniversal source to

the BS cache

No

No

No

Yes

Yes

Yes

Fig. 2: Content request management in the edge network.

Our contents are scalable coded (SVC) videos. Each contentis of high quality (HQ) consisting of one base and oneenhancement layer. For standard quality content consumption,the base layer is sufficient whereas both layers are requiredfor HQ visualization. The request rate for HQ contents in ournetwork scenario is pk ∈ [0, 1]. We define each layer of a givencontent’s particular chunk uniquely as a content unit tuple byits content, chunk and layer ids respectively as {i, j, k}. Eachsuch tuple is mapped to a unique content unit identifier ufor tractability. The average content sizes are 322 and 474Mbits for SQ and HQ SVC videos, respectively [9]. Forthe calculation of these values, QCIF-formatted and an hourlong temporal scalable encoded multimedia are exploited [31].In [32], the calculation formula for the mean video frame sizesof different layers is provided. Some utilized video samples areCitizen Kane, Jurassic Park I , Star Wars IV , Aladdinand Tonight Show. For the full video list, please refer to ourprevious work [9]. In Section IV, we preserve the contentcharacteristics of our content model and only change the totalnumber of contents to push the system to its limits for thefeasibility inspection of the time complexity analysis. In theperformance evaluation section, we also keep the total numberof contents fixed and investigate the impact of some othersystem parameters as described in Section VI.

We extend the wireless D2D network in our previouswork [9] with cellular support. In this context, the BS trans-mission power PBS and BS transmission path loss exponentnθBS are introduced for the calculation of the BS powerstrength in the BS channel model. The general content requestmanagement scheme is shown in Fig. 2. First, the local cacheis looked up for a requested content unit. If that unit is notfound in the local cache, then D2D mode is chosen as longas that requested unit is available in at least one device in thereception range of (at most RD2D away from) the requesterdevice. We assume the inter-device distances are known byuser devices according to a signaling scheme to discoverneighbour devices [33]. Thereby, devices in the receptionrange of each other can determine inter-node distances. TheBS serves when that requested unit is not found in any device

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in the reception range of the requester. This case branchesinto two scenarios: i) that unit is available in the BS cache,ii) that unit is not available in the BS cache. In the scenario-i,the BS cache directly serves that unit. In the scenario-ii, thatunit is first fetched from the universal source to the BS andthen served to the requester to allow access to the exterior ofthe edge network system. Note that the multi-mode serviceoperations (local hit, D2D mode, BS mode) in cellular D2Dnetworks are applicable as shown in [34]. All requests andnetwork using operation modes ( 2 - 4 ) acquire the samenetwork access priority. If a content unit cannot be serveddue to all channels being busy, then that unit and prospectiveunits of that content are all dropped.

The BS and devices have storages for caching multimediacontents. In this paper, we mainly study on the cache replace-ment techniques running both on user devices and the BS.In the cache replacement procedure, the system unit (device/BS) evicts its cache until there is sufficient free space for therequested and retrieved video content unit. The decision forthe evictions will be explained in the next section.

IV. OPTIMAL AND ENERGY PRIORITIZED D2D CACHING(EPDC)

5G systems is posed to be an enabler for connected multime-dia services. However, the tremendous demand for the multi-media services raises the energy consumption of the wirelessnetworks, leading to a fundamental cost and environmentalissue that needs to be addressed. To this end, 5G communica-tions need to improve energy efficiency performance [35]. TheD2D edge network is one the 5G technologies that providesservice capabilities closer to end users and thus reduces theenergy burden on the network. Similarly, in-network cachingis an important mechanism to reduce network transmissionsand enhance the energy efficiency as well. In that regard,we formulate our cache replacement problem in D2D edgenetwork for decreasing energy consumption in this section.Subsequently, optimal and heuristic approaches are employedto solve it for our system setup.

Initially, we solve the scalable video caching in D2Dnetworks with the backhaul support optimally. For the easeof tractability, the model and system parameters are listed inTable I. Say the content units residing in the local cache ofsome user are denoted by C. Some user requests a contentunit u′ and it is retrieved from some other system componentvia wireless transmission. If the size of content units in the setC and new arrived unit u′ together exceed the cache capacityCDev, then a subset of content units C residing in the localcache need to be replaced. The eviction decision is essentiallya 0/1 Knapsack problem [14]. For each content unit you eitherdecide to sustain that unit in the local cache or remove it.The content units that are decided to remain in the localcache are designated by C. In our network architecture ateach caching decision phase, we want to minimize prospectiveenergy consumption. Thereof, we sustain content unit set Cthat would induce the largest total energy expenditure. Thisway, content units with lower energy consumption will beevicted. In the prospective requests for them, they will be

fetched from other system components with less cost. Theoptimization problem is stated as follows:

max∑u∈C

E(u)all 1[u∈C] (1)

s.t. s(u′) +∑u∈C

s(u) 1[u∈C] ≤ CDev (2)

with the indicator function 1[x] set to one if x is true and zero

TABLE I: Notations.

Parameter ExplanationNc The total number of contentss The Zipf distribution skewness parameterλ The Weibull distribution scale parameterk The Weibull distribution shape parameterpi The probability of content i being requestedpj The probability of content chunk j being requestedpk The probability of high quality contents being requested{i, j, k} The unique content unit tuple (The ith content’s chunk j

of layer k)u The unique content unit identifier such that each

{i, j, k} 7→ us(u) The size of the content unit uRD2D The maximum allowable distance between a requester and

transmitter for D2D operationNngh The number of neighbouring devices at most RD2D away

from a requesterCDev The device cache capacityCBS The base station cache capacityCloc The expected service capacity of content unit local hitCD2D The expected service capacity of content unit retrievals

via D2D techniqueCBS The expected service capacity of content unit retrievals

from the BS cacheCBS(U) The expected service capacity of content unit retrievals

from the universal source to the BS cachePloc The local hit service power levelPD2D The transmission power level of any devicePBS The base station transmission power levelPBS(U) The base station reception power levelθloc The local hit service power parameterθBS The base station reception power parameterδDev The incremental units for the device cacheδBS The incremental units for the BS cache

otherwise. Our objective function∑u∈C E

(u)all 1[u∈C] in (1)

gives the total energy consumption of units across the networkthat are not evicted from the cache set C and residing in C.With constraint (2), we ensure that the aggregate size of thenew unit u′ and the units not evicted from the cache doesnot exceed the cache capacity. We formulate the prospectiveenergy consumption of any content unit u as E(u)

all in (3). Thisenergy is branched into the four scenarios that are shown inFig. 1: 1 Local hit, 2 Transmission via D2D technique, 3Transmission from the BS cache, 4 Transmission from theuniversal source across the BS

With the probability p(u)loc the first scenario occurs and E(u)loc

will be the corresponding prospective energy expenditure forthe local hit of content unit u. The second scenario consumesE

(u)D2D energy when the content unit will not be available in

the local cache but retrievable from some other device withprobability (1 − p(u)loc )p

(u)D2D. If no device in the transmission

range (centered at the requester with radius RD2D) can servedue to the lack of unit, the BS takes action and will serve thecontent unit from the BS cache with the energy expenditure

5

level E(u)BS . Unless the relevant unit is in the BS cache, the

transmission path from the universal source to the BS cacheand then from there to the requester device will be utilized with(1−p(u)loc )(1−p

(u)D2D)(1−p

(u)BS) probability and E(u)

BS(U) energywill be consumed. The expected energy consumption of unitu based on listed four scenarios is given in (3). The functionscorresponding to the probability of content unit availability fordifferent system components are provided in the Appendix.

E(u)all := p

(u)locE

(u)loc + (1− p(u)loc )p

(u)D2DE

(u)D2D

+ (1− p(u)loc )(1− p(u)D2D)p

(u)BSE

(u)BS

+ (1− p(u)loc )(1− p(u)D2D)(1− p

(u)BS)E

(u)BS(U) (3)

The expected energy expenditure of the given four scenariosare listed as follows:

E(u)loc := Ploc ·

s(u)

Cloc(4)

E(u)D2D := PD2D ·

s(u)

CD2D(5)

E(u)BS := PBS ·

s(u)

CBS(6)

E(u)BS(U) := [PBS(U) ·

s(u)

CBS(U)] + E

(u)BS (7)

The expected energy expenditures are calculated by theproduct of power in some service type and its expectedservice duration for a given content unit. During local hits,a device consumes the least energy compared to other systemcomponents. We define this power Ploc as PD2D

θlocwhile its

expected service duration is s(u)Cloc

. The largest service rateamong the system components is Cloc. The product of Plocand s(u)

Clocgives the expected local hit energy consumption E(u)

loc

for some content unit u as shown in (4). The product of thedevice transmission power PD2D and its expected prospectiveservice duration s(u)

CD2Dgives the expected D2D transmission

energy E(u)D2D (in 5) for unit u. CD2D is calculated by taking

the average distance RD2D

2 for future D2D transmissions. Thedevices do not know the cache status of others, and for futurepredictions they tune to average values for the calculationof prospective energy figures. In (6), the expected energyconsumption for a transmission of some unit u from the BScache is calculated similar to the E(u)

D2D. When we consider thefourth scenario, the content unit retrieval basically branchesinto two parts: i) from the universal source to the BS cache,ii) from the BS cache to the requester device. The retrieval toBS consumes PBS(U) ·

s(u)CBS(U)

expected energy while the rest

has E(u)BS as shown in (7). For the retrieval to the BS cache, its

reception power is PBS(U):=PBSθBSand its expected prospective

reception period is s(u)CBS(U)

.Dynamic programming algorithm is one of the techniques

to solve the 0-1 knapsack problem optimally [36]. In ouroptimal solution, we utilize dynamic programming given inAlgorithm 1. In this algorithm, if the cache capacity CDev

does not suffice for the residing content units set C and thenewly requested one u′, then a subset of C will be evictedfor the sake of newly arrived unit u′. Our main motivation is

Algorithm 1 Dynamic Programming Caching AlgorithmOPT(C, u′,CDev){

Capacity ← TotalSize(C);if (Capacity + s(u′) ≤ CDev) then

return C ∪ {u′}; %the set kept in the cacheelse

%traverse all content units in the local device cachefor all (i = 1 : 1 : |C|) do

%traverse weights with δDev (= 0.01 Mbs) incremental units

for all j = 1 : 1 :

⌊Capacity−s(u′)

δDev

⌋do

if ((i == 1) ∨ (j == 1)) thenEcum(i, j) ← 0; %first row and column are set to zero

else if (s(i) < j) then%take maximum cumulative prospective energy consumptionof in-cache units by either excluding ith unit or including itEcum(i, j)← max{Ecum(i−1, j), E

(i)all+Ecum(i−1, j−

s(i))};elseEcum(i, j)← Ecum(i− 1, j);

end ifend for

end for

%start from the last row and column of Ecum backtrack and mark unitsthat will continue to reside in the local device cache as CC ← backtrack(Ecum);return C ∪ {u′};

end if}

to keep content units in the local cache that would otherwiseresult in large prospective energy consumption. We considerthe cache as the knapsack. Each content unit u is an itemthat is weighted by its size s(u) and valued by its energyconsumption E(u)

all . In dynamic programming, we break the op-timization problem into subproblems, recursively solve thesesubproblems and store their results in Ecum array as givenin Algorithm 1. By backtracking Ecum, we select the unitswith the largest energy sum to continue residing in the cache.These units are designated by the set C. However, the timecomplexity of this algorithm is O(|C| ·W ) where W is theresidual cache capacity after the new unit is inserted and |C|is the number of content units in a given device cache [14].This complexity does not provide a practical calculation time.Thereof, we propose a new energy prioritized D2D cachingalgorithm given in Algorithm 2. The core idea of this greedyalgorithm is to utilize our analytically calculated expectedenergy consumption of units E

(i)all to alleviate the energy

burden on the network system. In this heuristic, at the evictiondecision phase, all content units in the set C are sorted basedon their E(i)

all from the largest to the smallest one. As shownin Algorithm 2 starting from the least energy consuming unitck, units are eliminated from the cache until the free space issuitable for storing new unit u′. Thus, unit(s) with low energyburden across the network are eliminated first. Large energyconsuming units over the network are preserved locally forless energy burden in future requests. Therefore, this schemeis named as energy prioritized D2D caching (EPDC). Thetime complexity of this procedure is bounded by the sortingprocedure of elements in the set C based on their E(i)

all values.It is O(|C| · log|C|) with |C| denoting the number of content

6

units in a given device cache.

Algorithm 2 Energy Prioritized D2D Caching Algorithm(EPDC)

EPDC(C, u′,CDev){

Capacity ← TotalSize(C);if (Capacity + s(u′) ≤ CDev) then

return C ∪ {u′}; %the set kept in the cacheelse

%sort units in C based on their E(alli) values (in (3)) in descending

order%Csort = {c1, c2, ..., ck} with c1 having largest Eall, ck lowestCsort ← sort(C, Eall, DESCEND);j = k;while (j ≥ 1) doCsort ← Csort \ {cj , cj+1, ...ck};if (Capacity + s(u′) −

∑kθ=j s(cθ) ≤ CDev) then

return Csort ∪ {u′}; %the set decided to be kept in the cacheend ifj ← j − 1;

end whileend if}

A. Time complexity analysis

Based on our complexity analysis, OPT algorithm hasinfeasible operation time. As shown in Algorithm 1, for allcached units OPT has an iteration range by the cache capacitywith δ incremental units. For devices we take δDev = 0.01Mbs and for the BS cache δBS = 0.1 Mbs respectively. Theaverage time consumed for devices and the BS cache by alltechniques is provided in Table II. Note that we test the timecomplexity in a laptop device with Intel core i7-6500 CPU@2.5GHz and 8 GB RAM in MATLAB R2019 environment.We apply any chosen algorithm not only in devices but also inthe BS cache for the sake of completeness and hence due to thelarge BS cache capacity even in a setup with moderate numberof contents, we present the impracticality of applying OPT inreal-time or near real-time scenarios. With CDev = 150 Mbsand CBS = 2.8 Gbs even with 150 contents, OPT performspoorer than EPDC in terms of service time especially forthe BS caching. This is because EPDC algorithm is onlybounded by the sorting of content units but not cache capacitywhile OPT algorithm acts an iteration over the cache capacityfor each in-cache content unit.

TABLE II: Time complexity.

Technique Total Local CachingTime (s)

Total BS Caching Time(s)

LRU 0.57 1.11PDC 0.53 2.65SXO 0.82 9.69OPT 18.94 7319.11EPDC 6.01 5.80

V. PERFORMANCE METRICS

We analyze optimal scalable video caching algorithm(OPT ) in D2D cellular networks with backhaul support andenergy prioritized D2D caching (EPDC) algorithm in terms

of service rate and energy expenditure. The system parame-ters are listed in Table III. We compare OPT and EPDCalgorithms to the commonly used baseline technique LeastRecently Used (LRU ). LRU technique does not consider con-tent features. Therefore, it used to compare the improvementof our algorithms over a classical non-content aware cachereplacement technique. In the literature, popularity basedcaching policies are also broadly utilized [37], [38], [39].As another comparison technique, we utilize the Popularity-driven caching (PDC) algorithm [34], that manages the cachereplacement with the aim of keeping popular contents incache with a greater probability. This technique is awareof content attribute popularity and decides on the evictionsaccordingly. As multimedia content caching is the main focusof our algorithms, we compare our algorithms to this content-aware cache replacement technique PDC. We also compareour algorithms to the SXO technique [40]. In this technique,content features size and order (access rate) are consideredfor the cache replacement decision where large contents withlow access rate are evicted first. Note that we will investigatethe service rate and energy expenditures in different operationmodes. In that regard, the energy consumption of our systemconsists of the following parts:

• Eloc for local hits• ED2D for D2D transmission• EBS for direct services of the BS• EBS(U) for indirect services of the BS• Eblock due to blocked services

Eloc, ED2D and Eblock are defined as in our previous work [9].One of our new contributions is the BS integration to our

TABLE III: System parameters.

Parameter ExplanationPBS The transmission power consumption of the BSPBS(U) The reception power consumption of the BSCBS(n) The channel capacity between the BS and the nth

deviceCBS(U) The capacity between the universal content repository

and the BSN The total number of devicesU The set of content units uniquely identifiable by con-

tent, chunk, layer idru The request for the content unit us(u) The size of the content unit uSBS(n)

The set of services from the BS to nth device

SBS(U)(n)

The set of services from the universal content reposi-tory to the nth device across the BS

D2D network architecture. Therefore, we define the BS energyexpenditure branched into i) direct services and ii) indirectservices as EBS and EBS(U) in (8) and (9), respectively.EBS is the overall transmission energy consumption of the BSserving requests directly from the BS cache whereas EBS(U) isthe energy consumption for services from the universal source

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across the BS to requesters.

EBS :=∑u∈U

∑n∈N

∑ru∈SBS(n)

PBS ·|s(u)|CBS(n)

(8)

EBS(U) :=∑u∈U

∑n∈N

∑ru∈SBS(U)

(n)

PBS · |s(u)|CBS(n)

+PBS(U) · |s(u)|

CBS(U)

(9)

By the summation of all the expenditures, we obtainEtotal := Eloc + ED2D + EBS + EBS(U) + Eblock the totalenergy consumption of our system.

VI. PERFORMANCE EVALUATION

We perform simulations for varying system parameterscache capacity and D2D transmission radius, and investigatehow these parameters impact the network for the service rateand energy expenditure. We compare EPDC and OPT algo-rithms to the LRU , PDC [34] and SXO [40]. The simulationparameters are listed in Table IV. In this list, the content unitpopularity and request parameters (s, λ, k, pk), the powerof system components (local, BS, device), local hit and BSreception power tune parameters (θloc, θBS), cache capacities(CDev, CBS), channel parameters, device density λNHU andthe maximum transmission radius of D2D mode RD2D aredefined. In Table IV, the local and D2D power consumptionsare in mW scale while the BS transmission/reception powersare at the order of Watts as observed in practical systems.The channel parameters B, d0 and nD2D are adopted fromour previous study [9]. We take the path loss exponent ofthe BS transmissions nBS greater than that of the D2D modenD2D as broadly employed in the literature [41], [42]. Wehave an event-based simulator that processes content unitrequest arrivals and service completions. Since we elaborateon the caching of multimedia contents, we simulate contentrequests according to a popularity scheme that utilizes Zipfdistribution with parameter s. Each content is partitionedinto chunks and the requests for these chunks follow theWeibull distribution with parameters λ and k. Due to thescalable content structure, our contents are layered into baseand enhancement. The high quality (HQ) content consumptionwith both layers is realized by the HQ request probability pk.For the event-based simulator that acts upon each content unitrequest arrival/completion, network operations require powerand channel parameters to actualize the arrivals. In that regard,these parameters are provided in the Table IV. In the followingsubsections, we vary the device cache capacity CDev and D2Dtransmission radius RD2D to elaborate on how the D2D cacheand service capability impact the system.

A. Impact of device cache capacity CDev

In this section, we investigate a key component in oursystem, the device cache capacity CDev. We enlarge/shrinkthe cache capacity CDev to observe how it impacts the cachingtechniques.

First, we compare our caching technique EPDC with theOPT and the alternative strategies LRU , PDC and SXO in

TABLE IV: Simulation parameters.

Symbol Explanation ValueTsim The simulation duration 400 ss The Zipf distribution skewness parameter 1λ The Weibull distribution scale parameter 5k The Weibull distribution shape parameter 0.8pk The probability of high quality contents

being requested1

Ploc The power consumption of local contentunit retrieval

40 mW

PD2D The transmission power consumption of adevice

80 mW

PBS The transmission power consumption ofthe BS

6 W

PBS(U) The reception power consumption of theBS

1.2 W

θloc The local hit service power parameter 2θBS The base station reception power parameter 5CDev The device cache capacity 150 MbitsCBS The base station cache capacity 2.8 GbitsB The channel bandwidth 2 MHzN0 The noise power density -158 dBmd0 The reference distance of device antenna 1 mnD2D The path loss exponent of D2D transmis-

sion3

nBS The path loss exponent of BS transmission 4.2λNHU The mean device density across the cell

according to Point Poisson Process (PPP)0.0015 user

m2

RD2D The maximum D2D transmission operationradius

200 m

terms of the local hit service rate and energy consumption. Forany fixed CDev value, the energy optimizing OPT attains thesmallest local service rate and in return the lowest local energyexpenditure given in Fig. 3a and 3b, respectively. Comparedto the optimal case, our heuristic EPDC is slightly worsein terms of energy consumption for local hits. However, theenergy improvement over LRU , PDC and SXO manifeststhe utilitarian nature of our proposal for local hits. Thisimprovement of EPDC over the alternatives becomes greaterfor decreased cache capacity. In the large cache capacityregime, the cache capacity has a greater impact on the energyexpenditure as requested contents can be found locally with agreater probability. With decreasing cache capacity, the impactof cache replacement procedure can be observed more clearly.For CDev = 300 Mbits the local hit energy consumptionimprovement rate of EPDC over LRU (PDC / SXO) is4.0% from 0.67 to 0.64 J (3.5% from 0.66 to 0.64 J / 3.2%from 0.66 to 0.64 J). With decreasing CDev to 100 Mbits,this improvement over LRU (PDC / SXO) is amplified to14.4% from 0.29 to 0.24 J (17.0% from 0.29 to 0.24 J / 15.4%from 0.29 to 0.24 J).

In all caching techniques, for increasing CDev, the directBS service usage and energy expense decline since large de-vice caches entail increased local and D2D service utilization.For an arbitrary CDev value, our EPDC technique achievesless direct BS mode energy consumption than LRU , PDCand SXO techniques. The direct BS energy improvement rateof EPDC over LRU (PDC) is at its best at CDev = 200Mbits with 7.3% from 1.65 to 1.53 kJ (12.5% from 1.75 to1.53 kJ). This improvement of EPDC over SXO reachesto its maximum at CDev = 300 Mbits with 12.4% 0.99 to0.87 kJ. EPDC falls back from the OPT for the BS energy

8

(a) Locally served content units (B: of base layer,E: of enhancement layer, S: successful).

(b) The energy consumed for the content units (B: ofbase layer, E: of enhancement layer, S: successful, F:fail, Remark: the energy consumption of failed servicesis very small (green and yellow components) comparedto the energy of successful services).

Fig. 3: Results for the local caches.

consumption. However, this degradation is at most 6.0% forCDev = 100 Mbits. Nevertheless, the evident improvementover LRU , PDC and SXO demonstrates the advantage ofour heuristic EPDC for the direct BS energy consumption.

In our construct for indirect services of the BS, a similarreasoning with direct BS services and corresponding energyexpenditures is valid. EPDC consumes less energy thanLRU , PDC and SXO shown in Fig. 4 for all CDev values.

The indirect BS energy expenditure improvement rate ofEPDC over LRU (PDC / SXO) is at most 11.1% from 5.63to 5.00 kJ (at most 10.8% from 4.38 to 3.91 kJ / 8.1% from3.40 to 3.12 kJ) for CDev = 100 (150 / 200) Mbits. EPDCachieves indirect BS energy results close to the optimal casewith at most 1.6% difference. Hence, our heuristic is practicalfor the energy reduction of the BS regarding the indirect BSservices.

For the D2D analysis, the corresponding service rate is notaffected by the varying CDev values evidently for different

Fig. 4: The energy consumed for retrievals in BS(U) mode (B:of base layer, E: of enhancement layer, S: successful, F: fail).

Fig. 5: The energy consumed for retrievals in D2D mode (B:of base layer, E: of enhancement layer, S: successful, F: fail).

caching policies. In correlation, the energy consumption ofD2D usages are not significantly impacted by the varyingdevice cache capacity CDev for any given caching technique.The reason is that the varying cache capacity particularlyimpacts the local hit results. When we compare EPDC tothe alternatives LRU , PDC and SXO for any CDev, weobserve a slight increase in D2D service rate. In that regard,the energy consumption due to D2D services for EPDC isincreased very slightly compared to LRU , PDC and SXOstrategies. The greatest increase in D2D energy consumptionof EPDC over LRU (PDC / SXO) is 3.6% from 92.43to 95.78 J (5.6% from 90.49 to 95.78 J / 4.0% from 92.12to 95.78 J) for CDev = 100 Mbits as shown in Fig. 5. Thealternatives do not consider prospective energy consumptionof the local, D2D, BS and BS(U) modes. However, ourtechnique makes use of them and favors the D2D paradigmin contrast to the BS transmissions since D2D technique ismore beneficial than cellular (BS) content transmissions interms of energy cost. Thereof, we observe slight increase inD2D service rate and corresponding energy consumption inEPDC technique compared to the alternative counterparts.

9

We expect to observe a major increase in D2D usage dueto its low power consumption. However, the limited devicecapacities compared to the BS and the high power of theBS than devices are dominating factors against reducing theoverall network energy consumption of EPDC. Thereof, wedo not observe a significant change in D2D preference as inBS preference between different policies.

Fig. 6: The total energy consumed for retrievals and local hits(B: of base layer, E: of enhancement layer, S: successful, F:fail).

Finally, we focus on the total service rate and energyconsumption of the network. As already mentioned, the D2Dservice rate is not impacted by the varying CDev for differentcaching policies. However, for increasing CDev, the localservice capacity rises (in Fig. 3a) while the BS service capacityreduces in all caching policies. The increase in local and de-crease in BS service capacities balance each other and the totalservice capacity is not changed evidently for varying CDev ineach caching policy. In all policies, with increasing CDev theenergy consumption trends for local service/D2D/BS/BS(U)service types are consistent with the corresponding servicecapacity behaviour. Although for all caching strategies the totalservice capacity of the network is not affected by differentCDev values, with increasing CDev the total network energyconsumption declines for all caching strategies and hence thenetwork-wide energy efficiency is improved.

As shown in Fig. 6, our proposed algorithm EPDC fallsback from the optimal with at most 3.5% (for CDev = 100Mbits) in our investigated CDev range and EPDC has veryclose results to the optimal policy especially for large CDev’s.Although for fixed CDev values the measured total networkservice capacity does not change significantly between differ-ent techniques, the observed total network energy expenditureof our technique EPDC is less and thus energy-wise morerewarding compared to LRU , PDC and SXO as depictedin Fig. 6. The greatest total network energy improvement ofEPDC compared to LRU (SXO) is with 6.7% from 5.08to 4.74 kJ (8.4% from 5.18 to 4.74 kJ) for CDev = 200Mbits. EPDC attains the maximum improvement over PDCat CDev = 150 Mbits with 9.6% from 7.15 to 6.46 kJ. Thus,we observe the beneficial nature of our proposal for energy-

(a) Locally served content units (B: of base layer, E:of enhancement layer, S: successful).

(b) The energy consumed for the content units (B: ofbase layer, E: of enhancement layer, S: successful, F:fail).

Fig. 7: Results for the local caches.

sensitive network scenarios.

B. Impact of D2D transmission radius RD2D

We investigate how different settings of D2D transmissionimpact the system. In that regard, we vary the D2D trans-mission radius RD2D. Initially, we study the local hit servicecapacity and corresponding energy consumption. As depictedin Fig. 7a, the local hit service capacity changes negligiblywith varying RD2D for all caching strategies. When a contentis available in the local cache, the service is locally providedand other network resources are not used. Hence, the D2Dfeatures do not impact the local hit service capacity. Besides,for all caching policies the local hit energy consumption is notaffected by RD2D (Fig. 7b).

When we compare our proposal EPDC to LRU , PDC,SXO and OPT , EPDC achieves lower local service capacityand, in correspondence with this, local energy consumptionimprovement compared to LRU , PDC and SXO cachingpolicies for any fixed RD2D value in the inspection range.Given in Fig. 7b, the greatest improvement for local hit energy

10

consumption of our proposal over the alternative LRU (PDC/ SXO) occurs at RD2D = 240 m attaining 9.8% from 0.39to 0.35 J (11.6% from 0.40 to 0.35 J / 11.1% from 0.39 to0.35 J). Even the least local energy consumption improvementof EPDC over LRU (PDC / SXO) is 5.6% (6.2% / 6.3%)at RD2D = 80 m. As expected, EPDC is not as good asthe optimal caching in terms of local energy expenditure.Nevertheless, the largest rise observed in terms of local energyconsumption of our proposal over the optimal policy is 3.3%only (from 0.35 to 0.34 J) at RD2D = 240 m. Hence, the localenergy expenditure improvement of EPDC over the baselineLRU and other comparison strategies is an indicator of theenergy-wise utility of EPDC for local services.

Next, we perform an analysis on the direct BS services.The increasing D2D transmission radius RD2D amplifies thechance of finding requested content units in neighbours andsubsequently the D2D service allocations are boosted. TheBS services are less required and the direct BS service ratedeclines for all caching policies. In accordance with thischange, in all policies the direct BS mode energy consumptionreduces with increasing RD2D. In our analysis, similarly adecrease is observed for indirect BS service rates with respectto increasing RD2D. Also, decrease in indirect BS energyconsumption with respect to increasing RD2D’s is observedat all caching techniques as shown in Fig. 8.

Fig. 8: The energy consumed for retrievals in BS(U) mode (B:of base layer, E: of enhancement layer, S: successful, F: fail).

For EPDC, the services supplied from the universal sourceacross the BS (indirect BS services) hits lower service ratethan the other algorithms for all RD2D’s. Accordingly, asshown in Fig. 8, EPDC achieves improvement in indirectBS energy consumption over the comparison algorithms forall RD2D’s. The optimal policy and our proposed algorithmEPDC are designed for minimizing the total network energyexpenditures. Hence, omitting such long routes (from theuniversal source across the BS to requesters) with large powerlevels is instrumental for reducing overall system energyconsumption. Considering policy comparisons for direct BSservices, the corresponding energy expenditure improvementover LRU (PDC / SXO) is 12.2% (19.4% / 10.2%) forthe largest RD2D = 240 m. EPDC falls back to the LRU ,

PDC and SXO with decreasing RD2D in terms of direct BSenergy consumption because the D2D service rate declineswith decreasing RD2D and this enforces the system to getdirect BS services for units available in the BS cache.

Fig. 9: The energy consumed for retrievals in D2D mode(B: of base layer, E: of enhancement layer, S: successful, F:fail).

For all caching policies, the D2D service rate and corre-sponding energy consumption increases with increasing RD2D

as illustrated in Fig. 9. The reason is that the number ofdevices available in reception range of requesters increases inthat case. Consequently, the probability of finding requestedcontent unit(s) in a neighbour device is higher accordingto (14) and hence D2D service rate is improved. Our algorithmEPDC achieves slightly better rate and correspondingly,slightly larger energy consumption compared to alternativealgorithms as shown in Fig. 9. As already explained in theprevious subsection, the high power level of the BS is the keyfactor in determining the overall network energy consumptionand EPDC algorithm chokes the BS selection rather thanincreasing the D2D mode selection. Hence, no significant D2Dusage change is observed between different policies.

Fig. 10: The total energy consumed for retrievals and localhits (B: of base layer, E: of enhancement layer, S: successful,F: fail).

11

We also inspect the total service rate and energy expenditureof the network with respect to varying D2D transmissionradius RD2D. For all policies, the total network service raterises with increasing RD2D from 80 m to 120 m. With furtherincrease, it becomes saturated in all policies. For all cachingalgorithms, we observe an increase in the total network servicerate for the greatest D2D service improvement rate (RD2D

from 80 m to 120 m) that is not canceled out by the BS servicerate drop. This is because the D2D service is more crucialwith its larger rate compared to the other service factors indetermining total network service rate. With further increasingRD2D values, we again observe recession in BS service ratesand this time they cancel the increase in D2D service rates.This is due to the slower D2D service improvement. Asalready mentioned, in all caching techniques the BS energyexpenditure decreases, the D2D energy consumption riseswhereas the local expenditure is stagnant with increasingRD2D’s. The BS services take longer service durations withhigher power levels in contrast to D2D mechanism. Thus, theBS manifests itself with its great energy consumption impact.Overall, for all caching strategies in Fig. 10, the total energyexpense of the network decreases with increasing RD2D’s.

For fixed RD2D values, the total network service rate doesnot change evidently among different caching techniques.However, as shown in Fig. 10 for all RD2D’s, the overallenergy consumption of the network by EPDC is less thanother algorithms. This energy expenditure improvement ofEPDC rises with increasing RD2D. This is basically dueto the difference in BS usage and corresponding energyconsumption shown in Fig. 8. The greatest decrease in thetotal network energy consumption of EPDC compared toLRU (PDC / SXO) is for RD2D = 240 m with 9.5%from 5.38 to 4.87 kJ (12.4% from 5.56 to 4.87 kJ / 10.6%5.45 to 4.87 kJ). When we compare our proposal EPDCwith the optimal counterpart, it slightly performs worse withat most 2.4% performance degradation in the total networkenergy consumption at RD2D = 240 m. In spite of this fallback, we observe improvement of EPDC over the comparedalgorithms for RD2D ≥ 120 m. As already mentioned, no ev-ident change in total network service rate is observed betweendifferent caching techniques for fixed RD2D values. Hence,especially for large RD2D’s, EPDC algorithm becomes moreenergy efficient than the alternative ones.

VII. CONCLUSIONS

D2D networking is an attractive technique for improvingsystem energy efficiency. Similarly, caching is a beneficialscheme used for boosting system capacity and reducing energyconsumption in wireless networks. To this end, we studythe cache replacement management in cellular D2D networksin this work. We formulate and solve the optimal cachingproblem minimizing the energy consumption in cellular D2Dnetwork for the video content consumption scenario. Besides,we propose an energy prioritized D2D caching algorithmconsidering the prospective energy consumption with the aimof reducing the overall system energy burden. For rigoroussystem analysis, we inspect the service rate and energy con-sumption of different service modes with respect to varying

device cache capacity and D2D transmission range. Basedon our evaluations, our proposed algorithm EPDC providesnetwork-wide energy efficiency gains compared to alternativealgorithms, especially for larger D2D transmission ranges.

ACKNOWLEDGMENTS

This work was supported by the Scientific and TechnicalResearch Council of Turkey (TUBITAK) under grant number116E245.

REFERENCES

[1] Cisco, “Cisco annual internet report (2018–2023) white paper,” 2020.[2] N. Choi, K. Guan, D. C. Kilper, and G. Atkinson, “In-network caching

effect on optimal energy consumption in content-centric networking.”2012 IEEE International Conference on Communications (ICC), June2012, pp. 2889–2894.

[3] Y. An and X. Luo, “An in-network caching scheme based on energy ef-ficiency for content-centric networks,” IEEE Access, vol. 6, pp. 20 184–20 194, 2018.

[4] C. Fang, F. R. Yu, T. Huang, J. Liu, and Y. Liu, “An energy-efficient dis-tributed in-network caching scheme for green content-centric networks,”Computer Networks, vol. 78, pp. 119 – 129, 2015.

[5] D. Prerna, R. Tekchandani, and N. Kumar, “Device-to-device contentcaching techniques in 5G: A taxonomy, solutions, and challenges,”Computer Communications, vol. 153, pp. 48 – 84, 2020.

[6] Y. Pan, M. Chen, N. Huang, and Y. Wang, “Power-efficient d2d relayingcellular network access,” Transactions on Emerging TelecommunicationsTechnologies, vol. 30, no. 3, p. e3576, 2019, e3576 ett.3576. [Online].Available: https://onlinelibrary.wiley.com/doi/abs/10.1002/ett.3576

[7] Z. Zhang, L. Wang, D. Liu, and Y. Zhang, “Peer discovery for D2Dcommunications based on social attribute and service attribute,” Journalof Network and Computer Applications, vol. 86, pp. 82 – 91, 2017,special Issue on Pervasive Social Networking.

[8] G. Gur and S. Kafiloglu, “Layered content delivery over satelliteintegrated cognitive radio networks,” IEEE Wireless CommunicationsLetters, vol. 6, no. 3, pp. 390–393, June 2017.

[9] S. S. Kafıloglu, G. Gur, and F. Alagoz, “Multidimensional contentmodeling and caching in D2D edge networks.” 2019 IEEE 30thAnnual International Symposium on Personal, Indoor and Mobile RadioCommunications (PIMRC), Sep. 2019, pp. 1–6.

[10] Z. Chen, N. Pappas, and M. Kountouris, “Probabilistic caching inwireless D2D networks: Cache hit optimal versus throughput optimal,”IEEE Communications Letters, vol. 21, no. 3, pp. 584–587, March 2017.

[11] C. Jarray and A. Giovanidis, “Successful file transmission in mobileD2D networks with caches,” Computer Networks, vol. 147, pp. 162 –179, 2018.

[12] A. S. Ali, K. R. Mahmoud, and K. M. Naguib, “Optimal caching policyfor wireless content delivery in D2D networks,” Journal of Network andComputer Applications, vol. 150, p. 102467, 2020.

[13] N. Zhao, X. Liu, Y. Chen, S. Zhang, Z. Li, B. Chen, and M. Alouini,“Caching D2D connections in small-cell networks,” IEEE Transactionson Vehicular Technology, vol. 67, no. 12, pp. 12 326–12 338, Dec 2018.

[14] G. Gur, “Energy-aware cache management at the wireless network edgefor information-centric operation,” Journal of Network and ComputerApplications, vol. 57, pp. 33 – 42, 2015.

[15] M. Lee and A. F. Molisch, “Caching policy and cooperation dis-tance design for base station-assisted wireless D2D caching networks:Throughput and energy efficiency optimization and tradeoff,” IEEETransactions on Wireless Communications, vol. 17, no. 11, pp. 7500–7514, Nov 2018.

[16] M.-C. Lee, M. Ji, A. Molisch, and N. Sastry, “Throughput–outageanalysis and evaluation of cache-aided D2D networks with measuredpopularity distributions,” IEEE Transactions on Wireless Communica-tions, vol. PP, pp. 1–1, 08 2019.

[17] B. Chen and C. Yang, “Caching policy for cache-enabled D2D commu-nications by learning user preference,” IEEE Transactions on Commu-nications, vol. 66, no. 12, pp. 6586–6601, Dec 2018.

[18] Z. Li, J. Chen, and Z. Zhang, “Socially aware caching in D2D enabledfog radio access networks,” IEEE Access, vol. 7, pp. 84 293–84 303,2019.

[19] Q. Wu, G. Y. Li, W. Chen, D. W. K. Ng, and R. Schober, “An overviewof sustainable green 5G networks,” IEEE Wireless Communications,vol. 24, no. 4, pp. 72–80, Aug 2017.

12

[20] S. Yang, X. Qiu, H. Xie, J. Guan, Y. Liu, and C. Xu, “Gdsoc:Green dynamic self-optimizing content caching in icn-based 5gnetwork,” Transactions on Emerging Telecommunications Technologies,vol. 29, no. 1, p. e3221, 2018, e3221 ett.3221. [Online]. Available:https://onlinelibrary.wiley.com/doi/abs/10.1002/ett.3221

[21] M. Chen, Y. Hao, L. Hu, K. Huang, and V. K. N. Lau, “Green andmobility-aware caching in 5G networks,” IEEE Transactions on WirelessCommunications, vol. 16, no. 12, pp. 8347–8361, Dec 2017.

[22] S. Lin, D. Cheng, G. Zhao, and Z. Chen, “Energy-efficient wirelesscaching in device-to-device cooperative networks.” 2017 IEEE 85thVehicular Technology Conference (VTC Spring), June 2017, pp. 1–5.

[23] B. Chen, C. Yang, and Z. Xiong, “Optimal caching and scheduling forcache-enabled D2D communications,” IEEE Communications Letters,vol. 21, no. 5, pp. 1155–1158, May 2017.

[24] R. Chai, Y. Li, and Q. Chen, “Joint cache partitioning, content place-ment, and user association for D2D-enabled heterogeneous cellularnetworks,” IEEE Access, vol. 7, pp. 56 642–56 655, 2019.

[25] M. Choi, J. Kim, and J. Moon, “Wireless video caching and dynamicstreaming under differentiated quality requirements,” IEEE Journal onSelected Areas in Communications, vol. 36, no. 6, pp. 1245–1257, June2018.

[26] B. Chen, C. Yang, and A. F. Molisch, “Cache-enabled device-to-devicecommunications: Offloading gain and energy cost,” IEEE Transactionson Wireless Communications, vol. 16, no. 7, pp. 4519–4536, 2017.

[27] D. Malak and M. Al-Shalash, “Optimal caching for device-to-devicecontent distribution in 5G networks.” 2014 IEEE Globecom Workshops(GC Wkshps), Dec 2014, pp. 863–868.

[28] H. ElSawy, E. Hossain, and M. Alouini, “Analytical modeling of modeselection and power control for underlay D2D communication in cellularnetworks,” IEEE Transactions on Communications, vol. 62, no. 11, pp.4147–4161, Nov 2014.

[29] L. Wang, S. Bayhan, and J. Kangasharju, “Optimal chunking and partialcaching in information-centric networks,” Computer Communications,vol. 61, pp. 48 – 57, 2015.

[30] X. Wei, P. Ding, L. Zhou, and Y. Qian, “QoE oriented chunk schedulingin P2P-VoD streaming system,” IEEE Transactions on Vehicular Tech-nology, vol. 68, no. 8, pp. 8012–8025, Aug 2019.

[31] P. Seeling, M. Reisslein, and B. Kulapala, “Network performanceevaluation using frame size and quality traces of single-layer and two-layer video: A tutorial,” IEEE Communications Surveys Tutorials, vol. 6,no. 3, pp. 58–78, Third 2004.

[32] M. Reisslein, J. Lassetter, S. Ratnam, O. Lotfallah, F. Fitzek, and S. Pan-chanathan, “Traffic and quality characterization of scalable encodedvideo: a large-scale trace-based study, part 1: Overview and definitions,”Arizona State Uni. Telecommunications Research Center, Tech. Rep,2002.

[33] D. Wu, L. Zhou, Y. Cai, and Y. Qian, “Collaborative caching andmatching for D2D content sharing,” IEEE Wireless Communications,vol. 25, no. 3, pp. 43–49, 2018.

[34] S. S. Kafıloglu, G. Gur, and F. Alagoz, “A markovian model for satelliteintegrated cognitive and D2D HetNets,” Computer Networks, vol. 169,p. 107083, 2020.

[35] M. Agiwal, A. Roy, and N. Saxena, “Next generation 5g wirelessnetworks: A comprehensive survey,” IEEE Communications SurveysTutorials, vol. 18, no. 3, pp. 1617–1655, 2016.

[36] X. Pan and T. Zhang, “Comparison and analysis of algorithms for the0/1 knapsack problem,” in Journal of Physics: Conference Series, vol.1069, no. 1. IOP Publishing, 2018, p. 012024.

[37] K. Suksomboon, S. Tarnoi, Y. Ji, M. Koibuchi, K. Fukuda, S. Abe,N. Motonori, M. Aoki, S. Urushidani, and S. Yamada, “Popcache:Cache more or less based on content popularity for information-centricnetworking.” 38th Annual IEEE Conference on Local ComputerNetworks, Oct 2013, pp. 236–243.

[38] B. Feng, H. Zhou, H. Zhang, J. Jiang, and S. Yu, “A popularity-based cache consistency mechanism for information-centric network-ing.” 2016 IEEE Global Communications Conference (GLOBECOM),Dec 2016, pp. 1–6.

[39] E. B. Abdelkrim, M. A. Salahuddin, H. Elbiaze, and R. Glitho, “Ahybrid regression model for video popularity-based cache replacementin content delivery networks.” 2016 IEEE Global CommunicationsConference (GLOBECOM), Dec 2016, pp. 1–7.

[40] Liangzhong Yin and Guohong Cao, “Supporting cooperative cachingin ad hoc networks,” IEEE Transactions on Mobile Computing, vol. 5,no. 1, pp. 77–89, 2006.

[41] J. Yang, M. Ding, G. Mao, and Z. Lin, “Interference management in in-band d2d underlaid cellular networks,” IEEE Transactions on CognitiveCommunications and Networking, vol. 5, no. 4, pp. 873–885, 2019.

[42] A. H. Sakr and E. Hossain, “Cognitive and energy harvesting-based d2dcommunication in cellular networks: Stochastic geometry modeling andanalysis,” IEEE Transactions on Communications, vol. 63, no. 5, pp.1867–1880, 2015.

APPENDIX

For the calculation of the prospective overall expectedenergy consumption E(u)

all of any content unit u that is mappedto some content unit tuple {i, j, k}, we utilize content unitavailability probabilities. The availability probability in thelocal cache of a requester of some arbitrary content unit u(with the one-to-one and onto correspondent content unit tuple{i, j, k}) is defined in (10) as p

(u)loc . The multiplication of

the ith content request probability pi, the jth chunk requestprobability pj and the kth layer request probability pk givesrequest probability of content unit tuple {i, j, k} (content unitu). Aside from the request characteristic, the requester devicestorage capability is eminently prominent for the calculation ofthe content unit availability probability at a requester device.For the integration of this aspect, the device capacity CDev isnormalized over the total size of all content space (

∑all s(u))

by F fitloc function in (11).

p(u)loc := pi · pj · pk · F fitloc (10)

F fitloc :=CDev∑all s(u)

(11)

The availability probability of some arbitrary content unit uin the BS cache p

(u)BS in (12) is calculated similarly. The

corresponding normalization function F fitBS that outputs the BSstorage capability is given in (13).

p(u)BS := pi · pj · pk · F fitBS (12)

F fitBS :=CBS∑all s(u)

(13)

Nngh is defined as the total number of devices that are atmost RD2D away from a requester. The availability probabilityof some content unit u in at least one of the neighbour devicesof a requester p(u)D2D is defined in (14). (1−p(u)loc )

Nngh gives theprobability of a requested content unit u not being available inany neighbouring device of a requester. By the complement,we obtain the availability probability of some content unit ubeing in at least one of the neighbours of a requester device.

p(u)D2D := 1− (1− p(u)loc )

Nngh (14)