Dimensioning and Profit Sharing in Hybrid LTE/DVB Systems to Offer Mobile TV Services

6314 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 12, DECEMBER 2013

Dimensioning and Profit Sharing in HybridLTE/DVB Systems to Offer Mobile TV Services

Amal Abdel Razzac, Salah Eddine Elayoubi, Tijani Chahed, and Bachar Elhassan

Abstract—Our aim in this work is to develop profit sharingstrategies for coooperative 4G Long Term Evolution (LTE) andDigital Video Broadcasting - Next Generation Handheld (DVB-NGH) systems offering mobile TV service. We first study thecapacity of the hybrid system for offering such a service andderive the associated cost for each network. We then focus onthe sharing of profit between LTE and DVB operators as wellas TV channels providers, taking into account the subscriptionrevenues as well as the infrastructure and operation costs. Weconsider two cases: one in which both LTE and DVB networksare managed by a single operator and one in which the operatorsare separate. In both cases, we derive closed-form expressionsfor each player profit share using coalition game concept Shapleyvalue. We further obtain the players optimal strategies, at theNash equilibrium, where each player tries to maximize its ownprofit.

Index Terms—Mobile TV, LTE, DVB-NGH, Shapley.

I. INTRODUCTION

3GPP and DVB are increasingly aware of the mutualbenefits that they can bring to each other in the case

of convergence for a common offer of mobile TV service:the former, with their widespread user equipment, sophisti-cated smartphones and tablets, can remedy to the problemof screening, while the latter can provide large bandwidthresources to offload 3GPP network’s load. This convergence isbeing currently discussed in the context of the new DVB-NextGeneration Handheld (DVB-NGH) standard [1][2], which is afollow up to DVB-T2 Lite, the mobile extension of DVB-T2[3][4], itself an improvement to DVB-T, and where DVB-NGHis intended to operate in conjunction with 3GPP Long TermEvolution (LTE).

Several works considered the potential benefits of such3GPP/DVB convergence, but they were mostly limited to theirmutual capacities management in the cases of file download(see [5] for instance) and video streaming applications de-livered in hotspot areas, as in [6][7], where the capacity ofUMTS in this case is not enough to serve requesting usersand so DVB-H was used to help deliver popular contents.

Specifically, a queuing analysis was done in [5] for the caseof a file download in a hybrid UMTS/DVB-H network so as

Manuscript received March 4, 2013; revised August 3, 2013; acceptedSeptember 26, 2013. The associate editor coordinating the review of thispaper and approving it for publication was L. Cai.

A. A. Razzac is with the Pierre and Marie Curie University, LIP6 Labo-ratory, Paris, France, and with the Lebanese University, LaSTRe Laboratory,Lebanon.

S. E. Elayoubi is with Orange Labs, Issy-les-Moulineaux, France (e-mail:[email protected]).

T. Chahed is with the Institut Mines-Telecom, Telecom SudParis, UMRCNRS 5157, Evry, France.

B. Elhassan is with the Lebanese University, LaSTRe Laboratory, Lebanon.Digital Object Identifier 10.1109/TWC.2013.110813.130397

to assess the impact of such a hybrid setting on the averageresponse time. The authors in [6] defined an inter-systemhandover mechanism between UMTS and DVB-H systemsvia an SMS server. The video streaming is provided by theUMTS bearer when the number of requests is low and byDVB-H when this number exceeds a given threshold. Theauthors considered a static number of available channels inboth networks and used a Markovian model to assess theprobability of failure in performing a handover from UMTSto DVB-H as well as from DVB-H to UMTS. In [7], theauthors took into account a target Grade Of Service (GoS)for streaming multimedia service and proposed a performancemodel and criteria bounds for load switching between UMTSand DVB-H. In [8], the authors first observed the traffic patternof the 3G networks in order to detect the period of low trafficand then proposed offline pre-scheduling of the services onboth 3G and DVB-H bearers, and enhanced the pre-schedulingoutputs by evaluating some economical utility functions.

To the best of our knowledge, and except reference [8],no work has addressed the economical issues of such aconvergence between cellular and broadcast operators. Andeven in [8], the proposed model did not address a completebusiness case for the money flow between the cooperatingparties. The absence of a clear and viable economical modelthat resolves the monetary conflicts between cellular andbroadcast operators was however one of the main drawbacksbehind the failure of mobile TV service offered by cooperatingUMTS/DVB-H: “The first refused to fund a new network (andthus new antennas), the second, paralysed by the collapse ofthe advertising market, also refused to spend a penny” as putby the author in [9].

Our aim in this work is to fill this gap, in the contextof forthcoming LTE/DVB-NGH, and propose a new businessmodel that helps overcome the selfish behaviour of the differ-ent parties which prevented cooperation towards a fair, self-enforcing agreement guaranteeing each party’s share of profit.In this, we are very much motivated by the positive atmospherethat is currently prevailing between broadcast and cellularorganisations, which resulted in many debates and projects,such as the Mobile Multi Media project [10]. Moreover,European operators can have faith again in Mobile TV after thesuccessful implementation of broadcast/cellular cooperativenetworks in some countries, especially Not TV in Japan [11],illustrating potentially successful coalitions amongst contentproviders and wireless service providers.

We specifically focus on three issues: i. dimensioning of thehybrid LTE/DVB system in the presence of unicast (voice anddata) as well as mobile TV users, ii. sharing of profit, in terms

1536-1276/13$31.00 © 2013 IEEE

RAZZAC et al.: DIMENSIONING AND PROFIT SHARING IN HYBRID LTE/DVB SYSTEMS TO OFFER MOBILE TV SERVICES 6315

Fig. 1. Service area.

of revenues and costs, between the different players whichare LTE and DVB operators and TV channel providers, usingcoalition game concept Shapley value [12], and iii. obtainingthe optimal strategies of the players, at the Nash equilibrium[13]. We consider two cases: one with a single operator havingboth cellular and DVB infrastructure and one where the twooperators are separate.

The remainder of this paper is organized as follows. InSection II, we describe the hybrid LTE/DVB system andderive the dimensioning and induced costs of such a systemin the presence of unicast and TV flows. In Section III, wefocus on the case of joint LTE/DVB operator and study theprofit sharing between the different players, operators andTV channel providers, and derive closed-form expressions foreach player profit share. We also investigate the case whereplayers try to maximize their own profits and study the optimalstrategies achieved therein. The same work is done for thecase of separate operators in Section IV. Concluding remarksand some future work perspectives are contained in the lastsection.

II. HYBRID LTE/DVB-NGH NETWORK

We consider a hybrid LTE/DVB-NGH system which can bemanaged by the same operator or by separate ones and whichoffers mobile TV service. The number of transmitters andthe Inter Site Distance (ISD) of the DVB system, originallydimensioned for rooftop fixed TV services, are set so that thisservice is universally ensured. The DVB-NGH system usesthis existing infrastructure to deliver an ”in-band” mobile TVservice, and so, each DVB transmitter has to serve mobile TVin a well known area of radius RS = ISD

2·cos(30) ; we refer tothis area as Service Area. However, due to many transmissionpenalties between fixed and mobile services, the DVB-NGHcoverage region is modelled as a circular area around theDVB transmitter, smaller than the fixed TV service area, whichcorresponds to the inner region in Fig. 1. On the other hand,the LTE cells, primarily dimensioned for handheld services,fully cover the service area.

User terminals are assumed to have both 3GPP and DVBreceivers and the hybrid LTE/DVB system operates as fol-lows: in the inner region, LTE offloads its mobile TV trafficto existing DVB infrastructure and serves only its classicalvoice/data unicast services. On the other hand, DVB relies onLTE cellular sites to offer the mobile TV service in the outerregion. Note that in the outer region, LTE has to upgrade itsnetwork by adding more sites in order to ensure the mobileTV service without degrading the Quality of Service (QoS)of its unicast users (voice and data). This is why the resultingLTE deployment is not uniform, as depicted in Fig. 1.

We next derive dimensioning expressions and identify op-erational costs for both LTE and DVB operators in such ahybrid network.

A. DVB-NGH system

1) DVB-NGH Capacity: DVB-NGH signal is intended tobe broadcast in the Future Extension Frame (FEF) of aTime Division Multiplexing (TDM) super frame composed ofsuccessive T2-Base Frames carrying DVB-T2 fixed receptionsignals and NGH Frames (FEF) targeting mobile receiver.

This technology inherits its physical layer, known as Phys-ical Layer Pipe (PLP), from the DVB-T2 Lite technology [4].It is a transparent physical layer that enables service specificrobustness. Each TV channel TVi, i ∈ [1, .., |KTV|] whereKTV is the set of TV channels, is carried in an independentPLP, with the possibility of having different modulation andcoding rate schemes (MODCOD), to meet different receptionconditions.

The net data rate of a PLP as well as the total capacity ofthe DVB-NGH system vary with different transmission param-eters (MODCOD of the PLPs) and super frame configuration[2][14]. For example, for a DVB-T2 super-frame containingtwo T2-Base frames and one FEF carrying the DVB-NGHsignal, of 250 ms each, we can serve a maximum of 4 TVchannels, requiring 512 Kbps each, if the chosen modulationis QPSK 3/5. We can, however, serve up to 8 TV channelswith 16-QAM 3/5.1

However, the choice of the modulation and coding schemeis not sufficient to design the system; the transmission powerhas also to be planned accordingly in order to cover thedesired service area (inner and outer regions in Figure 1). Itscalculation is presented next.

2) DVB-NGH transmission power and the associated cost:The DVB transmission power, which we denote by PD , isthe most important parameter to consider when designing aDVB-NGH system because the energy costs are preponderantin comparison to the cost of DVB base stations infrastructure.PD is a function of the chosen modulation and coding ratescheme which satisfy the required capacity (Section II-A1)and the target coverage area radius RD.

To have a good coverage, a required Carrier to NoiseRatio (C/N) of TV services has to be ensured, knowing thepropagation environment and the possible locations of thereceivers (on rooftops for terrestrial services and handheldfor mobile TV). A simple link budget analysis, as the onedepicted in Table I, allows us to derive the maximal permittedsignal degradation due to the transmission trajectory, knownas the pathloss, when the transmission powers are known.The coverage area can then be obtained depending on thepropagation model. We use in this paper the Okumura-Hatapropagation model and its ITU-R P.529-3 modification, forcovered distance above 20 Km [16], and present in Figure2 the transmission powers as a function of coverage radii,for different modulation and coding rate schemes and thusdifferent C/N ratios.

1Due to the lack of space, we omit the section detailing the PLPs (TVchannels) admission control. Interested readers are kindly referred to [14]for an easy explanation, and can then verify the results with the T2Xpresssoftware [15]


TABLE ICOVERAGE PLANNING PARAMETERS

DVB-NGH* Fixed***EIRP [dBm] (a) PD Pf

Receiver Noise [dBm] (b) -99.11 -99.11required C/N [dB] (C/N)D (C/N)fReceiver sensitivity [dBm] (d) (b) + (C/N)D (b) + (C/N)fAntenna Gain [dBi] (e) 0 12.15Cable Loss [dB] (f) 0 4Total Receiver Gain [dBm] (g) (d)-(e)+(f)building/vehicle loss [dB] (h) 8 0s.d. building loss [dB] (i) 6 0standard deviation (s.d.)[dB](j) 5.5 5.5Total standard deviation [dB] (k)

√(i)2 + (j)2

Distribution Factor (l) it depends on the targetcoverage probability (μc).It is equal to 1.64 when μc = 95%and 2.33 for μc = 99%

Correction factor [dB] (m) (k) · (l)Total Margins [dB] (n) (h) + (m)PathLoss [dB] (o) (a) − (g)− (n)

0 5 10 15 20 25 300

10

20

30

40

50

60

70

Coverage Radius [Km]

Tra

nsm

issi

on P

ower

[dB

]

Fixed reception (256−QAM 2/3 Rice)Mobile TV Indoor (64−QAM 2/3 Rayleigh)Mobile TV Indoor (QPSK 3/5 Rayleigh)Mobile TV Indoor (16−QAM 3/5 Rayleigh)

Fig. 2. The required transmitter power PD function of the target coverageradius and PLP modulation.

It is obvious that a much higher power than that of DVB-T2(targeting fixed reception) is needed for DVB-NGH in orderto have the same system coverage. And for a given mobileTV service area radius, the transmitter power increases withthe modulation order.

Knowing the modulation and coding rate scheme neededfor serving the set of TV channels KTV (Sec. II-A1), and thetarget radius area RD, we can obtain the required DVB-NGHemission power PD(RD,KTV) using Fig. 2. For example,to serve 5 TV channels of 512 Kbps each, we need to use16 − QAM 3/5 modulation (Sec. II-A1). We can thus useFigure 2 to compute the needed transmission power, i.e., 56dBW, to cover a region of radius 25 Km.

We now compute the cost of the DVB system. The transmit-ter consumed power Pc(RD,KTV) is higher than the radiatedpower (ERP). It includes a component that is proportional tothe ERP and another one that is consumed independently ofthe average transmit power [17]:

Pc(RD,KTV) = αnPD(RD,KTV) + βn (1)

where αn is a scaling coefficient due to amplifier and feederlosses as well as cooling of sites and βn is an offset due tosignal processing, battery backup.

Eventually, the total monthly cost of one DVB-NGH trans-mitter covering a region of radius RD and serving the set ofTV channels KTV in a hybrid LTE/DVB-NGH network iscomposed of power consumption costs and equipment costs

CrentD [18] and is given by:

CD(RD,KTV) = αePc(RD,KTV).H + CrentD (2)

where αe is the electricity cost of one kWh and H is thenumber of operating hours per month.

B. LTE system

As stated previously, the LTE network has to fill thecoverage gap between DVB fixed and mobile coverage area(Fig. 2) and serve TV channels in the area that is not coveredby DVB-NGH (outer region in Fig. 1). However, LTE has tobe able to deliver Mobile TV service without compromisingthe QoS of its voice and data unicast services. We hence derivefirst the capacity requirements of these unicast services, andthen study the required cell capacity and the extra neededinfrastructure when mobile TV enters the market.

1) LTE capacity for unicast services: The resources to beshared in LTE, known as Physical Resource Blocks (PRBs),are the chunks of 12 narrowband sub-carriers of 15 KHz each[19]. The total number of those PRBs depends on the LTEbandwidth.

Real time voice calls are prioritized over the elastic dataservices and are served first. A voice call with requiredthroughput Dv and located at position z in the cell, needsa number of PRBs equal to Dv

DRB(z,RL) , where DRB(z,RL)is the throughput achieved by a PRB at position z in a LTEcell of radius RL. This throughput can be obtained based onstatic simulations that calculate the Signal-to-Interference plusNoise Ratio (SINR) at each position in the cell and associateit to a throughput, defined by link level curves. So, if NL

RB

is the number of available PRBs for unicast usage (voice anddata), the admission control constraint in the LTE cell is givenby:

Z∑

z=1

nv(z)Dv

DRB(z,RL)≤ NL

RB (3)

where nv(z) is the number of voice users located in positionz.

The blocking probability is the main performance metric forvoice calls. Given the voice traffic λv (in Erlang/Km2) that isto be served by the LTE network, the steady-state distributionof the number of PRBs occupied by voice users Pr[Nv

RB =n/{RL, N

LRB}] where n ∈ [0, NL

RB] can be easily calculatedby the multi-Erlang law, using Kaufman-Roberts algorithm[21].

Data services, however, usually share the capacity that isleft over by voice users and have more rapid dynamics thanthe latter. Using the quasi-stationarity approximation [22], itcan be easily shown that, when Nv

RB PRBs are occupied byvoice users, the average remaining capacity for data servicesis given by:

Cd(NvRB, RL, N

LRB) = (NL

RB −NvRB)DRB(RL) (4)

where NLRB is the number of available PRBs for unicast users,

NvRB is the number of PRBs allocated for voice calls and

DRB(RL) = (∑Z

z=11

ZDRB(z,RL) )−1 is the harmonic mean

of the PRB throughput over the cell surface2. We then obtain

2The derivation is based on the processor sharing analysis of [23].


the average flow throughput for a single data service whenNv

RB PRB are allocated for voice calls:

Dd(NvRB, RL, N

LRB) =Cd(N

vRB , RL, N

LRB)

× (1− ρd(NvRB , RL, N

LRB))

(5)

where ρd(NvRB , RL, N

LRB) = λdSL(RL)

Cd(NvRB ,RL,NL

RB)is the data

load in the cell of area SL(RL) (in Km2), knowing that NvRB

PRB are allocated for voice calls, and λd (in Kbps/Km2) isthe offered data traffic.

Eventually, as a performance metric for data network, wecalculate the average data flow throughput weighted by theprobability of the number of PRBs occupied by the voice calls:

Dd(RL, NLRB) =

NLRB∑

NvRB=0

Dd(NvRB , RL, N

LRB)Pr[Nv

RB ] (6)

2) Mobile TV in LTE: In LTE, TV channels are broadcastusing the Single Frequency Network (SFN) technology, wherecells are synchronized so that TV signals are received atthe receiver with a low relative delay and can be viewed ascopies of the same signal [24]. In this case, the classical SINRanalysis is not sufficient as the nature of interference changes.Indeed, cells are grouped into clusters where transmissionsfrom all cells are synchronized. Portions of the signals re-ceived from other cells, and that would have been countedas a pure destructive interference in unicast settings, are nowviewed as useful signals [25].

Another major difference between broadcast and unicasttransmission in LTE is that, in the latter, adaptive modulationand coding is used while, in the former, the same signal istransmitted to all users with the same Modulation and CodingScheme (MCS) in all the network. A compromise is thusto be found, in SFN, between throughput and coverage (arobust MCS allows a larger coverage but with lower through-put). Based on static simulations, authors in [24] derived thethroughput achieved by 95% of the users for different MCSand different cell ranges. Let DSFN (m,RL) be the PRBthroughput for 95% of users when using MCS m and whenthe cell radius is equal to RL. Given RL, the MCS used inthe network is determined so that

ˆMCS(RL) = argmaxm

DSFN(m,RL) (7)

For example, based again on [24], MCS 64 QAM 3/4 isto be used for cell ranges lower than 350 meters, while onlyQPSK 3/4 can be used for cell ranges greater than 500 meters.Knowing the choice of the MCS, we can assess the numberof PRBs to be reserved for transmitting on LTE a TV channelrequiring a bitrate of dTV :

NTVRB (RL) =

dTV

DSFN ( ˆMCS(RL), RL)(8)

3) Cost of upgrading the LTE network: Mobile TV, voicecalls and data services must share the overall LTE resources.Given the “always on” nature of Mobile TV, the LTE operatorhas to prioritize the TV service over unicast, voice and dataservices, without altering their QoS.

In order to serve the set of TV channels KTV, we nowdescribe the strategy to follow so as to update the LTE networkto meet all service requirements:

1) We start with already existent LTE network (with no TVservice), having cell radius RL = RL(0) and overallnumber of available PRBs: Nmax

RB .2) We calculate the number of PRBs allocated for a

TV channels NTVi

RB (RL) requiring a bitrate of dTVi

using Eqn. (8). We then calculate the number ofthe remaining PRBS for unicast services as follows:NL

RB(KTV, RL) = NmaxRB −∑|KTV|

i=1 NTVi

RB (RL)3) Referring to Section II-B1, we calculate the QoS metrics

for voice (blocking rate) and data services (averagethroughput). If these metrics meet a maximal blockingprobability Bv and minimal data user throughput Dd,respectively, the considered cell radius is optimal andwe denoted by RL(KTV). Otherwise, the cell radiusneeds to be decreased and we repeat steps 2-3.

Once we obtain the optimal cell radius, we calculate theadditional number of LTE sites needed to serve mobile TVservice. Referring to Figure 1, there are two LTE regions:in the inner region, DVB-NGH is able to serve all users,so LTE operator does not need to upgrade its network. Theouter region, of area π(R2

S − R2D), is however not covered

by DVB-NGH, and so LTE has to upgrade its network so asto serve alone mobile TV users. The number of LTE sitesto be added, per DVB transmitter, in this region is given by:ΔL(RD,KTV) = π(R2

S − R2D)( 1

SL(RL(KTV))− 1

SL(RL(0))),

where SL(RL(KTV)) is the LTE cell surface for cell radiusRL(KTV) when the set of TV channels to be served is KTV.

The monthly LTE network upgrading cost is given by:

CL(RD,KTV) = αLΔL(RD,KTV) (9)

where αL is the monthly cost of a new LTE site, includingoperational cost as well as equipment and installation costs.

III. OPTIMAL NETWORK CONFIGURATION: CASE OF

JOINT LTE/DVB OPERATOR

LTE and DVB operators, channel providers as well as anyagent in the mobile TV value chain, seek a monetary profit.Each player will try to adopt a network configuration thatdecreases its own costs in order to maximize its profits. Inthis section, we make use of the Shapley value mechanismwhich proved to be very effective in profit sharing in a multi-player context where several types of relationships, bilateraland multi-lateral, are involved [26]. The idea is that eachplayer will have a profit share proportional to its contributionin the network setting and the added value it brings to theoverall value chain. We treat in this section the case of asingle, joint DVB/LTE operator. The case of separate operatorsis deferred to the next section.

A. The Shapley Value: definition and properties

We denote by N the set of players and S a given coalitionformed by a subset of these players. The worth function V (S)denotes the weight or payoff of coalition S. The Shapley valueφi(S, V ) defined by L. Shapley [12] is the share gained byplayer i when he is in coalition S. This value is given by:

φi(S, V ) =1

N !

∑

π∈Π

Δi(V, S(π, i))∀i ∈ N (10)


where Π is the set of all N ! players permutation, S(π, i) isthe coalition formed by players from rank 1 till i in a givenpermutation π ∈ Π and Δi(V, S(π, i)) = V (S) − V (S\{i})is the marginal contribution of player i in coalition S, definedas the difference between the worth functions of (S) and(S\{i}), and representing the benefits or losses that playeri could bring if he entered coalition (S\{i}).

1) Properties:: The Shapley value has the following prop-erties:

a. Additivity: If the worth function V (S) can be dividedinto two components V (S) = V1(S) + V2(S), then theShapley value φi(S, V ) = φi(S, V1) + φi(S, V2)

b. Efficiency: There is a conservation of the total value ofthe coalition:

∑i∈S φi(S, V ) = V (S)

c. Balance contribution: For any two players i and j, theShapley values are balanced as follows:

φi(S, V )− φi(S\{j}, V ) = φj(S, V )− φj(S\{i}, V )(11)

2) Stability: The Shapley distribution is stable if it is in thecore of the game. The latter is defined in [27] as ”the set offeasible payoff vectors for the grand coalition that no coalitioncan upset”. So the Shapley value profit sharing is stable ifwe cannot find any coalition whose players may earn morethan if they stick to the largest coalition (the grand coalition).Formally, it should verify the following condition:

∑

(i∈S)

φi(P′, V ′) ≥ V ′(S) ∀S ⊆ P ′ (12)

B. Profit sharing using Shapley value

As stated earlier, we consider in this section a hybridLTE/DVB system owned and managed by a single operator.In this case, profit sharing is between the operator and theTV channel providers. We denote the set of players Po by thegrand coalition composed of the operator and a set KTV ofK = |KTV| TV channel providers. We consider that eachTV channel provider sells one TV channel. Let N denote thenumber of players in the set Po: N = |Po| = K + 1.

The profit is the difference between the total revenue andcosts, and is to be shared among the different players in thesystem. Using the above-defined additivity property, the worthfunction of any coalition S, i.e., its payoff V (S), is simplythe difference of the revenue worth function Vr(S) and thecost worth function Vc(S). This yields the profit share of eachplayer i as follows:

φi(S, V ) = φri (S, Vr)− φc

i (S, Vc) (13)

r is the revenue component and c is the cost. We consider asingle DVB tower. The profits are thus given per service areaand can be scaled to obtain the overall profits.

We now derive closed-form expressions for the Shapleyvalue so as to ease its numerical computation and overcomethe exhaustive summation in Eqn. (10).

1) Revenue Sharing: Revenue depends on the pricingmodel and the willingness of customers to subscribe togiven channel(s). In general, operators offer various channelbouquets with a flat rate for each one. But, by observingthe popularity of each channel, operators can estimate the

individual revenue generated by each channel apart. Let δ bethe subscription fee to a certain bouquet and let X be thenumber of subscriptions to it. δi = p(i)δX is the subscriptionfee paid by mobile TV user to channel i with popularity p(i) inthis bouquet. The revenue worth function is defined as follows:

Vr(S) = [∑

i∈S

δi]I{operator∈(S)} (14)

where IB = 1 if condition B is true and 0 otherwise.By additivity, this function can be also re-written as:

Vr(S) =∑

i Vir (S) where:

V ir (S) = δiI{operator and i∈(S)} (15)

This simplifies the computation. For each (S, V ir ), we elim-

inate channels j, ∀j �= i, as these channels are dummy playersfor this worth function [12]. The revenue sharing is then easilyobtained by applying Eqn. (10) to the remaining two players(operator and channel i) given the worth function V i

r . Weobtain thus the operators revenue share φr

o(S, Vir ) = δi

2 andthe share of channel i φr

i (S, Vir ) =

δi2 . Finally, as the operator

is serving a set KTV of TV channels, its revenue share is thesum of its share in every channel revenue and is given by Eqn.(16). The revenue share of the TV channel provider i is givenby Eqn. (17)3:

φro(RD, Po, Vr) =

∑|KTV|i δi2

(16)

φri (RD, Po, Vr) =

δi2

(17)

2) Cost Sharing: As we consider, in this section, that asingle operator runs the hybrid network, the total operator costincludes DVB (Eqn. (2)) as well as LTE (Eqn. (9)) costs. Thecost worth function is:Vc(RD, S) =

[CD(RD,kTV) + CL(RD,kTV) +

|KTV|∑i=1/i∈(S)

ci]I{operator ∈(S)}

(18)where kTV is the subset of TV channels in coalition S, KTV

is the total set of TV channels and ci is channel i contentscost.

The previous worth function could be divided into fourcomponents: the power cost worth function V P

c (RD, S) =αe·H ·PD(RD,kTV)I{operator ∈(S)}, the broadcast equipmentcost worth function V rent

c (RD, S) = CrentD I{operator ∈(S)}

due to needed updates of antennas, cooling systemand other communication material needed to supportthe Mobile TV service the infrastructure cost worthfunction in number of additional LTE base stationsV bsc (RD, S) = CL(RD,kTV)I{operator ∈(S)}, and finally,

the content cost worth function V contentc (RD, S) =

(∑|KTV|

i=1/i∈(S) ci)I{operator ∈(S)} due to production costs or forbuying contents from other production companies other thanthe operator. Using the Shapley definition (Eqn. (10)), weobtain the expressions for the four components of cost shareof the operator (see Appendix A):

3If a TV channel provider sells a set L of more than one TV channel, itsrevenue share is the sum of the revenue share obtained by each channel in Lgiven by Eqn. 17


i. The operator power cost share is given by:

φPo (RD, Po, V

Pc ) =

αe.H

N∑i=2

(i− 1)!(mi−1∑

j=1

Pc(RD, (ei−1)j∗))(N − i)!

N !(19)

ii. The operator cellular infrastructure cost share is equalto:

φbso (RD, Po, V

bsc ) =

N∑i=2

(i− 1)!(mi−1∑

j=1

CL(RD, (ei−1)j∗))(N − i)!

N !(20)

where:- N is the total number of players (N = |KTV|+1),- ei−1 is a (mi−1×|KTV|) matrix. Each column k in

this matrix corresponds to the channel k in the setKTV. The number of its lines is mi−1 =

(|KTV|i−1

).

Each jth line (ei−1)j∗ in this matrix represents adifferent combination of i− 1 served TV channels.We note (ei−1)jk = 1 if the TV channel k is to beserved and zero otherwise

- Pc(RD, (ei−1)j∗) and CL(RD, (ei−1)j∗) are thepower consumption (Eqn. (1)) and the additionalcost of LTE infrastructure sites (Eqn. 9)) when theDVB coverage radius is RD and the set of TVchannels to be served is (ei−1)j∗.

iii. The operator share in the broadcast equipments andinfrastructure rent costs is:

φrento (RD, Po, V

rentc ) =

N − 1

N.Crent

D (21)

iv. The operator share of the content costs (Eqn.(22)) is calculated by the same way as Eqn.(16)) given the worth function V content

c (RD, S) =

(∑|KTV|

i=1/i∈(S) ci)I{operator ∈(S)}:

φcontento (RD, Po, V

contentc ) =

|KTV|∑

i=1

ci2

(22)

The overall cost share of the operator φco(RD, Po, Vc) is the

sum of these four components.By the balance property defined in Eqn. (11), we obtain the

cost share of channel provider i as a function of the cost shareof the operator:

φci (RD, Po, Vc) = φc

o(RD, Po, Vc)− φco(RD, Po\{i}, Vc)

(23)3) Profit Sharing: The profit distribution of each player

is simply the difference between its revenue share and costshare derived above. The money flow is represented in Figure3 where the revenue and cost flows are illustrated.

The channel providers pay the operator an amount of moneyequal to Ci to participate to the paid network costs (CD +CL), and the operator pays them back Ri [euros/month] whichrepresents their revenue share as well as a part of the contentcosts.

As we saw, the Shapley solution requires the exchange ofrevenue and cost information between the different players,

),(),( TVTV KK DLDD RCRC +

LTE

DVB

1

2

X.δc1

c2

Channel providers

2),,( i

roDrii

cVPRR += ϕ

2),,( i

roDcii

cVPRC −= ϕ

TVKcTVK

Fig. 3. The money flow between players in a joint LTE/DVB operator.

TABLE IIINPUT PARAMETERS

Number of subscribers 200000Monthly LTE infrastructure costs αL [euros/month] 833*Total Content Costs [euros] 2000Number of TV channels 5 channelsTV channels requirements [Kbps] 512 each **Total subscriber fees [euros/month] 7ISD in the existent DVB system [Km] 43.31* Price of an e-Node=30000 euros , Life time is 3 Years, so the cost isin average 833 [euros/month]** The MODCOD 16-QAM 3/5 is satisfying

and so, for trustfulness issues, they might make use of a trustedthird party, e.g., a joint venture, who would hold and manageall the needed information in this cooperative business model.

C. Illustration of the profit sharing strategy

To illustrate profit sharing between players in the system,we consider the input parameters shown in Table II:

We implement on MATLAB the closed-form expressionswe derived above. We plot in Figure 4 the single operator profitfor a set of 5 TV channels with a required capacity of 512Kbps each (as indicated in Table II), as a function of increasingDVB radius RD (equivalently, increasing transmission powerPD) until we reach the service area radius RS = ISD

2·cos(30) =25 Km. As the electricity price is a parameter that dependson the country (e.g., its energy policy and the availability of areliable electricity grid), we plot the profit for different valuesof electricity prices.

As we can see from Figure 4, the profit of the operatoralways increases when DVB-NGH coverage increases for alow electricity price. This is however not true when the elec-tricity price is high, in which case profit reaches a maximumfor a certain DVB-NGH radius RD and decreases when thisradius exceeds a certain limit. This RD limit decreases withthe increase of the electricity costs. So, for electricity costremarkably lower than the LTE infrastructure, the operatorhas an incentive to choose to offer mobile TV by DVB-NGH bearer alone. It would however use both LTE andDVB infrastructures in an optimal network configuration (RD

maximizing the profit) when the electricity and cellular costsare comparable.

As of TV channel providers, according to Eqn. (23), all


0 5 10 15 20 251

2

3

4

5

6

7x 10

5

DVB Radius [Km]

Pro

fits

[eur

os/m

onth

]

αe=0.15 [euros/kWh]

αe=0.4 [euros/kWh]

αe=0.80 [euros/kWh]

αe=1 [euros/kWh]

O indicates the Maximum

Fig. 4. Profits of the operator for different DVB-NGH radius RD anddifferent values of electricity costs.

0 5 10 15 20 255

6

7

8

9

10

11

12x 10

4

DVB radius [Km]

Net

wor

k C

osts

Sha

re (

Pow

er a

nd In

fras

truc

ture

) [e

uros

/mon

th]

TV 1TV 2TV 3TV 4TV 5

Fig. 5. Network infrastructure and power costs share payed by each TVchannel when αe = 0.4 and αL = 833.

the TV channels that entail the same infrastructure and powercosts when they enter the game (with same required bitrate)will pay the same share of costs regardless of their revenues(subscription fees). The infrastructure and power costs paid byeach TV channel provider is depicted in Figure 5, for monthlyelectricity costs αe = 0.4 and monthly LTE infrastructurecosts αL = 833 [euros/month] (This value is explicited inTable II).

The profit earned by a channel provider depends on itscontribution to the revenues. For a set of 5 TV channelsKTV = [TV1 TV2 TV3 TV4 TV5] with total subscription fees7 (euros/month), as indicated in Table II, and considering thatTV channel popularities are given by Zipf distribution with pa-rameter αZipf = 1.1, the individual subscription fees of eachTV channel is thus estimated as [3.25 1.51 0.97 0.71 0.55](euros) (Sec. III-B1); the profit of each channel provider isillustrated in Figure 6.

At this point, we can prove by counterexample that theShapley Value is not always stable (Sec. III-A2). In fact, wecan see that the lower revenue channels (which can representniche channels) might experience, for certain network con-figurations (in our case for RD = 25 Km), a negative profitand decide to leave this coalition (the negative value of profitis not the only case for leaving the coalition, a channel mayleave if its profits do not reach a certain target). And so, forsolid dimensioning, the operator has to find a stable set of TVchannels, where none of them has the incentive to leave thecoalition. This is discussed in the next section.

0 5 10 15 20 25−1

−0.5

0

0.5

1

1.5

2

2.5

3x 10

5

DVB radius [Km]

Pro

fit [e

uros

/mon

th]


Fig. 6. Profit share of the TV channels when αe = 0.4 and αL = 833.

D. Evolution of the coalition and Nash equilibrium

When a player finds itself unsatisfied by its profits, it willact to increase its gains or leave the game. The operator set ofactions Ao is the set of possible transmission powers (Ao ={PD}). A channel has two actions: either decide to enter thegame and be broadcast, or leave the system following its profittarget (recall Figure 6). The game evolves until reaching anetwork configuration and a set of TV channels where allthe players are satisfied and do not have incentive to leave,defining the Nash Equilibrium (NE)[13].

Formally, the Nash equilibrium is defined in [28] as the setA∗ = (a∗1, ..., a

∗N ), defining the action a∗i of each player i. It

has the property that no player i can do better by choosingan action different from a∗i , given that every other player jadheres to a∗j . Based on this definition, we implement onMATLAB the Best Response method [28] to compute theNash Equilibrium of the system. For the numerical setting ofTable II and for an electricity costs αe = 0.4 (euros/month),we find that the equilibrium corresponds to the combinationof the 4 most popular TV channels with a network completelycovered by DVB (RD = 25 Km), assuming that the TVchannel providers will accept any positive profit. This meansthat it is more profitable for the operator, in this case, to usea DVB infrastructure for delivering the mobile TV service,and to reserve LTE system to unicast services. Even thoughchannel TV5 is not to be served, the operator will gain moreprofit than if it was delivered, since it entails high costs whilehaving very low revenues.

IV. OPTIMAL NETWORK CONFIGURATION: CASE OF

SEPARATE LTE AND DVB OPERATORS

We now consider the case where the LTE and DVB opera-tors are separate. The set of players becomes P1, and includesthe LTE operator with XL subscribers and a total revenue ofδL, the DVB-NGH operator with XD subscribers and a totalrevenue of δD, a set of KTV served TV channels and soK = |KTV| TV channel owners. We now proceed with theprofit distribution and coalition evolution analysis, as we didfor the single operator case in the previous section.

A. Revenue Sharing

As stated previously (Section III-B1), each channel i has anamount of subscription fees equal to δLi = p(i)δLXL on LTE


bearer (L) and δDi = p(i)δDXD on DVB bearer (D). For thehybrid network configuration shown in Figure 1, we considerthat each channel i is broadcast by DVB in DVB coverageregion and by LTE in regions where this channel cannot beserved by DVB, so as to ensure continuity of mobile TVservice delivery. So, the revenue worth function of a certainsubset of players defined by coalition S could be seen as theaddition of the elementary revenue worth functions V ′i

r (S)defined by:

V ′ir (S) = δLi ·I{{L,i}∈(S) ,{D}/∈(S)}+δDi ·I{{D,i}∈(S) ,{L}/∈(S))}

(24)where IB = 1 if condition B is true and 0 otherwise.

Given (S, V ′ir ), we begin by the LTE share and reason as

in Section III-B1: We eliminate the dummy players (whichare the DVB operator (D) and any channel j �= i) and applyShapley distribution (Eq. (10)) to the rest (L and i). We dothe same for DVB. We aggregate then the elementary sharesto obtain:

φrL(RD, P1, V

′r ) =

∑|KTV|i δLi

2(25)

φrD(RD, P1, V

′r ) =

∑|KTV|i δDi

2(26)

φ′ri (RD, P1, V

′r ) =

δLi + δDi2

(27)

where KTV is the total set of served TV channels.

B. Cost Sharing

The system total costs will be shared by all players (i.e.,LTE will pay a share in the DVB cost and vice versa). Inthis case also, we divide the costs worth function using theadditivity property into four elementary worth functions:

B.1- Power consumption worth function:

V′Pc (RD, S) =Pc(RD, S\{D,L})I{D,L∈(S)}

+Pc(Rs, S\{D})I{D∈(S),L/∈(S)}(28)

where RS is the radius of the target service area, RD is theradius of the area covered by DVB-NGH (see Figure 1), Land D represent the LTE and DVB operators respectively,Pc(RD, S\{D,L}) is the DVB-NGH power consumptionwhen the latter covers only a region of radius RD (Eqn.(1)) and cooperate with LTE to serve the set of TV channelsexisting in coalition (S) (all players other than the operatorand represented by S\{D,L}) and finally Pc(RS , S\{D})is the maximal power consumption costs when DVB-NGHcovers the total service area of radius R = RS and servesalone the Mobile TV service defined by the set of TVchannels in coalition (S) (i.e., S\{D} since D is the onlyoperator in this case).

B.2- DVB transmitter and equipments rent costs worthfunction:

The term CrentD in Eqn. (2) is due to the rent of the DVB

transmitter and equipment from fixed TV operator or theirupdates to deliver mobile TV by DVB-NGH operator. Therent worth function is:

V′rentc (RD, S) = Crent

D I{D∈(S)} (29)

Using Eqn. (10), we obtain the share of DVB-NGH in powerconsumption φP

D(RD, P1, V′Pc ) and the broadcast transmitter

rent costs φrentD (P1, V

′rentc ) given by Eqns. (30) and (31)

below (see Appendix A):

φPD(RD, P1, V

Pc ) =

αe.H

N1−1∑i=2

i(i− 1)!(mi−1∑

j=1

Pc(RD, (ei−1)j∗))(N1 − i− 1)!

N1!

+αe.H

N1−1∑i=2

(i − 1)!(mi−1∑

j=1

Pc(RS , (ei−1)j∗))(N1 − i)!

N1!(30)

φrentD (RD, P1, V

rentc ) =

N1 − 2

N1 − 1Crent

D (31)

By the balance property (Eqn. (11)), we obtain the broadcastpower transmission and transmitter rent costs share due to LTEoperator (Eqns. (32) and (33) respectively):

φPL(RD, P1, V

Pc ) =

αe.H

N1−1∑i=2

i(i− 1)!(mi−1∑

j=1

Pc(RD, (ei−1)j∗))(N1 − i− 1)!

N1!

−αe.H

N1−1∑i=2

i(i− 1)!(mi−1∑

j=1

Pc(RS, (ei−1)j∗))(N1 − i− 1)!

N1!(32)

φrentL (RD, P1, V

rentc ) = 0 (33)

where, again, N1 is the total number of players (N1 = K+2),ei−1 is the same (mi−1 × |KTV|) matrix defined in SectionIII-B2, the set of TV channels to be served is given by its jth

line (ei−1)j∗ and Pc(RD, (ei−1)j∗) is the power consumption(Eqn. (1)) needed when the DVB coverage radius is RD.

Note that φPL (RD, P1, V

′Pc ) ≤ 0 because the transmitted

power and hence the consumed one for a given set of servedTV channels (ei−1)j∗ and covering the whole service area(RD = RS) is higher than the power needed to cover onlya portion of the area (RD < Rs) : Pc(RS , (ei−1)j∗) ≥Pc(RD, (ei−1)j∗)). And so, φP

L (RD, P1, V′Pc ) is the gain

paid by the DVB-NGH operator to LTE for using LTE’sinfrastructure to offer mobile TV in the outer region (Fig.1) and thus reducing its (DVB’s) transmission power.

Finally, we obtain each TV channel i broadcast costs (powerconsumption and equipment rent costs) share (also by applyingthe balance property):

φP ′i (RD, P1, V

′Dc ) =φP ′

D (RD, P1, V′Dc )

+ φrentD (RD, P1, V

rentc ))

− φP ′D (RD, P1\{i}, V ′D

c )

− φrentL (RD, P1\{i}, V rent

c )

(34)

B.3- LTE infrastructure worth function:

V′bsc (S) =CL(RD, S\{L,D})I{L,D∈(S)}

+CL(RS , S\{L})I{L∈(S),D/∈(S)}(35)

where CL(RD, S\{L,D}) is the additional infrastructurecosts induced when we serve the set S\{L,D} of TV


channels without any compromise on unicast services qual-ity, in a cooperative LTE and DVB system (Eqn. 9), andCL(RS , S\{L,D}) is the maximal additional infrastructurecosts in a standalone system where LTE covers the wholeservice area of radius RS .

Using Eqn. (10) and the other Shapley value properties,we obtain the infrastructure distribution (i.e., the share eachplayer has to pay for the total cellular infrastructure costs).The infrastructure costs share of LTE and DVB are givenrespectively in Eqns. (36) and (37).

φbsL (RD, P1, V

′bsc ) =

N1−1∑i=2

i(i− 1)!(mi−1∑

j=1

CL(RD, (ei−1)j∗))(N1 − i− 1)!

N1!

+

N1−1∑i=2

(i − 1)!(mi−1∑

j=1

CL(RS , (ei−1)j∗))(N1 − i)!

N1!(36)

and

φbsD (RD, P1, V

′bsc ) =

N1−1∑i=2

i(i− 1)!(mi−1∑

j=1

CL(RD, (ei−1)j∗))(N1 − i− 1)!

N1!

−

N1−1∑i=2

i(i− 1)!(mi−1∑

j=1

CL(RS , (ei−1)j∗))(N1 − i − 1)!

N1!(37)

Here also, we see that the DVB-NGH operator will receivea gain −φbs

D (RD, P1, V′bsc ) from the LTE operator for using

its infrastructure to serve LTE users in some regions.Again, by applying the balance property (Eqn. (11)), we

obtain the infrastructure cost share of each TV channel i:

φbs′i (RD, P1, V

′bsc ) =φbs

L (RD, P1, V′bsc )

− φbs′L (RD, P1\{i}, V ′bs

c )(38)

B.4- Content costs worth function:

V′Cc (S) = [

|KTV|∑

i=1

ci]I{D and/or L and i∈(S)} (39)

Calculations lead to the following distribution:

φ′contentD (P1, V

′contentc ) =

|KTV|∑

i=1

ci6

(40)

φ′contentL (P1, V

′contentc ) =

|KTV|∑

i=1

ci6

(41)

φ′contenti (P1, V

′contentc ) =

2ci3

(42)

where, again, L refers to the LTE operator, D to DVB and ciis the content cost of TV channel i.

C. Incentives for Cooperation To Minimize The OperatorsCosts

Thanks to its “fairness”, the profit distribution under Shap-ley value is appealing in cooperative games. Each player isrewarded a profit proportional to its contribution in the overallprofit. The proof of the following proposition can be found inthe Appendix.

Proposition 1: Under the Shapley profit distribution, LTEand DVB operators have always the incentive to cooperate toreduce their costs when offering mobile TV service.

The incentive of cooperation and the fairness of the profitdistribution under Shapley value mechanism do not mean theabsence of disputes and competition between players. In fact,each player in this game will seek the network configurationthat maximizes its individual profit (in our case, the networkconfiguration corresponds to radius RD, i.e., area covered byDVB-NGH in Fig. 1).

Knowing that the operators have incentive to cooperate, wealso prove in the appendix the following proposition:

Proposition 2: Under the Shapley profit distribution, bothLTE and DVB operators have the same optimal configuration(RD) that minimizes their cost share.

As in the case of joint LTE/DVB-NGH operator, the in-centive for cooperation to minimize the operator costs, andthe convergence of LTE and DVB decision about the optimalnetwork configuration will not always lead to a stable mobileTV market. Since the TV channel providers may not besatisfied (recall Figures 5 and 6). Once again, the NashEquilibrium gives the optimal solution. We characterize itnext.

D. Nash Equilibrium

As in the case of joint LTE/DVB-NGH, the Nash Equi-librium is the stable solution that defines the optimal set ofTV channels to be served and the corresponding networkconfiguration (for definition refreshing see sec. III-D). In thiscase we have (|KTV|+2) players: |KTV| channel providers,each offering one TV channel, LTE and DVB operators. Theplayers action profiles are defined as follows:

- LTE operator can choose whether to cooperate with DVBor deliver the mobile TV service alone (using only its own in-frastructure). If LTE cooperates, it dimensions its system so asto cover all the area not covered by DVB. The correspondingset of actions is AL = {cooperation, no cooperation}.

- DVB operator enters the game by adjusting its trans-mission power either cooperatively with LTE or by settingit to some maximal value on its own in case it decides orLTE decides not to cooperate. The corresponding action isAD = {cooperation(PD), no cooperation}.

- The channel providers decide whether they wish tobe broadcast or not (with respect to their target prof-its) when the operators decide to cooperate, or whichoperator to join (or both or none) when the latter de-cide not to cooperate. The actions for the coopera-tive case are Aicoop = {broadcast, not broadcast},and for the non-cooperative case are Aino−coop ={not broadcast, LTE,DV B,LTE and DV B}.


0 5 10 15 20 25−4

−3

−2

−1

0

1

2

3

4

5

6x 10

5

DVB Radius [Km]

Net

wor

k C

osts

[eur

os/m

onth

]

LTEDVBStandalone LTEStandalone DVB

Fig. 7. Operators cost share (power and infrastructure) for αe = 0.18euros/kWh.

0 5 10 15 20 25−1

0

1

2

3

4

5

6x 10

5

DVB Radius [Km]

Net

wor

k C

osts

[eur

os/m

onth

]

LTEDVBStandalone LTEStandalone DVB

Fig. 8. Operators cost share (power and infrastructure) for αe = 0.8euros/month.

E. Numerical applications

We consider the inputs given in Table II in the previoussection. We plot in Figures 7 and 8 the costs paid by bothLTE and DVB operators for moderate (αe = 0.18) and high(αe = 0.8) electricity price, respectively.

We observe that under the Shapley distribution, both LTEand DVB operators will agree on the same network configu-ration choice (RD) as proved in Section IV-C. Indeed, bothoperators have the lowest induced costs for RD = 25Kmfor moderate electricity price level and RD = 23Km forhigher electricity price. This means that the best configurationis to use the infrastructure of the network with the lowestcost as compared to the other network. It is also clear thatfor both electricity price levels, the mobile TV network costspaid by the operators in a hybrid network are lower than thosepaid in a standalone network, even when the optimal networkconfiguration is to use only one operator (as in the case ofαe = 0.18 and the optimal network configuration is to coverthe whole area with DVB signal RD = 25Km). This is dueto the fact that under Shapley profit distribution, not only therevenue but also the network costs are shared fairly among theplayers. As a result, the LTE operator will pay DVB an amountof φbs

D (RD, P1, V′bsc ) euros/month (Eqn. (37)), for offloading

a part of its traffic on DVB infrastructure at lower costs. Thesenew DVB revenues are shown in Figure 9 as being a negativecost share.

The DVB operator will also pay LTE an amount ofφPL (RD, P1, V

′Pc ) euros/month (Eqn. (32))), represented by

0 5 10 15 20 25−4

−3

−2

−1

0

1

2

3

4

5

6x 10

5

DVB Radius [Km]

Cel

lula

r In

fras

truc

ture

Cos

ts [e

uros

/mon

th]

LTEDVBStandalone LTE

Fig. 9. Operators cellular infrastructure costs share for αe = 0.18euros/kWh.

0 5 10 15 20 25−6

−4

−2

0

2

4

6

8x 10

4

DVB Radius [Km]P

ower

Cos

ts [e

uros

/mon

th]

LTEDVBStandalone DVB

Fig. 10. Operators power costs share for αe = 0.18 euros/kWh.

0 5 10 15 20 25−2

−1

0

1

2

3

4

5

6

7x 10

5

DVB Radius [Km]

Pro

fits

[eur

os/m

onth

]

LTE Profit: case 1DVB Profit: case 1LTE Profit: case 2DVB Profit: case 2

Users Penetration (LTE, DVB)Case 1: (80%,20%)Case 2: (50%,50%)

Fig. 11. Profits of the operator for different DVB subscription penetrationwith αe = 0.18 euros/kWh.

the negative power cost share of LTE in Figure 10.We next plot, in Figure 11, the profit for each operator for

two penetration percentages: one with 80% subscribers forLTE and 20% subscribers for DVB, and one with 50% each.For a moderate electricity price of 0.18 euros/month.

We observe that for the low LTE user penetration rate (50%), LTE will not be able to serve the mobile TV users alone; ifLTE does not increase its subscription fees, its profits will benegative in a standalone network. If it however cooperates withDVB, it will be able to serve mobile TV without increasing itssubscription fees and its profit will be positive starting fromRD ≥ 18 Km.

In Figure 12 we plot the profit shares of the TV channels,LTE and DVB-NGH operators for an equal users penetrationrate (50 %) and for an electricity price αe = 0.4 euros/kWh.


0 5 10 15 20 25−2

−1

0

1

2

3

4

5

6x 10

5

DVB Radius [Km]

Pro

fit [e

uros

/mon

th] ,

pen

etra

ion

50%

0 5 10 15 20 25−1

−0.5

0

0.5

1

1.5

2

2.5x 10

5

DVB Radius [Km]

Pro

fit [e

uros

/mon

th] ,

pen

etra

ion

50%

LTEDVB


Fig. 12. Operators and channel providers profits for equal user penetrationand αe = 0.4 euros/kWh.

We see that TV channels 5, 4 and 3 have negative profitunder the optimal LTE and DVB-NGH network configurationsetting (RD = 25 km), and they will not have incentive to takepart in this offer. In this case, the LTE and DVB operators willhave four Nash Equilibria (stable dimensioning strategies):

1) LTE/DVB cooperation; set of TV channels: TV1 , TV2,TV4, TV5; RD = 25 Km



4) Standalone DVB network; set of TV channels: TV1 ,TV2, TV3, TV4 (broadcast on DVB only)

From these Nash results, we see that for the given subscriptionfees, LTE is not able to serve alone any set of TV chan-nels. DVB however can serve alone the 4 most popular TVchannels, but the latter will make more profit if they considercooperation with LTE. So in this case, the optimal mobile TVnetwork will be obtained by the cooperation of LTE and DVBto offer the 4 most popular TV channels (channels 1, 2, 3and 4) with a DVB radius RD = 25 Km (Nash Equilibriumnumber 3). By this cooperation, LTE will be able to offer theservices without increasing the fees and DVB will make moreprofit.

For higher LTE penetration, for example 80%, we obtainthree Nash Equilibria:



3) LTE/DVB cooperation; set of TV channels: TV1 , TV2,

Player 1 Player 2 ... Player i (O) Player i+1 ... Player N

(S) (N-i) Players

Fig. 13. Representation of a permutation.

TV3, TV4; RD = 25 KmThe Nash Equilibrium number 3 is again the optimal config-uration, as it bring more profits to operators.

V. CONCLUSION

We investigated in this paper the engineering and profitsharing of a hybrid LTE/DVB system, in cases where theoperators are joint or separate. We first derived the capacityin both networks and showed how and at what cost theyneed to be upgraded so as to support a mobile TV servicewithout degrading the QoS of other unicast flows: voice anddata. We then derived close-form equations for the profitsharing between the different players in the system, namely theoperators and the TV channels, using coalition games conceptShapley, and showed how this profit varies with differentsystem parameters and market penetration rates. We eventuallyfocused on the case where each player tries to maximize itsown profit and obtained the players optimal strategies at theNash equilibrium.

Our perspectives are mostly on the user side where thelatter can also play a game in choosing to which operatorto subscribe, and the TV channels which can also make useof advertisement so as to increase their popularities and hencesubscription rates.

ACKNOWLEDGEMENT

This work was partially funded by the ANR project IDEFIXunder the grant number ANR-13-INFR-0006

APPENDIX

A. Expression details

1) Expressions (19)-(21): The shapley value correspond-ing to the operator is obtained by the sum of the operatorMarginal Contributions (MC) over all the possible orderingcombinations (permutations) divided by the total number ofthose permutations (Eqn. (10)). We have N = |KTV| + 1players, let Π the set of the N ! possible permutations. Anexample of permutation π ∈ Π is represented as follows:

MC of the operator (denoted by O in this permutation) :Δo(V, S(π, o)), is the difference between the worth functionV (S) of coalition (S) containing players of order 1 till i andthe worth function V (S\{i}) of the coalition of players fromorder 1 to i− 1.

For each network configuration RD and the set of TVchannels kTV in (S), the worth function V (S) is thepower cost in Eqn. (19), and is given by: αe · H ·Pc(RD,kTV)I{operator ∈(S)}. It is the infrastructure costs inEqn. (20)) and is given by CL(RD,kTV)I{operator ∈(S)}. Andfinally it is the equipment costs in Eq. (21)) (V rent

c (RD, S) =Crent

D I{operator ∈(S)}). It is clear that those latter worth func-tions are null if the operator is not in the coalition, and thismeans that V (S\{i}) = 0 and finally Δo(V, S(π, o)) = V (S).


Then, we have to sum over all possible permutations. Toease the computation of this sum, we divide the permutationsset Π into N set of ordering Πi where i ∈ (1, .., N). Wedefine Πi as being the set of all possible ordered combinationsof players where the operator is the ith player.

For each permutation in the ordering set Πi represented byFigure 13 :

- The coalition (S) is a combination of (i−1) TV channelschosen from the (N − 1) ones and the operator. So we canhave mi−1 =

(N−1i−1

)different sets of i − 1 TV channels and

thus mi−1 different coalitions (Sj) with j = {1, ..,mi−1}.Let the worth function V (Sj) be the cost to serve a particularset of (i − 1) TV channels chosen from the mi−1 possiblesets.

- The order of TV channels in the coalition is taken intoaccount, and so, using the permutation theory, each coalition(Sj) is repeated (i − 1)! times.

- each coalition (Sj) is also repeated (N − i)! times bypermuting the (N − i) other players.

So, the sum of the operator marginal cost, in a givenordering Πi is given by:

(i− 1)!

mi−1∑

j=1

V (Sj)(N − i)! (43)

We sum this latter over all orderings and divide it by thetotal number of permutations (N !) (Eqn. (10)):

φo(RD, V ) =

N∑i=2

(i− 1)!(mi−1∑

j=1

V (Sj))(N − i)!

N !(44)

We note that for i = 1, V (Sj) = 0 ∀j ∈ {1, ...mi−1}, sincein this case coalition (Sj) contains only the operator. And so,there is not any TV channel to deliver and thus there is notany cost.

We recall that V (Sj) is αe · H · Pc(RD, Sj) in Eqn. (19)and CL(RD, Sj) in (19). To ease further the computation,we memorize the mi−1 coalitions (Sj), representing thecombination of i − 1 TV channels, in a matrix denoted byei−1. It is a (mi−1 × |KTV|) matrix. Each column k in thismatrix corresponds to channel k in the set KTV. Each jth line(ei−1)j∗ in this matrix represents a different combination ofi−1 served TV channels (so it is Sj). We denote (ei−1)jk = 1if TV channel k is to be served and zero otherwise. However,V (Sj) = Crent

D , ∀(Sj) and thus simplifications in Eqn. (44)will lead to Eqn. (21 ).

2) Expressions (30)-(37): : We consider now the case ofseparate operators. we have N1 = |KTV| + 2 players. Wereason as previously on the N1! permutations.

We begin by the share of the DVB-NGH operator (denotedby D) in the power cost (Eqn. (30)). For each ordering π (Fig.16), the DVB operator marginal contribution (MC) is given by:

ΔD(V, S(π,D)) =

{αe · P (RD,kTV) ·H if L ∈ (S\{i})αe · P (RS,kTV) ·H if L /∈ (S\{i})

(45)

To get the sum of these MC over all possible permutations,we reason as we did in the previous section of this Appendix(B.1), by dividing the total set of permutation Π into N1 sets

where each set Πi contains the different permutations in whichthe DVB operator is the ith player. However in this case, eachset Πi can be also grouped into two subsets: Π1

i containingthe permutations with the LTE operator is in coalition (S\{i})and Π2

i containing the other permutations of Πi. The sum ofthe MC of each ordering set Πi is thus composed of two parts:

-Part 1: Sum of MC of Π1i :

• Coalition (S) is a combination of (i − 2) TV channelschosen from the (N1 − 2) ones, and the LTE and DVBoperators. So we can have mi−2 =

(N1−2i−2

)different sets

of i− 2 TV channels and thus mi−2 different coalitions(S). Let the worth function V (Sj) be the cost to servea particular set of (i − 2) TV channels chosen from themi−2 possible sets (j = {1, ..,mi−2}).

• Taking into account the (i − 2)! permutation of the TVchannels in (Sj), without forgetting that the LTE operatorcan take any order from 1 to i− 1, we will have (i− 1) ·(i − 2)! coalitions with the same worth function V (Sj).However, each ordered coalition is repeated (N1 − i)!times (permutation of the (N1 − i) other players).

And so, the sum of the MC in the set Π1i is given by:

(i − 1)(i− 2)!(mi−1∑

j=1

P (RD, Sj))(N1 − i) (46)

We note that this sum is null for ordering 1 and 2 since in thiscases coalition (S\{i}) will only contain the DVB operatorfor i = 1 and the LTE and DVB operators for i = 2 (no TVchannels, no costs).

-Part 2: Sum of MC of Π2i :

Coalition (S) in this case is an ordered combination of only(i − 1) TV channels and the DVB operator. So the sum isobtained by the same reasoning of Eqn. (43), we only replaceN by N1 and RD by RS because in this case the DVBoperator is alone in the operating coalition and has to servethe total service area. We note that Π2

i exists for i < N1 − 1.And the sum of its MC is equal to zero for i = 1, becausein this latter ordering, (S) contains only the DVB operatorwithout any TV channel.

By summing those two parts over the N1! permutations, weobtain the DVB share in the power cost:

φPD(RD, P1, V

Pc ) =

αe.H

N1∑i′=3

(i′ − 1)(i′ − 2)!(mi′−2∑

j=1

P (RD, Sj))(N1 − i′)!

N1!

+αe.H

N1−1∑i=2

(i− 1)!(mi−1∑

j=1

Pc(RS , Sj))(N1 − i)!

N1!(47)

Finally, by replacing i′ by i = i′ − 1, and Sj by the line(ei−1)j∗ of the previously defined matrix (ei−1 (appendix B.1), we obtain equation (30).

On the other hand, the LTE share in the power costs Eqn. 32is obtained in terms of the DVB share by the balance property(11):

φPL(RD, P1, V

′Pc ) =φP

D(RD, P1, V′Pc )

− φPD(RS , P1\{L}, V ′

c )(48)


with φPD(RS , P1\{L}, V ′

c ) is the DVB power cost share whenit serves alone the Mobile TV service. It can be obtained byreplacing N by N1 − 1 in Eqn. (44).

After the subtraction, we obtain Eqn. (32).By replacing the consumed power cost αe ·H ·Pc(R,Sj) in

the previously developed equations with the LTE infrastructurecost CL(R,Sj) we obtain the LTE share in the latter costs(Eqn. (36))) and then, by the balance property, we obtain theshare of the DVB operator Eqn. (37). Finally, we replace itwith Crent

D , ∀Sj and do some mathematical simplificationsto obtain Eqn. (31).

B. Proof of Proposition 1

We have to prove that the cost share of DVB and LTEoperators in the cooperative network is lower than the stan-dalone network cost share by proving Eqns. (49) and (50)respectively:

φcD(RD, P1, V

′c ) ≤ φc

D(RS , P1\{L}, V ′c ) (49)

andφcL(RD, P1, V

′c ) ≤ φc

L(RS , P1\{D}, V ′c ) (50)

We begin by the DVB cost; it is given by the sum ofequations (30), (31), (37) and (40) in a cooperative LTE/DVBnetwork and can be written as:

φcD(RD, P1, V

′c ) =φP

D(RD, P1, V′Pc )

+φbsL (RD, P1, V

′bsc )− φbs

L (RS , P1\{D}, V ′c )

+K∑i=1

ci6

(51)and in a standalone DVB network it is given by:

φcD(RS , P1\{L}, V ′

c ) =φPD(RS , P1\{L}, V ′

c )

+

K∑

i=1

ci2

(52)

DVB has the incentive to cooperate with LTE if we canprove that:

φPD(RD, P1, V

′Pc ) + φbs

L (RD, P1, V′Lbsc )

+K∑i=1

ci6

≤ φPD(RS, P1\{L}, V ′

c ) + φbsL (RS, P1\{D}, V ′

c )

+K∑i=1

ci2

(53)This is true as:

φPD(RD, P1, V

′Pc )− φP

D(RS , P1\{L}, V ′c ) =

φPL (RD, P1, V

′Pc )

(54)

where φPL(RD, P1, V

′Pc ) is the LTE power costs share given

by eq. (32) and proven to be negative. so:

φPD(RD, P1, V

′Pc ) ≤ φP

D(RS , P1\{L}, V ′c ) (55)

In the same way we prove:

φbsL (RD, P1, V

′bsc ) ≤ φbs

L (RS , P1\{D}, V ′c ) (56)

Finally:∑K

i=1ci6 <

∑Ki=1

ci2 By adding those inequalities

we obtain our goal equation (53).In the same way we prove eq. (50).Finally we conclude that

under the shapley distribution both LTE and DVB operatorshave the incentive for cooperation to reduce their networkscosts.

C. Proof of Proposition 2

If we consider R∗D the optimal radius of DVB-NGH area

that maximizes the profit of LTE:

φcL(R

∗D, P1, V

′c ) ≤ φc

L(RD, P1, V′c ) (57)

By detailing the cost share φcL, into power, infrastructure and

content costs we obtain:

φbsL (R∗

D, P1, V′bsc )φP

D(R∗D, P1, V

′Pc )

− φPD(RS, P1\{L}, V ′

c )

≤ φbsL (RD, P1, V

′bsc ) + φP

D(RD, P1, V′Pc )

− φPDV B(RS , P1\{L}, Vc′)

(58)

We can easily omit the standalone DVB constant costsφPD(RS , P1\{L}, V ′P

c ) and introduce the standalone LTE con-stant costs φbs

L (RS , P1\{D}, V ′c )

φbsL (R∗

D, P1, V′bsc ) + φbs

D (R∗D, P1, V

′Pc )

−φbsL (RS , P\{D}, V ′bs

c )

≤ φbsL (RD, P1, V

′bsc ) + φP

D(RD, P1, V′Pc )

− φbsL (RS, P1\{D}, V ′bs

c )(59)

by reorganizing the terms we obtain:

φPD(R∗

D, P1, V′Pc )

+φbsL (R∗

D, P ′, V′bsc )

−φbsL (P ′\{D}, V ′bs

c )

≤ φPD(RD, P ′, V

′Pc )

+ φbsL (RD, P1, V

′bsc )

− φbsL (RS , P1\{D}, V ′bs

c )

(60)

and finally:

φcD(R∗

D, P1, V′c ) ≤ φc

D(RD, P1, V′c ) (61)

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Amal Abdel Razzac is a Ph.D. student jointlyin University of Paris VI, France, and LebaneseUniversity, Lebanon. She received her MS degreein Telecommunication System technologies and aME in Computer Science and Telecommunicationsin 2011 from the Lebanese University. Her researchinterests are on dimensioning and performance eval-uation in wireless networks.

Salah Eddine Elayoubi received his MS in telecom-munications and networking from the National Poly-technic Institute at Toulouse, France, in 2001, andhis Ph.D. and Habilitation in Computer sciencefrom the University of Paris VI in 2004 and 2009,respectively. Since then, he has been working inOrange Labs, the research and development divi-sion of France Telecom group. He is now a seniorresearch engineer, involved in several EU-funded re-search projects. His research interests include radioresource management, modelling and performance

evaluation of mobile networks.

Tijani Chahed holds BS and MS degrees in Electri-cal and Electronics Engineering from Bilkent Uni-versity, Turkey, and Ph.D. and Habilitation a Dirigerdes Recherches (HDR) degrees in Computer Sciencefrom the University of Versailles and the Universityof Paris 6, France, respectively. He is currentlya Professor in the Telecommunication Networksand Services department in the Telecom SudParis,France. His research interests are in the area ofperformance evaluation, resource allocation and tele-traffic engineering, notably in wireless networks.

Bachar Elhassan got his engineering Diploma in1991 from the Lebanese university, Tripoli Lebanon,his MS in signal processing in 1992 from theNational polytechnic institute (INPG) of Grenoble,France and his Ph.D. in electronics in 1995 from theINPG-France in collaboration with France Telecom.Since 1996, he has been working at the facultyof engineering of the Lebanese university TripoliLebanon where he is currently an associate profes-sor. He founded the Telecommunications and Net-working research team at the laboratory of Electron-

ics Systems, Telecommunication and Networking (LaSTRe) of the DoctoralSchool of Sciences and Technologies (EDST), Lebanon. He is the chair ofIEEE ComSoc Lebanon chapter since Jan 2013. His research interests concerndigital communication and wireless sensor networks.

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Dimensioning and Profit Sharing in Hybrid LTE/DVB Systems to Offer Mobile TV Services