Research ArticlePricing Resources in LTE Networks throughMultiobjective Optimization
Yung-Liang Lai1 and Jehn-Ruey Jiang2
1 Department of Computer Science and Information Engineering Taoyuan Innovation Institute of Technology TaoyuanJhongli 32001 Taiwan
2Department of Computer Science and Information Engineering National Central University Taoyuan Jhongli 32001 Taiwan
Correspondence should be addressed to Yung-Liang Lai yunglianglaigmailcom
Received 31 August 2013 Accepted 17 October 2013 Published 2 January 2014
Academic Editors T Chen and J Yang
Copyright copy 2014 Y-L Lai and J-R Jiang This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
The LTE technology offers versatile mobile services that use different numbers of resources This enables operators to providesubscribers or users with differential quality of service (QoS) to boost their satisfaction On one hand LTE operators need to pricethe resources high for maximizing their profits On the other hand pricing also needs to consider user satisfaction with allocatedresources and prices to avoid ldquouser churnrdquo which means subscribers will unsubscribe services due to dissatisfaction with allocatedresources or prices In this paper we study the pricing resources with profits and satisfaction optimization (PRPSO) problem in theLTE networks considering the operator profit and subscribersrsquo satisfaction at the same timeThe problem is modelled as nonlinearmultiobjective optimization with two optimal objectives (1) maximizing operator profit and (2) maximizing user satisfaction Wepropose to solve the problem based on the framework of the NSGA-II Simulations are conducted for evaluating the proposedsolution
1 Introduction
The 3rd generation partnership project (3GPP) long-termevolution (LTE) technology is one of the major candidates ofthe fourth generation (4G) wireless communication systems[1] It offers versatile mobile services using different numbersof resources and enables operators to provide subscribers orusers with differential quality of service (QoS) for maximiz-ing subscriber satisfaction The LTE operators seek the de-ployment of spectrum-efficient ubiquitous always-on andinteroperable mobile broadband wireless access whose goalis to provide peak data rates of 100Mbps for high-mobilitysubscribers and 1 Gbps for low-mobility subscribers [2]
Due to scarcity of resources (eg spectrum) in the LTEnetwork the resources are usually costlyThe operators investhuge funds in capital expenditure (CAPEX) and operationalexpenditure (OPEX) for spectrum licensing and infrastruc-ture construction and management [3] in order to reserveenough resources for subscribers to boost their satisfactionOn one hand LTE operators need to price the resources high
for maximizing their profits On the other hand pricing alsoneeds to consider user satisfaction with allocated resourcesand prices to avoid the ldquouser churnrdquo [4] which means sub-scribers will unsubscribe services due to dissatisfaction withallocated resources or prices It is important to study how toprice the resources for maximizing the operator profit andmaximizing the subscriber satisfaction at the same time inLTE networks
This paper investigates the pricing resources with profitand satisfaction optimization (PRPSO) problem in the LTEnetworks to simultaneouslymaximize the operator profit andsubscriber satisfaction The problem is modelled as a multi-objective problem with two conflicting objectives (1) maxi-mizing operator profit and (2) maximizing user satisfactionThe PRPSO problem is modeled on the resource block allo-cation model defined in the 3GPP LTE standard [2] For anLTE operator the solutions of the PRPSO problem are helpfulfor analyzing realistic impacts of investment in spectrumsince the PRPSO problem is formulated on the resourceblocks which are the units of allocation mechanism for
Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 394082 9 pageshttpdxdoiorg1011552014394082
2 The Scientific World Journal
allocating spectrum resources for subscribers and are theunits for providing enough quality of services in the LTEnetwork
Due to the hardness of solving this problem we develop aheuristic genetic optimization algorithm called the PRPSOalgorithm to find the solution based on the nondominatedsorting genetic algorithm (NSGA-II) in [5] For an analyst ofpricing resources in LTE networks the solutions found by thePRPSO algorithm are useful for analyzing the subscribersrsquosatisfaction and the operatorrsquos profit based on subscribersrsquosatisfaction models and costs for acquiring spectrum Theoptimal solutions found by the PRPSO algorithm are thePareto fronts in the multiobjective decision theory ThePareto fronts are a set of choices that are nondominated byother choices which are helpful formaking tradeoff decisionsto achieve two conflicting objectives subscribersrsquo satisfactionand operatorrsquos profits in LTE networks
Some optimization studies are proposed for resourcepricing resource reservation and load balancing in LTE net-worksHuang et al in [6] proposed an adaptive call admissioncontrol and resource (or bandwidth) reservation schemeusing fuzzy logic control and particle swarm optimization(PSO) for 4G networks Huang et al in [7] proposed a re-source (or bandwidth) reservation mechanism for neighbor-ing 4G cells based on grey prediction theory and swarm intel-ligence Dixit et al in [8] studied the dynamic pricing pro-blem on maximizing operator revenue in LTE networksHowever the problem of reserving and pricing LTE wirelessresources tomaximize both the operator profit and subscribersatisfaction is not fully studied
The rest of this paper is organized as follows In Section 2the PRPSO problem is formulated The proposed heuristicgenetic PRPSO algorithm to solve the problem is introducedand evaluated in Sections 3 and 4 respectively And finallysome concluding remarks are drawn in Section 5
2 Modeling and Problem Formulation
In this section we introduce the resource allocation modelthe user satisfaction model and the PRPSO problem in LTEnetworks
21 Resource AllocationModel in LTENetworks TheLTEnet-work uses an IP-based network architecture to provide voiceand data services Based on the architecture the operator candesign and sell the products by combining different QoS ser-vices The LTE air interface uses orthogonal frequency divi-sion multiplexing (OFDM) with advanced antenna tech-niques to transmit voice and data simultaneously [2] Thescheduler in the base station (called eNodeB or eNB) is resp-onsible for dynamically scheduling the LTE air interface inboth the downlink and uplink directions for subscribersrsquo userequipment (UE) As shown in Figure 1(a) much UE accessesan eNB at the same time and the eNB needs to provide dif-ferential services for the UEs
The LTE standard provides a diversity of classes of QoSservices [9] A traffic class or a QoS class is defined accordingto the restrictions and the limitations of the radio interface
Based on the traffic sensitivity to the packet delay four classesare defined the conversational streaming interactive andbackground classes The conversational class is meant for thetraffic that has a high sensitivity to delay (eg VoIP) while thebackground class deals with the traffic that has a low sen-sitivity to delay (eg background downloading files or send-ing emails) The streaming class is real time based and canpreserve time relation (variation) between information enti-ties of streams (say video streams)The interactive class is besteffort based and follows a request-response pattern in appli-cations such as web browsing
In LTE networks a set of resource blocks is allocated to asubscriber [10] to provide the services The more resourceblocks are allocated to the subscriber the better experience ofservice is and thus the satisfaction is increased As shown inFigure 1(b) the downlink (eNB to UE) and uplink (UE toeNB) in the air interface are divided into a number of 15 kHzsubchannels in the frequency domain and a number of 05mstime slots in the time domain The resource block (RB) is themain unit used to schedule transmissions over the air inter-face (refer to Figure 1(b)) An RB contains 12 contiguous sub-channels and 7 symbols (duration is 05ms) In general anumber of RBs are allocated to an UE according to its qualityof service (QoS) [11] Statistically the more the resourceblocks are allocated to the UE of a subscriber the more thesubscriber is satisfied with the service In Figure 1(b) thenumber of allocated resource blocks of User 1 is higher thanthat of User 2 which implies that the satisfaction of theUser 2is higher than User 1
The resource block based model is more accurate in ana-lysing the channel resources used in the LTE network since itconsiders not only the cost of transmitting data but also theoverhead cost (such as retransmissions when packets are cor-rupted) It is notable that most of studies on pricing are basedon the received usage based model to charge subscribersbased on the amount of received packets which do not in-clude the overhead cost
22 User Satisfaction Model An operator allocates or res-erves resources to subscribers to provide them with differen-tial QoS levels The satisfaction of subscribers is important tothe operatorWithout sufficient resources allocated to the ser-vices subscribers will feel dissatisfied For example the ac-ceptable one-way (speakerrsquos mouth to listenerrsquos ear) delay ofvoice communication forVoIP applications recommended byITU [12] is at most 150msThe subscriber of VoIP service willfeel dissatisfied if transmission delay is more than 150ms dueto the insufficiency of allocated resources Dissatisfied sub-scribers may unsubscribe some services which will damagethe operatorrsquos profits They may unsubscribe all services andmigrate to another operator causing the ldquouser churnrdquo prob-lem reported in [4]
Lin et al in [13] proposed a method to approximate thesubscriberrsquos satisfaction with the allocated resources by a sig-moid function In this paper we also adopt the sigmoid func-tion to model the user satisfaction The sigmoid function isuseful for modeling natural processes or system learning cur-ves since it can represent a history dependent progression
The Scientific World Journal 3
LTE based station (eNodeB)
User equipment UE1
User equipment UE2
User equipment UE3
(a)
7 symbols (duration is 05 ms)
12 subcarriers
Resource blocks for User1
Resource blocks for User2
Frequency domain
Spectrum
Resource blocks
Time domain
(b)
Figure 1 Illustration of services controlled and resources allocated by an LTE based station (eNodeB) in the LTE network (a) UE withdifferential QoS requirements of services and (b) resource blocks allocated for a UE by a eNodeB in the frequency domain and time domain
approaching a limit It depends on a random variable 119909 to re-present the occupation of resources for the subscriber Thesigmoid function is formulated as follows
Ψ (119909) =1
(1 + 119890minus120572(119909minus120573)) (1)
where 120572 and 120573 are the steepness and the middle of the curverespectively
Figure 2 plots curves of the sigmoid functions where 120572
stands for the sensitivity and120573 is themedian value of the satis-faction curve As shown in Figure 2(a) the curve is withhigher steepness as 120572 is higher As shown in Figure 2(b) thestarting point of the curve is farther away from zero as 120573 ishigher
In subscriberrsquos point of view the value of 120572 indicates thesubscriberrsquos sensitivity to the degradation of service while 120573
indicates the acceptable level for the service It is remarkablethat 120573 decides when the satisfaction starts to increase and 120572
decides how fast the satisfaction increases
23 The Pricing Resources with Profit and Satisfaction Opti-mization (PRPSO) Problem We formulate the pricing re-sources with profit and satisfaction optimization (PRPSO)problem in this subsectionThemain goals of the problem are(1) to maximize the operatorrsquos profit and (2) to maximize theusersrsquo satisfactionThe formulation is based on a fixed periodof time 119879 say 1 day 1 month 2 months 1 year and so on
The first goal is to maximize the operatorrsquos profit Equa-tion (2) is used to formulate the operatorrsquos profit 119875 whichconsists of two factors revenue from subscribers (RS) andcost of spectrum (CS) Below we explain the meaning of (2)and describe some assumptions and notations used in it
We assume an operator has a set of spectrum segments(notated byΦ) For segment 119894 isin Φ 119861
119894
represents the quantityof units occupied in segment 119894 and 119862
119894
represents the cost perunit of segment 119894 Thus the operator pays CS = sum
119894isinΦ
119861119894
119862119894
foracquiring the spectrums for period 119879 We also assume theoperator sells a set of services (notated by Ω) to subscribersBy statistics or by predictions the operator totally allocates119876
119904
4 The Scientific World Journal
05
055
06
065
07
075
08
085
09
095
1
0 25 5 75 10
Sigm
oid
func
tion
x
120572 = 02
120572 = 04
120572 = 06
120572 = 08
(a) Curves of the sigmoid function with 120573 = 0 and different 120572
05
055
06
065
07
075
08
085
09
095
1
0 25 5 75 10
Sigm
oid
func
tion
x
120573 = 0
120573 = 2120573 = 4120573 = 6
(b) Curves of the sigmoid function with 120572 = 1 and different 120573
Figure 2 Curves of the sigmoid functions
resource blocks for each service 119904 isin Ω over period 119879 There-fore if the subscribers pay the price119875
119904
for each resource blockallocated to service 119904 for period 119879 the operator has revenueRS = sum
119904isinΩ
119876119904
119875119904
from the subscribers For example assume aservice 119878119886 is averagely allocated 100 resource blocks per dayand the price of each resource block allocated to service 119878119886 is12 dollar It means 119876
119904119886
is 100 resource blocks and 119875119904119886
is 12dollar per day thus the revenue is 120 dollar per day for ser-vice 119878119886 Consider
119875 = RS minus CS = sum119904isinΩ
119876119904
119875119904
minus sum119894isinΦ
119861119894
119862119894
(2)
119875119904
denotes the price per resource block allocated to ser-vice 119904 In reality 119875
119904
is a bounded price variable and 119875119904
isin
[119875min 119875max] as shown in
119875min le 119875119904
le 119875max (3)
The second goal is to maximize the subscribersrsquo satisfac-tion Equation (4) is used to formulate the satisfaction perpaid price 119880 In (4) 120595
119904
(119876119904
) is used to formulate the satisfac-tion for service 119904 it is a sigmoid function of119876
119904
the number ofresource blocks allocated to service 119904 Note that 119876
119904
119875119904
is theprice a subscriber pays for using service 119904 Therefore120595119904
(119876119904
)119876119904
119875119904
is the satisfaction per unit of paid price for ser-vice 119904119880 is hence the overall subscribersrsquo satisfaction per unitof paid price
119880 = sum119904isinΩ
120595119904
(119876119904
)
119876119904
119875119904
(4)
Given 119876119904
119861119894
119862119894
and 120595119904
(119876119904
) forall 119894 isin Φ 119904 isin Ω the PRPSOproblem is to find a price set PS formaximizing both the oper-atorrsquos profit and subscribersrsquo satisfaction defined as
Maximize 119875
Maximize 119880(5)
Now we discuss some issues of estimating parameters inthe PRPSO problemThe PRPSO problem is an optimizationproblem to decide prices based on given information Thequantity119876
119904
of resource blocks allocated to service 119904 is possiblyestimated from historic usage of resource blocks allocated toservice 119904 over the fixed period of time 119879 The per-unit cost 119862
119894
of spectrum segment 119894 is also possibly estimated as the averagecost of acquiring and managing spectrum over the timeperiod119879When the solutions of PRSP problem are found theoutput prices are also on the basis of time period119879 For exam-ple if 119876
119904
and 119862119894
are estimated over the period of one monththe prices are on the basis of onemonth It is also notable thatthe parameters 120572 and 120573 of 120595
119904
can be adjusted according tosubscribersrsquo experiences to shape the sigmoid function prop-erly
3 The Pricing Resources withProfit and Satisfaction Optimization(PRPSO) Algorithm
In this section we present our multiobjective pricing algo-rithm called the PRPSO algorithm to solve the pricing re-sources with profit and satisfaction optimization (PRPSO)problemThe proposed PRPSO algorithm is based on an evo-lutionary genetic algorithm (GA) approach which is used toheuristically find the solutions of optimization problemsTheGA approach is to mimic natural selection in the biology
The Scientific World Journal 5
where individuals with higher fitness can survive to next gen-eration [14]
In the GA approach the population (a set of individualsor solutions) is randomly generated in the initial step Thenthe population evolves in the generation loop for MAX GENtimes In each generation fundamental operations such asselection crossover and mutation are used to generate indi-viduals into the next generationWhen the generation loop isterminated the solution is made by decoding the best indi-viduals in the decode step
Based on the above steps and based on the nondominatedsorting genetic algorithm II (NSGA-II) algorithm in [5] wedesign the PRPSO algorithm for finding good solutions to thePRPSO problem The basic idea of the NSGA-II algorithm isto find from the solutions of the current and the next gen-erations the optimal front (called Pareto front) which is theset of nondominated feasible solutions (or front points) thatare not dominated by any others It is noted that a solution 119909
is said to dominate another solution119910 if and only if119909 is betterthan 119910 in at least one evaluation of objectives and 119909 is notworse than 119910 in all evaluations of objectives
119873 solutions in the Pareto front are selected to evolve asthe population is assumed to be of size119873 for each generationIf the first-found optimal front (or call the first optimal front)has less than 119873 front points then the second optimal frontshould also be found The second optimal front is the setof nondominated feasible solutions over all populationmem-bers except for those in the first optimal front If the first andthe second optimal fronts totally have less than 119873 membersthen the third optimal front should be found further and soon Not all the front points in the last-found optimal front areselectedThey are in practice selected according to the fitness(ie the nondomination) and the spread of solutions so thatthe optimal front found in the final generationwill have betterconvergence near the true Pareto front It is noted that thenotion of crowding distance is used for evaluating the degreeof spread of solutions
Nowwe introduce how to evaluate an individual of a pop-ulation in the proposed algorithm Each individual (say 119909)in the population has two attributes (1) nondomination 119909rankand (2) crowding distance (119909
119888 dist) where 119909 has rank 1 (or2 3 ) if it belongs to the 1st (2nd 3rd ) optimal front andthe crowding distance is the summation of distances between119909 and two adjacent individuals in every evaluation of objec-tives (please refer to [5] for the details of crowding distancecalculation) A partial order ≺
119899
is defined between two indi-viduals 119909 and 119910 in
In (6) between two individuals or solutionswith differingnondomination ranks we prefer the solution with the lower(better) rank Otherwise if both solutions belong to the samefront then we prefer the solution that is located in a lesscrowded region
The PRPSO algorithm runs generation by generation Ineach generation a front set 119865 = 119865
1
1198652
119865119903
is producedfrom both populations of the current and the previous
OF1
OF2
F3
F2F1
Figure 3 Illustration of a front set 119865 where 119865 = 1198651
1198652
1198653
Each point represents one feasible solution in one front in the 2-dimensional space 119865
1
(resp 1198653
) is best (resp worst) front and thesolutions in 119865
1
1198652
and 1198653
have the nondomination rank of 1 2 and3 respectively
generations where 1198651
1198652
119865119903
are the 1st 2nd 119903thoptimal fronts and 119903 is the maximum number of fronts to beaccommodate in a population of size 119873 (ie |119865
1
| + |1198652
| +
sdot sdot sdot |119865119903minus1
| lt 119873 and |1198651
|+ |1198652
|+ sdot sdot sdot |119865119903minus1
| ge 119873) As shown in theexample in Figure 3 there are three fronts (119865
1
1198652
and 1198653
)produced on the two dimensional space where the twodimensions correspond to the two objective functions OF1and OF2 Front 119865
1
is the set of solutions that are not domin-ated by any others Each solution in front 119865
119894
is not dominatedby any solution in front 119865
119895
for all 119895 gt 119894 ge 1 The optimizationgoals in the PRPSO problem are to maximize the OF1 (ieprofit P defined in (3)) and OF2 (ie satisfactionU definedin (4)) so an optimal front is the farthest from the originpoint
Since the populations are generated from the parents withthe best finesses of the previous generation the goodness ofpopulationswill be improved after some generations In addi-tion the diversity of solutions is kept by the crowding distanceso that the solutionswidely spread In this way when the algo-rithm terminates the returned optimal front 119865
1
will be veryclose to the real Pareto front
The pseudocode of the PRPSO algorithm is shown inAlgorithm 1 Initially the generation counter 119905 is 0 and thepopulation119875
119905
is randomly generated where amember in119875119905
isan individual (or a solution) consisting of the price variablewhich is a vector formultiple service cases An offspring pop-ulation 119876
119905
is set as empty initiallyAs illustrated inAlgorithm 1 in step S1 we set119867
119905
to be theunion of119875
119905
and119876119905
The step S1 is also illustrated in Figure 4 Instep S2 the algorithm evokes the Nondominated Fronts Sort(119867119905
PU) subroutine to sort solutions according to their non-domination ranks to have a front set 119865 = 119865
1
1198652
119865119903
The step S3 is to set the population 119875
119905+1
to be empty andset the counter 119894 to be 1 before the algorithm enters the loop instep S4 The step S4 is to insert the nondominated solutionsinto119875
119905+1
The step S5 is to generate a sorted119865119894
by the crowdingdistance in the descending order The step S6 is to insert themost widely spread (119873 minus |119875
119905+1
|) solutions using the crowdingdistance values in the sorted front 119865
119894
into the 119875119905+1
The step S7 is to create new offspring population 119876
S4 While (1003816100381610038161003816119875119894+11003816100381610038161003816 +
10038161003816100381610038161198651198941003816100381610038161003816 lt 119873) Do 119875
119905+1
= 119875119905+1
cup 119865119894
119894 + +
S5 Crowding Distance Sort(119865119894
)
S6 Insert the first (119873 minus1003816100381610038161003816119875119905+1
1003816100381610038161003816) elements in the sorted 119865119894
into 119875119905+1
S7 119876119905+1
larr GenerateNewPouluation(119875119905+1
)
S8 If (119905 ltMAX GEN)Then 119905 = 119905 + 1Goto S1 Else Return the Pareto front 1198651
Algorithm 1 Pricing resources with profit and satisfaction optimization (PRPSO) algorithm
Crowding distance sort
F1
F2
F1
F2
Ht =
Nondominated fronts sort
F3
middot middot middot
F 9984003
Nso
lutio
ns
Pt
Qt
Pt cup Qt
Figure 4 Procedures of generating new population119875119905+1
from119875119905
and119876119905
where 119875119905
is the parent population and119876119905
is the child population
size of119876119905+1
is119873 In step S8 the algorithm checks whether themaximum generation is reached If the generation counter 119905is less than the maximum value (MAX GEN) then 119905 is in-creased by 1 and then the algorithm goes to step S1 otherwisethe algorithm terminates
4 Evaluation
In this section we evaluate the effectiveness of proposed algo-rithm The simulation is conducted by the simulator devel-oped on Matlab [15] The simulation of the proposed algo-rithm is conducted with following setting in Table 1
The parameters used in the simulation are listed as fol-lows The initial population is created using a uniform ran-dom distributionThe population size is 15 sdot |119883| where |119883| isthe number of prices each of which corresponds to a serviceThe price is a real number whose range is from 1 to 2 We setthe Pareto fraction as 035 whichmeans the algorithmwill tryto limit the number of individuals in the current population
Table 1 Parameter setting
Parameter ValuesNumber of prices (services) |119883| where |119883| is 3 5 17Initial population Uniform random distributionPopulation size 15 sdot |119883|
Range of price variable (119883) (1 2)Pareto fraction 035StallGenLimit 100Toleratethreshold 1 times 10minus6
MAX GEN 200 sdot |119883|
that are on the Pareto front to 35 percent of the populationsize
In the simulation two conditions are used to determinewhether to stop the algorithm execution In Condition-1 thealgorithm stops when the maximum number of generations(MAX GEN) is reached where theMAX GEN is 200 sdot |119883| InCondition-2 the algorithm stops if the average change in thespread of the Pareto front over the ldquoStallGenLimitrdquo genera-tions is less than the tolerable threshold (TolerateThresold)The algorithm stops when either of the conditions is satisfied
41 Evaluation of Tradeoff Relationship of Two ConflictingObjectives We first simulate the proposed algorithm in thebasic setting which is to decide price variables for three ser-vices for the evaluation of tradeoff relationship of twoconflicting objectives The simulation results are shown inFigure 5 whereObjective 1 is operatorrsquos profit andObjective 2is subscribersrsquo satisfaction per unit of paid price Several frontpoints are plotted in Figure 5 which form the Pareto front ofthe multiobjective optimization theory Each point has twovalues which are the operatorrsquos profit and the subscriberrsquos sat-isfaction As shown in Figure 5 the lower profit implies thehigher satisfaction while the higher profit implies the lowersatisfaction In summary it is impossible to increase the profitand satisfaction at the same time and thus there is tradeoff
The Scientific World Journal 7
0 20 40 60 80 100 1200
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
Figure 5 Results of pricing under two conflicting objectives whereObjective 1 is the operatorrsquos profit and Objective 2 is subscribersrsquosatisfaction
between the two objectives the operatorrsquos profits and sub-scribersrsquo satisfaction
42 Evaluation of Impacts of Raising Prices of Two ConflictingObjectives In this section we study the effectiveness of rais-ing prices of the services We add into (2) an additional vari-able for controlling price raising factor 120575 to have (7) wherethe price raising factor 120575 is 1 12 2
119875 = sum119904isinΩ
119876119904
(120575 sdot 119875119904
) minus sum119894isin119861
119861119894
119862119894
(7)
As shown in Figure 6 the maximum values of profit(Objective 1) of Pareto fronts move to the right if the priceraising factor 120575 is increased It reflects the effectiveness of rais-ing prices to increase the profit
The solutions found by the proposed algorithm are stablesince the results do not fluctuate along the curves as shownin Figure 6 Moreover the effect of raising prices can be easilyobserved in the results For example the maximal profit oforiginal curve (120575 = 1) is 108 and the maximal profit ofadjusted curve (120575 = 2) is 214 as shown in the Figure 6There-fore the maximum profit is almost doubled meaning theeffect of raising price is obvious
43 Evaluation of Impacts of Raising Prices of Two ConflictingObjectives We study in this section the effect of changing ofthemedian value (120573) of the satisfaction of servicesWe set themedian value (120573) as 2 4 12 in order to analyze the corres-ponding results As shown in Figure 7 if 120573 is increased sat-isfaction is decreased This is because a subscriber starts tofeel satisfied only after a lot of resources are allocated to himher for the cases of higher 120573 values
The results show that the difference of satisfactions for dif-ferent subscriber types is obvious by the results found bythe PRPSO algorithm Moreover the characteristics of rela-tionship of operator profit and subscriber satisfaction can be
0 50 100 150 200 2500
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
120575 = 1
120575 = 18
120575 = 2
120575 = 16120575 = 14120575 = 12
Figure 6 Evaluation of the effect of raising prices by adjusting theprice raising factor 120575
0 20 40 60 80 100 1200
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
120573 = 2
120573 = 12
120573 = 4
120573 = 6
120573 = 8120573 = 10
Figure 7 Evaluation of the effect of changing sensitivity of satisfac-tion on services
easily observed based on the results For example in the 120573 =
12 case the satisfaction is almost the same even if the profitreaches the maximum value
44 Evaluation of Efficiency of Finding Pareto Fronts Fourthwe evaluate the qualitymetrics of forming the Praetor front indifferent number of decision variablesThequalitymetrics are(1) the average distance of Pareto front and (2) number ofpoints of Pareto front In general a smaller average distanceindicates that the solutions on the Pareto front are evenly dis-tributedThe average distance is the crowding distance whichis the perimeter of the cuboid formed by using the nearestneighbors as the vertices in the Pareto front please refer tothe paper [5] for more detailsThe number of points of Paretofront indicates the tractability of the Pareto front for a deci-sionmakerWhen the number of points or solutions of Pareto
8 The Scientific World Journal
0
0005
001
0015
002
0025
003
0
50
100
150
200
250
300
350
3 5 7 9 11 13 15 17Number of decision variables
Average of distance
Num
ber p
oint
s of P
aret
o
Number of points of Pareto front
Aver
age o
f dist
ance
Figure 8 Evaluation of the Pareto front in terms of (1) the numberof points of Pareto front and (2) the average of distance where theright-side 119910-axis is the average distance of the Pareto front the left-side 119910-axis is the number of points of the Pareto front and the 119909-axisis the number of decision variables which is the number of prices (orservices)
front are too large then the solutions may be intractable for adecision maker
As shown in Figure 8 the number of points of the Paretofront is increased but the average distance is decreased whenthe number of decision variables is increased It implies thatmore points are included in the Pareto front when the num-ber of decision variables is larger Selecting a pricing solutionfrom a larger set is more intractable for a decision maker fac-ing higher numbers of price variables Hence the decisionmaker needs to carefully make decisions when they face ahigher number of price variables
5 Conclusions
The operators invest huge funds for acquiring the spectrumresources in the LTE network The operator profit and thesubscriber satisfaction are two most important factors Thusit is necessary to consider the operator profit factor and sub-scriber satisfaction factor for pricing resources in the LTEnetworks Howevermost of existing studies only consider theproblem about maximizing operator profitThis paper inves-tigates the pricing resources with profit and satisfaction opti-mization (PRPSO) problem in the LTE network to simulta-neously maximize the operator profit and subscriber satisfac-tion This paper contributes a theoretical framework to helpdecision makers in pricing resources based on the heuristicoptimization algorithmmdashPRPSO algorithm Compared withthe algorithm only solving a single pricing optimization goalthe PRPSO algorithm solves the optimal problem with theconsideration of two important goals which is more helpfulfor making decisions in pricing
The PROSO algorithm has been verified and tested by thesimulations on the basis of convergence and diversity perfor-mance metrics to guarantee the quality of optimal solutionsfound The simulation results show that the difference of sat-isfactions for different subscriber types is obvious Moreover
the characteristics of relationship of the operator profit andthe subscriber satisfaction can also be easily observed basedon the results
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this article
References
[1] F Beltran J AGutierrez and J LMelus ldquoTechnology andmar-ket conditions toward a new competitive landscape in the wire-less access marketrdquo IEEE Communications Magazine vol 48no 6 pp 46ndash52 2010
[2] D Astely E Dahlman A Furuskar Y Jading M Lindstromand S Parkvall ldquoLTE the evolution ofmobile broadbandrdquo IEEECommunications Magazine vol 47 no 4 pp 44ndash51 2009
[3] P Bhat S Nagata L Campoy et al ldquoLTE-advanced an operatorperspectiverdquo IEEE CommunicationsMagazine vol 50 no 2 pp104ndash114 2012
[4] K Coussement and D Van den Poel ldquoChurn prediction in sub-scription services an application of support vector machineswhile comparing two parameter-selection techniquesrdquo ExpertSystems with Applications vol 34 no 1 pp 313ndash327 2008
[5] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast andelitist multiobjective genetic algorithm NSGA-IIrdquo IEEE Trans-actions on Evolutionary Computation vol 6 no 2 pp 182ndash1972002
[6] C-J Huang Y-T Chuang and D-X Yang ldquoImplementation ofcall admission control scheme in next generation mobile com-munication networks using particle swarm optimization andfuzzy logic systemsrdquo Expert Systems with Applications vol 35no 3 pp 1246ndash1251 2008
[7] C-J Huang H-Y Shen and Y-T Chuang ldquoAn adaptive band-width reservation scheme for 4G cellular networks using flex-ible 2-tier cell structurerdquo Expert Systems with Applications vol37 no 9 pp 6414ndash6420 2010
[8] S Dixit S Periyalwar and H Yanikomeroglu ldquoSecondary useraccess in LTE architecture based on a base station centric frame-work with dynamic pricingrdquo IEEE Transactions on VehicularTechnology vol 62 no 1 pp 284ndash296
[9] H Ekstrom ldquoQoS control in the 3GPP evolved packet systemrdquoIEEE Communications Magazine vol 47 no 2 pp 76ndash83 2009
[10] A Ghosh R Ratasuk B Mondal N Mangalvedhe and TThomas ldquoLTE-advanced next-generation wireless broadbandtechnologyrdquo IEEE Wireless Communications vol 17 no 3 pp10ndash22 2010
[11] B Sadiq R Madan and A Sampath ldquoDownlink scheduling formulticlass traffic in LTErdquo Eurasip Journal on Wireless Commu-nications and Networking vol 2009 Article ID 510617 18 pages2009
[13] H Lin M Chatterjee S K Das and K Basu ldquoARC an inte-grated admission and rate control framework for CDMA datanetworks based on non-cooperative gamesrdquo in Proceedings ofthe 9th Annual International Conference on Mobile Computingand Networking (MobiCom rsquo03) pp 326ndash338 ACM September2003
The Scientific World Journal 9
[14] D E Goldberg and J H Holland ldquoGenetic algorithms andmachine learningrdquoMachine Learning vol 3 no 2-3 pp 95ndash991988
allocating spectrum resources for subscribers and are theunits for providing enough quality of services in the LTEnetwork
Due to the hardness of solving this problem we develop aheuristic genetic optimization algorithm called the PRPSOalgorithm to find the solution based on the nondominatedsorting genetic algorithm (NSGA-II) in [5] For an analyst ofpricing resources in LTE networks the solutions found by thePRPSO algorithm are useful for analyzing the subscribersrsquosatisfaction and the operatorrsquos profit based on subscribersrsquosatisfaction models and costs for acquiring spectrum Theoptimal solutions found by the PRPSO algorithm are thePareto fronts in the multiobjective decision theory ThePareto fronts are a set of choices that are nondominated byother choices which are helpful formaking tradeoff decisionsto achieve two conflicting objectives subscribersrsquo satisfactionand operatorrsquos profits in LTE networks
Some optimization studies are proposed for resourcepricing resource reservation and load balancing in LTE net-worksHuang et al in [6] proposed an adaptive call admissioncontrol and resource (or bandwidth) reservation schemeusing fuzzy logic control and particle swarm optimization(PSO) for 4G networks Huang et al in [7] proposed a re-source (or bandwidth) reservation mechanism for neighbor-ing 4G cells based on grey prediction theory and swarm intel-ligence Dixit et al in [8] studied the dynamic pricing pro-blem on maximizing operator revenue in LTE networksHowever the problem of reserving and pricing LTE wirelessresources tomaximize both the operator profit and subscribersatisfaction is not fully studied
The rest of this paper is organized as follows In Section 2the PRPSO problem is formulated The proposed heuristicgenetic PRPSO algorithm to solve the problem is introducedand evaluated in Sections 3 and 4 respectively And finallysome concluding remarks are drawn in Section 5
2 Modeling and Problem Formulation
In this section we introduce the resource allocation modelthe user satisfaction model and the PRPSO problem in LTEnetworks
21 Resource AllocationModel in LTENetworks TheLTEnet-work uses an IP-based network architecture to provide voiceand data services Based on the architecture the operator candesign and sell the products by combining different QoS ser-vices The LTE air interface uses orthogonal frequency divi-sion multiplexing (OFDM) with advanced antenna tech-niques to transmit voice and data simultaneously [2] Thescheduler in the base station (called eNodeB or eNB) is resp-onsible for dynamically scheduling the LTE air interface inboth the downlink and uplink directions for subscribersrsquo userequipment (UE) As shown in Figure 1(a) much UE accessesan eNB at the same time and the eNB needs to provide dif-ferential services for the UEs
The LTE standard provides a diversity of classes of QoSservices [9] A traffic class or a QoS class is defined accordingto the restrictions and the limitations of the radio interface
Based on the traffic sensitivity to the packet delay four classesare defined the conversational streaming interactive andbackground classes The conversational class is meant for thetraffic that has a high sensitivity to delay (eg VoIP) while thebackground class deals with the traffic that has a low sen-sitivity to delay (eg background downloading files or send-ing emails) The streaming class is real time based and canpreserve time relation (variation) between information enti-ties of streams (say video streams)The interactive class is besteffort based and follows a request-response pattern in appli-cations such as web browsing
In LTE networks a set of resource blocks is allocated to asubscriber [10] to provide the services The more resourceblocks are allocated to the subscriber the better experience ofservice is and thus the satisfaction is increased As shown inFigure 1(b) the downlink (eNB to UE) and uplink (UE toeNB) in the air interface are divided into a number of 15 kHzsubchannels in the frequency domain and a number of 05mstime slots in the time domain The resource block (RB) is themain unit used to schedule transmissions over the air inter-face (refer to Figure 1(b)) An RB contains 12 contiguous sub-channels and 7 symbols (duration is 05ms) In general anumber of RBs are allocated to an UE according to its qualityof service (QoS) [11] Statistically the more the resourceblocks are allocated to the UE of a subscriber the more thesubscriber is satisfied with the service In Figure 1(b) thenumber of allocated resource blocks of User 1 is higher thanthat of User 2 which implies that the satisfaction of theUser 2is higher than User 1
The resource block based model is more accurate in ana-lysing the channel resources used in the LTE network since itconsiders not only the cost of transmitting data but also theoverhead cost (such as retransmissions when packets are cor-rupted) It is notable that most of studies on pricing are basedon the received usage based model to charge subscribersbased on the amount of received packets which do not in-clude the overhead cost
22 User Satisfaction Model An operator allocates or res-erves resources to subscribers to provide them with differen-tial QoS levels The satisfaction of subscribers is important tothe operatorWithout sufficient resources allocated to the ser-vices subscribers will feel dissatisfied For example the ac-ceptable one-way (speakerrsquos mouth to listenerrsquos ear) delay ofvoice communication forVoIP applications recommended byITU [12] is at most 150msThe subscriber of VoIP service willfeel dissatisfied if transmission delay is more than 150ms dueto the insufficiency of allocated resources Dissatisfied sub-scribers may unsubscribe some services which will damagethe operatorrsquos profits They may unsubscribe all services andmigrate to another operator causing the ldquouser churnrdquo prob-lem reported in [4]
Lin et al in [13] proposed a method to approximate thesubscriberrsquos satisfaction with the allocated resources by a sig-moid function In this paper we also adopt the sigmoid func-tion to model the user satisfaction The sigmoid function isuseful for modeling natural processes or system learning cur-ves since it can represent a history dependent progression
The Scientific World Journal 3
LTE based station (eNodeB)
User equipment UE1
User equipment UE2
User equipment UE3
(a)
7 symbols (duration is 05 ms)
12 subcarriers
Resource blocks for User1
Resource blocks for User2
Frequency domain
Spectrum
Resource blocks
Time domain
(b)
Figure 1 Illustration of services controlled and resources allocated by an LTE based station (eNodeB) in the LTE network (a) UE withdifferential QoS requirements of services and (b) resource blocks allocated for a UE by a eNodeB in the frequency domain and time domain
approaching a limit It depends on a random variable 119909 to re-present the occupation of resources for the subscriber Thesigmoid function is formulated as follows
Ψ (119909) =1
(1 + 119890minus120572(119909minus120573)) (1)
where 120572 and 120573 are the steepness and the middle of the curverespectively
Figure 2 plots curves of the sigmoid functions where 120572
stands for the sensitivity and120573 is themedian value of the satis-faction curve As shown in Figure 2(a) the curve is withhigher steepness as 120572 is higher As shown in Figure 2(b) thestarting point of the curve is farther away from zero as 120573 ishigher
In subscriberrsquos point of view the value of 120572 indicates thesubscriberrsquos sensitivity to the degradation of service while 120573
indicates the acceptable level for the service It is remarkablethat 120573 decides when the satisfaction starts to increase and 120572
decides how fast the satisfaction increases
23 The Pricing Resources with Profit and Satisfaction Opti-mization (PRPSO) Problem We formulate the pricing re-sources with profit and satisfaction optimization (PRPSO)problem in this subsectionThemain goals of the problem are(1) to maximize the operatorrsquos profit and (2) to maximize theusersrsquo satisfactionThe formulation is based on a fixed periodof time 119879 say 1 day 1 month 2 months 1 year and so on
The first goal is to maximize the operatorrsquos profit Equa-tion (2) is used to formulate the operatorrsquos profit 119875 whichconsists of two factors revenue from subscribers (RS) andcost of spectrum (CS) Below we explain the meaning of (2)and describe some assumptions and notations used in it
We assume an operator has a set of spectrum segments(notated byΦ) For segment 119894 isin Φ 119861
119894
represents the quantityof units occupied in segment 119894 and 119862
119894
represents the cost perunit of segment 119894 Thus the operator pays CS = sum
119894isinΦ
119861119894
119862119894
foracquiring the spectrums for period 119879 We also assume theoperator sells a set of services (notated by Ω) to subscribersBy statistics or by predictions the operator totally allocates119876
119904
4 The Scientific World Journal
05
055
06
065
07
075
08
085
09
095
1
0 25 5 75 10
Sigm
oid
func
tion
x
120572 = 02
120572 = 04
120572 = 06
120572 = 08
(a) Curves of the sigmoid function with 120573 = 0 and different 120572
05
055
06
065
07
075
08
085
09
095
1
0 25 5 75 10
Sigm
oid
func
tion
x
120573 = 0
120573 = 2120573 = 4120573 = 6
(b) Curves of the sigmoid function with 120572 = 1 and different 120573
Figure 2 Curves of the sigmoid functions
resource blocks for each service 119904 isin Ω over period 119879 There-fore if the subscribers pay the price119875
119904
for each resource blockallocated to service 119904 for period 119879 the operator has revenueRS = sum
119904isinΩ
119876119904
119875119904
from the subscribers For example assume aservice 119878119886 is averagely allocated 100 resource blocks per dayand the price of each resource block allocated to service 119878119886 is12 dollar It means 119876
119904119886
is 100 resource blocks and 119875119904119886
is 12dollar per day thus the revenue is 120 dollar per day for ser-vice 119878119886 Consider
119875 = RS minus CS = sum119904isinΩ
119876119904
119875119904
minus sum119894isinΦ
119861119894
119862119894
(2)
119875119904
denotes the price per resource block allocated to ser-vice 119904 In reality 119875
119904
is a bounded price variable and 119875119904
isin
[119875min 119875max] as shown in
119875min le 119875119904
le 119875max (3)
The second goal is to maximize the subscribersrsquo satisfac-tion Equation (4) is used to formulate the satisfaction perpaid price 119880 In (4) 120595
119904
(119876119904
) is used to formulate the satisfac-tion for service 119904 it is a sigmoid function of119876
119904
the number ofresource blocks allocated to service 119904 Note that 119876
119904
119875119904
is theprice a subscriber pays for using service 119904 Therefore120595119904
(119876119904
)119876119904
119875119904
is the satisfaction per unit of paid price for ser-vice 119904119880 is hence the overall subscribersrsquo satisfaction per unitof paid price
119880 = sum119904isinΩ
120595119904
(119876119904
)
119876119904
119875119904
(4)
Given 119876119904
119861119894
119862119894
and 120595119904
(119876119904
) forall 119894 isin Φ 119904 isin Ω the PRPSOproblem is to find a price set PS formaximizing both the oper-atorrsquos profit and subscribersrsquo satisfaction defined as
Maximize 119875
Maximize 119880(5)
Now we discuss some issues of estimating parameters inthe PRPSO problemThe PRPSO problem is an optimizationproblem to decide prices based on given information Thequantity119876
119904
of resource blocks allocated to service 119904 is possiblyestimated from historic usage of resource blocks allocated toservice 119904 over the fixed period of time 119879 The per-unit cost 119862
119894
of spectrum segment 119894 is also possibly estimated as the averagecost of acquiring and managing spectrum over the timeperiod119879When the solutions of PRSP problem are found theoutput prices are also on the basis of time period119879 For exam-ple if 119876
119904
and 119862119894
are estimated over the period of one monththe prices are on the basis of onemonth It is also notable thatthe parameters 120572 and 120573 of 120595
119904
can be adjusted according tosubscribersrsquo experiences to shape the sigmoid function prop-erly
3 The Pricing Resources withProfit and Satisfaction Optimization(PRPSO) Algorithm
In this section we present our multiobjective pricing algo-rithm called the PRPSO algorithm to solve the pricing re-sources with profit and satisfaction optimization (PRPSO)problemThe proposed PRPSO algorithm is based on an evo-lutionary genetic algorithm (GA) approach which is used toheuristically find the solutions of optimization problemsTheGA approach is to mimic natural selection in the biology
The Scientific World Journal 5
where individuals with higher fitness can survive to next gen-eration [14]
In the GA approach the population (a set of individualsor solutions) is randomly generated in the initial step Thenthe population evolves in the generation loop for MAX GENtimes In each generation fundamental operations such asselection crossover and mutation are used to generate indi-viduals into the next generationWhen the generation loop isterminated the solution is made by decoding the best indi-viduals in the decode step
Based on the above steps and based on the nondominatedsorting genetic algorithm II (NSGA-II) algorithm in [5] wedesign the PRPSO algorithm for finding good solutions to thePRPSO problem The basic idea of the NSGA-II algorithm isto find from the solutions of the current and the next gen-erations the optimal front (called Pareto front) which is theset of nondominated feasible solutions (or front points) thatare not dominated by any others It is noted that a solution 119909
is said to dominate another solution119910 if and only if119909 is betterthan 119910 in at least one evaluation of objectives and 119909 is notworse than 119910 in all evaluations of objectives
119873 solutions in the Pareto front are selected to evolve asthe population is assumed to be of size119873 for each generationIf the first-found optimal front (or call the first optimal front)has less than 119873 front points then the second optimal frontshould also be found The second optimal front is the setof nondominated feasible solutions over all populationmem-bers except for those in the first optimal front If the first andthe second optimal fronts totally have less than 119873 membersthen the third optimal front should be found further and soon Not all the front points in the last-found optimal front areselectedThey are in practice selected according to the fitness(ie the nondomination) and the spread of solutions so thatthe optimal front found in the final generationwill have betterconvergence near the true Pareto front It is noted that thenotion of crowding distance is used for evaluating the degreeof spread of solutions
Nowwe introduce how to evaluate an individual of a pop-ulation in the proposed algorithm Each individual (say 119909)in the population has two attributes (1) nondomination 119909rankand (2) crowding distance (119909
119888 dist) where 119909 has rank 1 (or2 3 ) if it belongs to the 1st (2nd 3rd ) optimal front andthe crowding distance is the summation of distances between119909 and two adjacent individuals in every evaluation of objec-tives (please refer to [5] for the details of crowding distancecalculation) A partial order ≺
119899
is defined between two indi-viduals 119909 and 119910 in
In (6) between two individuals or solutionswith differingnondomination ranks we prefer the solution with the lower(better) rank Otherwise if both solutions belong to the samefront then we prefer the solution that is located in a lesscrowded region
The PRPSO algorithm runs generation by generation Ineach generation a front set 119865 = 119865
1
1198652
119865119903
is producedfrom both populations of the current and the previous
OF1
OF2
F3
F2F1
Figure 3 Illustration of a front set 119865 where 119865 = 1198651
1198652
1198653
Each point represents one feasible solution in one front in the 2-dimensional space 119865
1
(resp 1198653
) is best (resp worst) front and thesolutions in 119865
1
1198652
and 1198653
have the nondomination rank of 1 2 and3 respectively
generations where 1198651
1198652
119865119903
are the 1st 2nd 119903thoptimal fronts and 119903 is the maximum number of fronts to beaccommodate in a population of size 119873 (ie |119865
1
| + |1198652
| +
sdot sdot sdot |119865119903minus1
| lt 119873 and |1198651
|+ |1198652
|+ sdot sdot sdot |119865119903minus1
| ge 119873) As shown in theexample in Figure 3 there are three fronts (119865
1
1198652
and 1198653
)produced on the two dimensional space where the twodimensions correspond to the two objective functions OF1and OF2 Front 119865
1
is the set of solutions that are not domin-ated by any others Each solution in front 119865
119894
is not dominatedby any solution in front 119865
119895
for all 119895 gt 119894 ge 1 The optimizationgoals in the PRPSO problem are to maximize the OF1 (ieprofit P defined in (3)) and OF2 (ie satisfactionU definedin (4)) so an optimal front is the farthest from the originpoint
Since the populations are generated from the parents withthe best finesses of the previous generation the goodness ofpopulationswill be improved after some generations In addi-tion the diversity of solutions is kept by the crowding distanceso that the solutionswidely spread In this way when the algo-rithm terminates the returned optimal front 119865
1
will be veryclose to the real Pareto front
The pseudocode of the PRPSO algorithm is shown inAlgorithm 1 Initially the generation counter 119905 is 0 and thepopulation119875
119905
is randomly generated where amember in119875119905
isan individual (or a solution) consisting of the price variablewhich is a vector formultiple service cases An offspring pop-ulation 119876
119905
is set as empty initiallyAs illustrated inAlgorithm 1 in step S1 we set119867
119905
to be theunion of119875
119905
and119876119905
The step S1 is also illustrated in Figure 4 Instep S2 the algorithm evokes the Nondominated Fronts Sort(119867119905
PU) subroutine to sort solutions according to their non-domination ranks to have a front set 119865 = 119865
1
1198652
119865119903
The step S3 is to set the population 119875
119905+1
to be empty andset the counter 119894 to be 1 before the algorithm enters the loop instep S4 The step S4 is to insert the nondominated solutionsinto119875
119905+1
The step S5 is to generate a sorted119865119894
by the crowdingdistance in the descending order The step S6 is to insert themost widely spread (119873 minus |119875
119905+1
|) solutions using the crowdingdistance values in the sorted front 119865
119894
into the 119875119905+1
The step S7 is to create new offspring population 119876
S4 While (1003816100381610038161003816119875119894+11003816100381610038161003816 +
10038161003816100381610038161198651198941003816100381610038161003816 lt 119873) Do 119875
119905+1
= 119875119905+1
cup 119865119894
119894 + +
S5 Crowding Distance Sort(119865119894
)
S6 Insert the first (119873 minus1003816100381610038161003816119875119905+1
1003816100381610038161003816) elements in the sorted 119865119894
into 119875119905+1
S7 119876119905+1
larr GenerateNewPouluation(119875119905+1
)
S8 If (119905 ltMAX GEN)Then 119905 = 119905 + 1Goto S1 Else Return the Pareto front 1198651
Algorithm 1 Pricing resources with profit and satisfaction optimization (PRPSO) algorithm
Crowding distance sort
F1
F2
F1
F2
Ht =
Nondominated fronts sort
F3
middot middot middot
F 9984003
Nso
lutio
ns
Pt
Qt
Pt cup Qt
Figure 4 Procedures of generating new population119875119905+1
from119875119905
and119876119905
where 119875119905
is the parent population and119876119905
is the child population
size of119876119905+1
is119873 In step S8 the algorithm checks whether themaximum generation is reached If the generation counter 119905is less than the maximum value (MAX GEN) then 119905 is in-creased by 1 and then the algorithm goes to step S1 otherwisethe algorithm terminates
4 Evaluation
In this section we evaluate the effectiveness of proposed algo-rithm The simulation is conducted by the simulator devel-oped on Matlab [15] The simulation of the proposed algo-rithm is conducted with following setting in Table 1
The parameters used in the simulation are listed as fol-lows The initial population is created using a uniform ran-dom distributionThe population size is 15 sdot |119883| where |119883| isthe number of prices each of which corresponds to a serviceThe price is a real number whose range is from 1 to 2 We setthe Pareto fraction as 035 whichmeans the algorithmwill tryto limit the number of individuals in the current population
Table 1 Parameter setting
Parameter ValuesNumber of prices (services) |119883| where |119883| is 3 5 17Initial population Uniform random distributionPopulation size 15 sdot |119883|
Range of price variable (119883) (1 2)Pareto fraction 035StallGenLimit 100Toleratethreshold 1 times 10minus6
MAX GEN 200 sdot |119883|
that are on the Pareto front to 35 percent of the populationsize
In the simulation two conditions are used to determinewhether to stop the algorithm execution In Condition-1 thealgorithm stops when the maximum number of generations(MAX GEN) is reached where theMAX GEN is 200 sdot |119883| InCondition-2 the algorithm stops if the average change in thespread of the Pareto front over the ldquoStallGenLimitrdquo genera-tions is less than the tolerable threshold (TolerateThresold)The algorithm stops when either of the conditions is satisfied
41 Evaluation of Tradeoff Relationship of Two ConflictingObjectives We first simulate the proposed algorithm in thebasic setting which is to decide price variables for three ser-vices for the evaluation of tradeoff relationship of twoconflicting objectives The simulation results are shown inFigure 5 whereObjective 1 is operatorrsquos profit andObjective 2is subscribersrsquo satisfaction per unit of paid price Several frontpoints are plotted in Figure 5 which form the Pareto front ofthe multiobjective optimization theory Each point has twovalues which are the operatorrsquos profit and the subscriberrsquos sat-isfaction As shown in Figure 5 the lower profit implies thehigher satisfaction while the higher profit implies the lowersatisfaction In summary it is impossible to increase the profitand satisfaction at the same time and thus there is tradeoff
The Scientific World Journal 7
0 20 40 60 80 100 1200
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
Figure 5 Results of pricing under two conflicting objectives whereObjective 1 is the operatorrsquos profit and Objective 2 is subscribersrsquosatisfaction
between the two objectives the operatorrsquos profits and sub-scribersrsquo satisfaction
42 Evaluation of Impacts of Raising Prices of Two ConflictingObjectives In this section we study the effectiveness of rais-ing prices of the services We add into (2) an additional vari-able for controlling price raising factor 120575 to have (7) wherethe price raising factor 120575 is 1 12 2
119875 = sum119904isinΩ
119876119904
(120575 sdot 119875119904
) minus sum119894isin119861
119861119894
119862119894
(7)
As shown in Figure 6 the maximum values of profit(Objective 1) of Pareto fronts move to the right if the priceraising factor 120575 is increased It reflects the effectiveness of rais-ing prices to increase the profit
The solutions found by the proposed algorithm are stablesince the results do not fluctuate along the curves as shownin Figure 6 Moreover the effect of raising prices can be easilyobserved in the results For example the maximal profit oforiginal curve (120575 = 1) is 108 and the maximal profit ofadjusted curve (120575 = 2) is 214 as shown in the Figure 6There-fore the maximum profit is almost doubled meaning theeffect of raising price is obvious
43 Evaluation of Impacts of Raising Prices of Two ConflictingObjectives We study in this section the effect of changing ofthemedian value (120573) of the satisfaction of servicesWe set themedian value (120573) as 2 4 12 in order to analyze the corres-ponding results As shown in Figure 7 if 120573 is increased sat-isfaction is decreased This is because a subscriber starts tofeel satisfied only after a lot of resources are allocated to himher for the cases of higher 120573 values
The results show that the difference of satisfactions for dif-ferent subscriber types is obvious by the results found bythe PRPSO algorithm Moreover the characteristics of rela-tionship of operator profit and subscriber satisfaction can be
0 50 100 150 200 2500
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
120575 = 1
120575 = 18
120575 = 2
120575 = 16120575 = 14120575 = 12
Figure 6 Evaluation of the effect of raising prices by adjusting theprice raising factor 120575
0 20 40 60 80 100 1200
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
120573 = 2
120573 = 12
120573 = 4
120573 = 6
120573 = 8120573 = 10
Figure 7 Evaluation of the effect of changing sensitivity of satisfac-tion on services
easily observed based on the results For example in the 120573 =
12 case the satisfaction is almost the same even if the profitreaches the maximum value
44 Evaluation of Efficiency of Finding Pareto Fronts Fourthwe evaluate the qualitymetrics of forming the Praetor front indifferent number of decision variablesThequalitymetrics are(1) the average distance of Pareto front and (2) number ofpoints of Pareto front In general a smaller average distanceindicates that the solutions on the Pareto front are evenly dis-tributedThe average distance is the crowding distance whichis the perimeter of the cuboid formed by using the nearestneighbors as the vertices in the Pareto front please refer tothe paper [5] for more detailsThe number of points of Paretofront indicates the tractability of the Pareto front for a deci-sionmakerWhen the number of points or solutions of Pareto
8 The Scientific World Journal
0
0005
001
0015
002
0025
003
0
50
100
150
200
250
300
350
3 5 7 9 11 13 15 17Number of decision variables
Average of distance
Num
ber p
oint
s of P
aret
o
Number of points of Pareto front
Aver
age o
f dist
ance
Figure 8 Evaluation of the Pareto front in terms of (1) the numberof points of Pareto front and (2) the average of distance where theright-side 119910-axis is the average distance of the Pareto front the left-side 119910-axis is the number of points of the Pareto front and the 119909-axisis the number of decision variables which is the number of prices (orservices)
front are too large then the solutions may be intractable for adecision maker
As shown in Figure 8 the number of points of the Paretofront is increased but the average distance is decreased whenthe number of decision variables is increased It implies thatmore points are included in the Pareto front when the num-ber of decision variables is larger Selecting a pricing solutionfrom a larger set is more intractable for a decision maker fac-ing higher numbers of price variables Hence the decisionmaker needs to carefully make decisions when they face ahigher number of price variables
5 Conclusions
The operators invest huge funds for acquiring the spectrumresources in the LTE network The operator profit and thesubscriber satisfaction are two most important factors Thusit is necessary to consider the operator profit factor and sub-scriber satisfaction factor for pricing resources in the LTEnetworks Howevermost of existing studies only consider theproblem about maximizing operator profitThis paper inves-tigates the pricing resources with profit and satisfaction opti-mization (PRPSO) problem in the LTE network to simulta-neously maximize the operator profit and subscriber satisfac-tion This paper contributes a theoretical framework to helpdecision makers in pricing resources based on the heuristicoptimization algorithmmdashPRPSO algorithm Compared withthe algorithm only solving a single pricing optimization goalthe PRPSO algorithm solves the optimal problem with theconsideration of two important goals which is more helpfulfor making decisions in pricing
The PROSO algorithm has been verified and tested by thesimulations on the basis of convergence and diversity perfor-mance metrics to guarantee the quality of optimal solutionsfound The simulation results show that the difference of sat-isfactions for different subscriber types is obvious Moreover
the characteristics of relationship of the operator profit andthe subscriber satisfaction can also be easily observed basedon the results
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this article
References
[1] F Beltran J AGutierrez and J LMelus ldquoTechnology andmar-ket conditions toward a new competitive landscape in the wire-less access marketrdquo IEEE Communications Magazine vol 48no 6 pp 46ndash52 2010
[2] D Astely E Dahlman A Furuskar Y Jading M Lindstromand S Parkvall ldquoLTE the evolution ofmobile broadbandrdquo IEEECommunications Magazine vol 47 no 4 pp 44ndash51 2009
[3] P Bhat S Nagata L Campoy et al ldquoLTE-advanced an operatorperspectiverdquo IEEE CommunicationsMagazine vol 50 no 2 pp104ndash114 2012
[4] K Coussement and D Van den Poel ldquoChurn prediction in sub-scription services an application of support vector machineswhile comparing two parameter-selection techniquesrdquo ExpertSystems with Applications vol 34 no 1 pp 313ndash327 2008
[5] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast andelitist multiobjective genetic algorithm NSGA-IIrdquo IEEE Trans-actions on Evolutionary Computation vol 6 no 2 pp 182ndash1972002
[6] C-J Huang Y-T Chuang and D-X Yang ldquoImplementation ofcall admission control scheme in next generation mobile com-munication networks using particle swarm optimization andfuzzy logic systemsrdquo Expert Systems with Applications vol 35no 3 pp 1246ndash1251 2008
[7] C-J Huang H-Y Shen and Y-T Chuang ldquoAn adaptive band-width reservation scheme for 4G cellular networks using flex-ible 2-tier cell structurerdquo Expert Systems with Applications vol37 no 9 pp 6414ndash6420 2010
[8] S Dixit S Periyalwar and H Yanikomeroglu ldquoSecondary useraccess in LTE architecture based on a base station centric frame-work with dynamic pricingrdquo IEEE Transactions on VehicularTechnology vol 62 no 1 pp 284ndash296
[9] H Ekstrom ldquoQoS control in the 3GPP evolved packet systemrdquoIEEE Communications Magazine vol 47 no 2 pp 76ndash83 2009
[10] A Ghosh R Ratasuk B Mondal N Mangalvedhe and TThomas ldquoLTE-advanced next-generation wireless broadbandtechnologyrdquo IEEE Wireless Communications vol 17 no 3 pp10ndash22 2010
[11] B Sadiq R Madan and A Sampath ldquoDownlink scheduling formulticlass traffic in LTErdquo Eurasip Journal on Wireless Commu-nications and Networking vol 2009 Article ID 510617 18 pages2009
[13] H Lin M Chatterjee S K Das and K Basu ldquoARC an inte-grated admission and rate control framework for CDMA datanetworks based on non-cooperative gamesrdquo in Proceedings ofthe 9th Annual International Conference on Mobile Computingand Networking (MobiCom rsquo03) pp 326ndash338 ACM September2003
The Scientific World Journal 9
[14] D E Goldberg and J H Holland ldquoGenetic algorithms andmachine learningrdquoMachine Learning vol 3 no 2-3 pp 95ndash991988
Figure 1 Illustration of services controlled and resources allocated by an LTE based station (eNodeB) in the LTE network (a) UE withdifferential QoS requirements of services and (b) resource blocks allocated for a UE by a eNodeB in the frequency domain and time domain
approaching a limit It depends on a random variable 119909 to re-present the occupation of resources for the subscriber Thesigmoid function is formulated as follows
Ψ (119909) =1
(1 + 119890minus120572(119909minus120573)) (1)
where 120572 and 120573 are the steepness and the middle of the curverespectively
Figure 2 plots curves of the sigmoid functions where 120572
stands for the sensitivity and120573 is themedian value of the satis-faction curve As shown in Figure 2(a) the curve is withhigher steepness as 120572 is higher As shown in Figure 2(b) thestarting point of the curve is farther away from zero as 120573 ishigher
In subscriberrsquos point of view the value of 120572 indicates thesubscriberrsquos sensitivity to the degradation of service while 120573
indicates the acceptable level for the service It is remarkablethat 120573 decides when the satisfaction starts to increase and 120572
decides how fast the satisfaction increases
23 The Pricing Resources with Profit and Satisfaction Opti-mization (PRPSO) Problem We formulate the pricing re-sources with profit and satisfaction optimization (PRPSO)problem in this subsectionThemain goals of the problem are(1) to maximize the operatorrsquos profit and (2) to maximize theusersrsquo satisfactionThe formulation is based on a fixed periodof time 119879 say 1 day 1 month 2 months 1 year and so on
The first goal is to maximize the operatorrsquos profit Equa-tion (2) is used to formulate the operatorrsquos profit 119875 whichconsists of two factors revenue from subscribers (RS) andcost of spectrum (CS) Below we explain the meaning of (2)and describe some assumptions and notations used in it
We assume an operator has a set of spectrum segments(notated byΦ) For segment 119894 isin Φ 119861
119894
represents the quantityof units occupied in segment 119894 and 119862
119894
represents the cost perunit of segment 119894 Thus the operator pays CS = sum
119894isinΦ
119861119894
119862119894
foracquiring the spectrums for period 119879 We also assume theoperator sells a set of services (notated by Ω) to subscribersBy statistics or by predictions the operator totally allocates119876
119904
4 The Scientific World Journal
05
055
06
065
07
075
08
085
09
095
1
0 25 5 75 10
Sigm
oid
func
tion
x
120572 = 02
120572 = 04
120572 = 06
120572 = 08
(a) Curves of the sigmoid function with 120573 = 0 and different 120572
05
055
06
065
07
075
08
085
09
095
1
0 25 5 75 10
Sigm
oid
func
tion
x
120573 = 0
120573 = 2120573 = 4120573 = 6
(b) Curves of the sigmoid function with 120572 = 1 and different 120573
Figure 2 Curves of the sigmoid functions
resource blocks for each service 119904 isin Ω over period 119879 There-fore if the subscribers pay the price119875
119904
for each resource blockallocated to service 119904 for period 119879 the operator has revenueRS = sum
119904isinΩ
119876119904
119875119904
from the subscribers For example assume aservice 119878119886 is averagely allocated 100 resource blocks per dayand the price of each resource block allocated to service 119878119886 is12 dollar It means 119876
119904119886
is 100 resource blocks and 119875119904119886
is 12dollar per day thus the revenue is 120 dollar per day for ser-vice 119878119886 Consider
119875 = RS minus CS = sum119904isinΩ
119876119904
119875119904
minus sum119894isinΦ
119861119894
119862119894
(2)
119875119904
denotes the price per resource block allocated to ser-vice 119904 In reality 119875
119904
is a bounded price variable and 119875119904
isin
[119875min 119875max] as shown in
119875min le 119875119904
le 119875max (3)
The second goal is to maximize the subscribersrsquo satisfac-tion Equation (4) is used to formulate the satisfaction perpaid price 119880 In (4) 120595
119904
(119876119904
) is used to formulate the satisfac-tion for service 119904 it is a sigmoid function of119876
119904
the number ofresource blocks allocated to service 119904 Note that 119876
119904
119875119904
is theprice a subscriber pays for using service 119904 Therefore120595119904
(119876119904
)119876119904
119875119904
is the satisfaction per unit of paid price for ser-vice 119904119880 is hence the overall subscribersrsquo satisfaction per unitof paid price
119880 = sum119904isinΩ
120595119904
(119876119904
)
119876119904
119875119904
(4)
Given 119876119904
119861119894
119862119894
and 120595119904
(119876119904
) forall 119894 isin Φ 119904 isin Ω the PRPSOproblem is to find a price set PS formaximizing both the oper-atorrsquos profit and subscribersrsquo satisfaction defined as
Maximize 119875
Maximize 119880(5)
Now we discuss some issues of estimating parameters inthe PRPSO problemThe PRPSO problem is an optimizationproblem to decide prices based on given information Thequantity119876
119904
of resource blocks allocated to service 119904 is possiblyestimated from historic usage of resource blocks allocated toservice 119904 over the fixed period of time 119879 The per-unit cost 119862
119894
of spectrum segment 119894 is also possibly estimated as the averagecost of acquiring and managing spectrum over the timeperiod119879When the solutions of PRSP problem are found theoutput prices are also on the basis of time period119879 For exam-ple if 119876
119904
and 119862119894
are estimated over the period of one monththe prices are on the basis of onemonth It is also notable thatthe parameters 120572 and 120573 of 120595
119904
can be adjusted according tosubscribersrsquo experiences to shape the sigmoid function prop-erly
3 The Pricing Resources withProfit and Satisfaction Optimization(PRPSO) Algorithm
In this section we present our multiobjective pricing algo-rithm called the PRPSO algorithm to solve the pricing re-sources with profit and satisfaction optimization (PRPSO)problemThe proposed PRPSO algorithm is based on an evo-lutionary genetic algorithm (GA) approach which is used toheuristically find the solutions of optimization problemsTheGA approach is to mimic natural selection in the biology
The Scientific World Journal 5
where individuals with higher fitness can survive to next gen-eration [14]
In the GA approach the population (a set of individualsor solutions) is randomly generated in the initial step Thenthe population evolves in the generation loop for MAX GENtimes In each generation fundamental operations such asselection crossover and mutation are used to generate indi-viduals into the next generationWhen the generation loop isterminated the solution is made by decoding the best indi-viduals in the decode step
Based on the above steps and based on the nondominatedsorting genetic algorithm II (NSGA-II) algorithm in [5] wedesign the PRPSO algorithm for finding good solutions to thePRPSO problem The basic idea of the NSGA-II algorithm isto find from the solutions of the current and the next gen-erations the optimal front (called Pareto front) which is theset of nondominated feasible solutions (or front points) thatare not dominated by any others It is noted that a solution 119909
is said to dominate another solution119910 if and only if119909 is betterthan 119910 in at least one evaluation of objectives and 119909 is notworse than 119910 in all evaluations of objectives
119873 solutions in the Pareto front are selected to evolve asthe population is assumed to be of size119873 for each generationIf the first-found optimal front (or call the first optimal front)has less than 119873 front points then the second optimal frontshould also be found The second optimal front is the setof nondominated feasible solutions over all populationmem-bers except for those in the first optimal front If the first andthe second optimal fronts totally have less than 119873 membersthen the third optimal front should be found further and soon Not all the front points in the last-found optimal front areselectedThey are in practice selected according to the fitness(ie the nondomination) and the spread of solutions so thatthe optimal front found in the final generationwill have betterconvergence near the true Pareto front It is noted that thenotion of crowding distance is used for evaluating the degreeof spread of solutions
Nowwe introduce how to evaluate an individual of a pop-ulation in the proposed algorithm Each individual (say 119909)in the population has two attributes (1) nondomination 119909rankand (2) crowding distance (119909
119888 dist) where 119909 has rank 1 (or2 3 ) if it belongs to the 1st (2nd 3rd ) optimal front andthe crowding distance is the summation of distances between119909 and two adjacent individuals in every evaluation of objec-tives (please refer to [5] for the details of crowding distancecalculation) A partial order ≺
119899
is defined between two indi-viduals 119909 and 119910 in
In (6) between two individuals or solutionswith differingnondomination ranks we prefer the solution with the lower(better) rank Otherwise if both solutions belong to the samefront then we prefer the solution that is located in a lesscrowded region
The PRPSO algorithm runs generation by generation Ineach generation a front set 119865 = 119865
1
1198652
119865119903
is producedfrom both populations of the current and the previous
OF1
OF2
F3
F2F1
Figure 3 Illustration of a front set 119865 where 119865 = 1198651
1198652
1198653
Each point represents one feasible solution in one front in the 2-dimensional space 119865
1
(resp 1198653
) is best (resp worst) front and thesolutions in 119865
1
1198652
and 1198653
have the nondomination rank of 1 2 and3 respectively
generations where 1198651
1198652
119865119903
are the 1st 2nd 119903thoptimal fronts and 119903 is the maximum number of fronts to beaccommodate in a population of size 119873 (ie |119865
1
| + |1198652
| +
sdot sdot sdot |119865119903minus1
| lt 119873 and |1198651
|+ |1198652
|+ sdot sdot sdot |119865119903minus1
| ge 119873) As shown in theexample in Figure 3 there are three fronts (119865
1
1198652
and 1198653
)produced on the two dimensional space where the twodimensions correspond to the two objective functions OF1and OF2 Front 119865
1
is the set of solutions that are not domin-ated by any others Each solution in front 119865
119894
is not dominatedby any solution in front 119865
119895
for all 119895 gt 119894 ge 1 The optimizationgoals in the PRPSO problem are to maximize the OF1 (ieprofit P defined in (3)) and OF2 (ie satisfactionU definedin (4)) so an optimal front is the farthest from the originpoint
Since the populations are generated from the parents withthe best finesses of the previous generation the goodness ofpopulationswill be improved after some generations In addi-tion the diversity of solutions is kept by the crowding distanceso that the solutionswidely spread In this way when the algo-rithm terminates the returned optimal front 119865
1
will be veryclose to the real Pareto front
The pseudocode of the PRPSO algorithm is shown inAlgorithm 1 Initially the generation counter 119905 is 0 and thepopulation119875
119905
is randomly generated where amember in119875119905
isan individual (or a solution) consisting of the price variablewhich is a vector formultiple service cases An offspring pop-ulation 119876
119905
is set as empty initiallyAs illustrated inAlgorithm 1 in step S1 we set119867
119905
to be theunion of119875
119905
and119876119905
The step S1 is also illustrated in Figure 4 Instep S2 the algorithm evokes the Nondominated Fronts Sort(119867119905
PU) subroutine to sort solutions according to their non-domination ranks to have a front set 119865 = 119865
1
1198652
119865119903
The step S3 is to set the population 119875
119905+1
to be empty andset the counter 119894 to be 1 before the algorithm enters the loop instep S4 The step S4 is to insert the nondominated solutionsinto119875
119905+1
The step S5 is to generate a sorted119865119894
by the crowdingdistance in the descending order The step S6 is to insert themost widely spread (119873 minus |119875
119905+1
|) solutions using the crowdingdistance values in the sorted front 119865
119894
into the 119875119905+1
The step S7 is to create new offspring population 119876
S4 While (1003816100381610038161003816119875119894+11003816100381610038161003816 +
10038161003816100381610038161198651198941003816100381610038161003816 lt 119873) Do 119875
119905+1
= 119875119905+1
cup 119865119894
119894 + +
S5 Crowding Distance Sort(119865119894
)
S6 Insert the first (119873 minus1003816100381610038161003816119875119905+1
1003816100381610038161003816) elements in the sorted 119865119894
into 119875119905+1
S7 119876119905+1
larr GenerateNewPouluation(119875119905+1
)
S8 If (119905 ltMAX GEN)Then 119905 = 119905 + 1Goto S1 Else Return the Pareto front 1198651
Algorithm 1 Pricing resources with profit and satisfaction optimization (PRPSO) algorithm
Crowding distance sort
F1
F2
F1
F2
Ht =
Nondominated fronts sort
F3
middot middot middot
F 9984003
Nso
lutio
ns
Pt
Qt
Pt cup Qt
Figure 4 Procedures of generating new population119875119905+1
from119875119905
and119876119905
where 119875119905
is the parent population and119876119905
is the child population
size of119876119905+1
is119873 In step S8 the algorithm checks whether themaximum generation is reached If the generation counter 119905is less than the maximum value (MAX GEN) then 119905 is in-creased by 1 and then the algorithm goes to step S1 otherwisethe algorithm terminates
4 Evaluation
In this section we evaluate the effectiveness of proposed algo-rithm The simulation is conducted by the simulator devel-oped on Matlab [15] The simulation of the proposed algo-rithm is conducted with following setting in Table 1
The parameters used in the simulation are listed as fol-lows The initial population is created using a uniform ran-dom distributionThe population size is 15 sdot |119883| where |119883| isthe number of prices each of which corresponds to a serviceThe price is a real number whose range is from 1 to 2 We setthe Pareto fraction as 035 whichmeans the algorithmwill tryto limit the number of individuals in the current population
Table 1 Parameter setting
Parameter ValuesNumber of prices (services) |119883| where |119883| is 3 5 17Initial population Uniform random distributionPopulation size 15 sdot |119883|
Range of price variable (119883) (1 2)Pareto fraction 035StallGenLimit 100Toleratethreshold 1 times 10minus6
MAX GEN 200 sdot |119883|
that are on the Pareto front to 35 percent of the populationsize
In the simulation two conditions are used to determinewhether to stop the algorithm execution In Condition-1 thealgorithm stops when the maximum number of generations(MAX GEN) is reached where theMAX GEN is 200 sdot |119883| InCondition-2 the algorithm stops if the average change in thespread of the Pareto front over the ldquoStallGenLimitrdquo genera-tions is less than the tolerable threshold (TolerateThresold)The algorithm stops when either of the conditions is satisfied
41 Evaluation of Tradeoff Relationship of Two ConflictingObjectives We first simulate the proposed algorithm in thebasic setting which is to decide price variables for three ser-vices for the evaluation of tradeoff relationship of twoconflicting objectives The simulation results are shown inFigure 5 whereObjective 1 is operatorrsquos profit andObjective 2is subscribersrsquo satisfaction per unit of paid price Several frontpoints are plotted in Figure 5 which form the Pareto front ofthe multiobjective optimization theory Each point has twovalues which are the operatorrsquos profit and the subscriberrsquos sat-isfaction As shown in Figure 5 the lower profit implies thehigher satisfaction while the higher profit implies the lowersatisfaction In summary it is impossible to increase the profitand satisfaction at the same time and thus there is tradeoff
The Scientific World Journal 7
0 20 40 60 80 100 1200
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
Figure 5 Results of pricing under two conflicting objectives whereObjective 1 is the operatorrsquos profit and Objective 2 is subscribersrsquosatisfaction
between the two objectives the operatorrsquos profits and sub-scribersrsquo satisfaction
42 Evaluation of Impacts of Raising Prices of Two ConflictingObjectives In this section we study the effectiveness of rais-ing prices of the services We add into (2) an additional vari-able for controlling price raising factor 120575 to have (7) wherethe price raising factor 120575 is 1 12 2
119875 = sum119904isinΩ
119876119904
(120575 sdot 119875119904
) minus sum119894isin119861
119861119894
119862119894
(7)
As shown in Figure 6 the maximum values of profit(Objective 1) of Pareto fronts move to the right if the priceraising factor 120575 is increased It reflects the effectiveness of rais-ing prices to increase the profit
The solutions found by the proposed algorithm are stablesince the results do not fluctuate along the curves as shownin Figure 6 Moreover the effect of raising prices can be easilyobserved in the results For example the maximal profit oforiginal curve (120575 = 1) is 108 and the maximal profit ofadjusted curve (120575 = 2) is 214 as shown in the Figure 6There-fore the maximum profit is almost doubled meaning theeffect of raising price is obvious
43 Evaluation of Impacts of Raising Prices of Two ConflictingObjectives We study in this section the effect of changing ofthemedian value (120573) of the satisfaction of servicesWe set themedian value (120573) as 2 4 12 in order to analyze the corres-ponding results As shown in Figure 7 if 120573 is increased sat-isfaction is decreased This is because a subscriber starts tofeel satisfied only after a lot of resources are allocated to himher for the cases of higher 120573 values
The results show that the difference of satisfactions for dif-ferent subscriber types is obvious by the results found bythe PRPSO algorithm Moreover the characteristics of rela-tionship of operator profit and subscriber satisfaction can be
0 50 100 150 200 2500
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
120575 = 1
120575 = 18
120575 = 2
120575 = 16120575 = 14120575 = 12
Figure 6 Evaluation of the effect of raising prices by adjusting theprice raising factor 120575
0 20 40 60 80 100 1200
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
120573 = 2
120573 = 12
120573 = 4
120573 = 6
120573 = 8120573 = 10
Figure 7 Evaluation of the effect of changing sensitivity of satisfac-tion on services
easily observed based on the results For example in the 120573 =
12 case the satisfaction is almost the same even if the profitreaches the maximum value
44 Evaluation of Efficiency of Finding Pareto Fronts Fourthwe evaluate the qualitymetrics of forming the Praetor front indifferent number of decision variablesThequalitymetrics are(1) the average distance of Pareto front and (2) number ofpoints of Pareto front In general a smaller average distanceindicates that the solutions on the Pareto front are evenly dis-tributedThe average distance is the crowding distance whichis the perimeter of the cuboid formed by using the nearestneighbors as the vertices in the Pareto front please refer tothe paper [5] for more detailsThe number of points of Paretofront indicates the tractability of the Pareto front for a deci-sionmakerWhen the number of points or solutions of Pareto
8 The Scientific World Journal
0
0005
001
0015
002
0025
003
0
50
100
150
200
250
300
350
3 5 7 9 11 13 15 17Number of decision variables
Average of distance
Num
ber p
oint
s of P
aret
o
Number of points of Pareto front
Aver
age o
f dist
ance
Figure 8 Evaluation of the Pareto front in terms of (1) the numberof points of Pareto front and (2) the average of distance where theright-side 119910-axis is the average distance of the Pareto front the left-side 119910-axis is the number of points of the Pareto front and the 119909-axisis the number of decision variables which is the number of prices (orservices)
front are too large then the solutions may be intractable for adecision maker
As shown in Figure 8 the number of points of the Paretofront is increased but the average distance is decreased whenthe number of decision variables is increased It implies thatmore points are included in the Pareto front when the num-ber of decision variables is larger Selecting a pricing solutionfrom a larger set is more intractable for a decision maker fac-ing higher numbers of price variables Hence the decisionmaker needs to carefully make decisions when they face ahigher number of price variables
5 Conclusions
The operators invest huge funds for acquiring the spectrumresources in the LTE network The operator profit and thesubscriber satisfaction are two most important factors Thusit is necessary to consider the operator profit factor and sub-scriber satisfaction factor for pricing resources in the LTEnetworks Howevermost of existing studies only consider theproblem about maximizing operator profitThis paper inves-tigates the pricing resources with profit and satisfaction opti-mization (PRPSO) problem in the LTE network to simulta-neously maximize the operator profit and subscriber satisfac-tion This paper contributes a theoretical framework to helpdecision makers in pricing resources based on the heuristicoptimization algorithmmdashPRPSO algorithm Compared withthe algorithm only solving a single pricing optimization goalthe PRPSO algorithm solves the optimal problem with theconsideration of two important goals which is more helpfulfor making decisions in pricing
The PROSO algorithm has been verified and tested by thesimulations on the basis of convergence and diversity perfor-mance metrics to guarantee the quality of optimal solutionsfound The simulation results show that the difference of sat-isfactions for different subscriber types is obvious Moreover
the characteristics of relationship of the operator profit andthe subscriber satisfaction can also be easily observed basedon the results
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this article
References
[1] F Beltran J AGutierrez and J LMelus ldquoTechnology andmar-ket conditions toward a new competitive landscape in the wire-less access marketrdquo IEEE Communications Magazine vol 48no 6 pp 46ndash52 2010
[2] D Astely E Dahlman A Furuskar Y Jading M Lindstromand S Parkvall ldquoLTE the evolution ofmobile broadbandrdquo IEEECommunications Magazine vol 47 no 4 pp 44ndash51 2009
[3] P Bhat S Nagata L Campoy et al ldquoLTE-advanced an operatorperspectiverdquo IEEE CommunicationsMagazine vol 50 no 2 pp104ndash114 2012
[4] K Coussement and D Van den Poel ldquoChurn prediction in sub-scription services an application of support vector machineswhile comparing two parameter-selection techniquesrdquo ExpertSystems with Applications vol 34 no 1 pp 313ndash327 2008
[5] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast andelitist multiobjective genetic algorithm NSGA-IIrdquo IEEE Trans-actions on Evolutionary Computation vol 6 no 2 pp 182ndash1972002
[6] C-J Huang Y-T Chuang and D-X Yang ldquoImplementation ofcall admission control scheme in next generation mobile com-munication networks using particle swarm optimization andfuzzy logic systemsrdquo Expert Systems with Applications vol 35no 3 pp 1246ndash1251 2008
[7] C-J Huang H-Y Shen and Y-T Chuang ldquoAn adaptive band-width reservation scheme for 4G cellular networks using flex-ible 2-tier cell structurerdquo Expert Systems with Applications vol37 no 9 pp 6414ndash6420 2010
[8] S Dixit S Periyalwar and H Yanikomeroglu ldquoSecondary useraccess in LTE architecture based on a base station centric frame-work with dynamic pricingrdquo IEEE Transactions on VehicularTechnology vol 62 no 1 pp 284ndash296
[9] H Ekstrom ldquoQoS control in the 3GPP evolved packet systemrdquoIEEE Communications Magazine vol 47 no 2 pp 76ndash83 2009
[10] A Ghosh R Ratasuk B Mondal N Mangalvedhe and TThomas ldquoLTE-advanced next-generation wireless broadbandtechnologyrdquo IEEE Wireless Communications vol 17 no 3 pp10ndash22 2010
[11] B Sadiq R Madan and A Sampath ldquoDownlink scheduling formulticlass traffic in LTErdquo Eurasip Journal on Wireless Commu-nications and Networking vol 2009 Article ID 510617 18 pages2009
[13] H Lin M Chatterjee S K Das and K Basu ldquoARC an inte-grated admission and rate control framework for CDMA datanetworks based on non-cooperative gamesrdquo in Proceedings ofthe 9th Annual International Conference on Mobile Computingand Networking (MobiCom rsquo03) pp 326ndash338 ACM September2003
The Scientific World Journal 9
[14] D E Goldberg and J H Holland ldquoGenetic algorithms andmachine learningrdquoMachine Learning vol 3 no 2-3 pp 95ndash991988
(a) Curves of the sigmoid function with 120573 = 0 and different 120572
05
055
06
065
07
075
08
085
09
095
1
0 25 5 75 10
Sigm
oid
func
tion
x
120573 = 0
120573 = 2120573 = 4120573 = 6
(b) Curves of the sigmoid function with 120572 = 1 and different 120573
Figure 2 Curves of the sigmoid functions
resource blocks for each service 119904 isin Ω over period 119879 There-fore if the subscribers pay the price119875
119904
for each resource blockallocated to service 119904 for period 119879 the operator has revenueRS = sum
119904isinΩ
119876119904
119875119904
from the subscribers For example assume aservice 119878119886 is averagely allocated 100 resource blocks per dayand the price of each resource block allocated to service 119878119886 is12 dollar It means 119876
119904119886
is 100 resource blocks and 119875119904119886
is 12dollar per day thus the revenue is 120 dollar per day for ser-vice 119878119886 Consider
119875 = RS minus CS = sum119904isinΩ
119876119904
119875119904
minus sum119894isinΦ
119861119894
119862119894
(2)
119875119904
denotes the price per resource block allocated to ser-vice 119904 In reality 119875
119904
is a bounded price variable and 119875119904
isin
[119875min 119875max] as shown in
119875min le 119875119904
le 119875max (3)
The second goal is to maximize the subscribersrsquo satisfac-tion Equation (4) is used to formulate the satisfaction perpaid price 119880 In (4) 120595
119904
(119876119904
) is used to formulate the satisfac-tion for service 119904 it is a sigmoid function of119876
119904
the number ofresource blocks allocated to service 119904 Note that 119876
119904
119875119904
is theprice a subscriber pays for using service 119904 Therefore120595119904
(119876119904
)119876119904
119875119904
is the satisfaction per unit of paid price for ser-vice 119904119880 is hence the overall subscribersrsquo satisfaction per unitof paid price
119880 = sum119904isinΩ
120595119904
(119876119904
)
119876119904
119875119904
(4)
Given 119876119904
119861119894
119862119894
and 120595119904
(119876119904
) forall 119894 isin Φ 119904 isin Ω the PRPSOproblem is to find a price set PS formaximizing both the oper-atorrsquos profit and subscribersrsquo satisfaction defined as
Maximize 119875
Maximize 119880(5)
Now we discuss some issues of estimating parameters inthe PRPSO problemThe PRPSO problem is an optimizationproblem to decide prices based on given information Thequantity119876
119904
of resource blocks allocated to service 119904 is possiblyestimated from historic usage of resource blocks allocated toservice 119904 over the fixed period of time 119879 The per-unit cost 119862
119894
of spectrum segment 119894 is also possibly estimated as the averagecost of acquiring and managing spectrum over the timeperiod119879When the solutions of PRSP problem are found theoutput prices are also on the basis of time period119879 For exam-ple if 119876
119904
and 119862119894
are estimated over the period of one monththe prices are on the basis of onemonth It is also notable thatthe parameters 120572 and 120573 of 120595
119904
can be adjusted according tosubscribersrsquo experiences to shape the sigmoid function prop-erly
3 The Pricing Resources withProfit and Satisfaction Optimization(PRPSO) Algorithm
In this section we present our multiobjective pricing algo-rithm called the PRPSO algorithm to solve the pricing re-sources with profit and satisfaction optimization (PRPSO)problemThe proposed PRPSO algorithm is based on an evo-lutionary genetic algorithm (GA) approach which is used toheuristically find the solutions of optimization problemsTheGA approach is to mimic natural selection in the biology
The Scientific World Journal 5
where individuals with higher fitness can survive to next gen-eration [14]
In the GA approach the population (a set of individualsor solutions) is randomly generated in the initial step Thenthe population evolves in the generation loop for MAX GENtimes In each generation fundamental operations such asselection crossover and mutation are used to generate indi-viduals into the next generationWhen the generation loop isterminated the solution is made by decoding the best indi-viduals in the decode step
Based on the above steps and based on the nondominatedsorting genetic algorithm II (NSGA-II) algorithm in [5] wedesign the PRPSO algorithm for finding good solutions to thePRPSO problem The basic idea of the NSGA-II algorithm isto find from the solutions of the current and the next gen-erations the optimal front (called Pareto front) which is theset of nondominated feasible solutions (or front points) thatare not dominated by any others It is noted that a solution 119909
is said to dominate another solution119910 if and only if119909 is betterthan 119910 in at least one evaluation of objectives and 119909 is notworse than 119910 in all evaluations of objectives
119873 solutions in the Pareto front are selected to evolve asthe population is assumed to be of size119873 for each generationIf the first-found optimal front (or call the first optimal front)has less than 119873 front points then the second optimal frontshould also be found The second optimal front is the setof nondominated feasible solutions over all populationmem-bers except for those in the first optimal front If the first andthe second optimal fronts totally have less than 119873 membersthen the third optimal front should be found further and soon Not all the front points in the last-found optimal front areselectedThey are in practice selected according to the fitness(ie the nondomination) and the spread of solutions so thatthe optimal front found in the final generationwill have betterconvergence near the true Pareto front It is noted that thenotion of crowding distance is used for evaluating the degreeof spread of solutions
Nowwe introduce how to evaluate an individual of a pop-ulation in the proposed algorithm Each individual (say 119909)in the population has two attributes (1) nondomination 119909rankand (2) crowding distance (119909
119888 dist) where 119909 has rank 1 (or2 3 ) if it belongs to the 1st (2nd 3rd ) optimal front andthe crowding distance is the summation of distances between119909 and two adjacent individuals in every evaluation of objec-tives (please refer to [5] for the details of crowding distancecalculation) A partial order ≺
119899
is defined between two indi-viduals 119909 and 119910 in
In (6) between two individuals or solutionswith differingnondomination ranks we prefer the solution with the lower(better) rank Otherwise if both solutions belong to the samefront then we prefer the solution that is located in a lesscrowded region
The PRPSO algorithm runs generation by generation Ineach generation a front set 119865 = 119865
1
1198652
119865119903
is producedfrom both populations of the current and the previous
OF1
OF2
F3
F2F1
Figure 3 Illustration of a front set 119865 where 119865 = 1198651
1198652
1198653
Each point represents one feasible solution in one front in the 2-dimensional space 119865
1
(resp 1198653
) is best (resp worst) front and thesolutions in 119865
1
1198652
and 1198653
have the nondomination rank of 1 2 and3 respectively
generations where 1198651
1198652
119865119903
are the 1st 2nd 119903thoptimal fronts and 119903 is the maximum number of fronts to beaccommodate in a population of size 119873 (ie |119865
1
| + |1198652
| +
sdot sdot sdot |119865119903minus1
| lt 119873 and |1198651
|+ |1198652
|+ sdot sdot sdot |119865119903minus1
| ge 119873) As shown in theexample in Figure 3 there are three fronts (119865
1
1198652
and 1198653
)produced on the two dimensional space where the twodimensions correspond to the two objective functions OF1and OF2 Front 119865
1
is the set of solutions that are not domin-ated by any others Each solution in front 119865
119894
is not dominatedby any solution in front 119865
119895
for all 119895 gt 119894 ge 1 The optimizationgoals in the PRPSO problem are to maximize the OF1 (ieprofit P defined in (3)) and OF2 (ie satisfactionU definedin (4)) so an optimal front is the farthest from the originpoint
Since the populations are generated from the parents withthe best finesses of the previous generation the goodness ofpopulationswill be improved after some generations In addi-tion the diversity of solutions is kept by the crowding distanceso that the solutionswidely spread In this way when the algo-rithm terminates the returned optimal front 119865
1
will be veryclose to the real Pareto front
The pseudocode of the PRPSO algorithm is shown inAlgorithm 1 Initially the generation counter 119905 is 0 and thepopulation119875
119905
is randomly generated where amember in119875119905
isan individual (or a solution) consisting of the price variablewhich is a vector formultiple service cases An offspring pop-ulation 119876
119905
is set as empty initiallyAs illustrated inAlgorithm 1 in step S1 we set119867
119905
to be theunion of119875
119905
and119876119905
The step S1 is also illustrated in Figure 4 Instep S2 the algorithm evokes the Nondominated Fronts Sort(119867119905
PU) subroutine to sort solutions according to their non-domination ranks to have a front set 119865 = 119865
1
1198652
119865119903
The step S3 is to set the population 119875
119905+1
to be empty andset the counter 119894 to be 1 before the algorithm enters the loop instep S4 The step S4 is to insert the nondominated solutionsinto119875
119905+1
The step S5 is to generate a sorted119865119894
by the crowdingdistance in the descending order The step S6 is to insert themost widely spread (119873 minus |119875
119905+1
|) solutions using the crowdingdistance values in the sorted front 119865
119894
into the 119875119905+1
The step S7 is to create new offspring population 119876
S4 While (1003816100381610038161003816119875119894+11003816100381610038161003816 +
10038161003816100381610038161198651198941003816100381610038161003816 lt 119873) Do 119875
119905+1
= 119875119905+1
cup 119865119894
119894 + +
S5 Crowding Distance Sort(119865119894
)
S6 Insert the first (119873 minus1003816100381610038161003816119875119905+1
1003816100381610038161003816) elements in the sorted 119865119894
into 119875119905+1
S7 119876119905+1
larr GenerateNewPouluation(119875119905+1
)
S8 If (119905 ltMAX GEN)Then 119905 = 119905 + 1Goto S1 Else Return the Pareto front 1198651
Algorithm 1 Pricing resources with profit and satisfaction optimization (PRPSO) algorithm
Crowding distance sort
F1
F2
F1
F2
Ht =
Nondominated fronts sort
F3
middot middot middot
F 9984003
Nso
lutio
ns
Pt
Qt
Pt cup Qt
Figure 4 Procedures of generating new population119875119905+1
from119875119905
and119876119905
where 119875119905
is the parent population and119876119905
is the child population
size of119876119905+1
is119873 In step S8 the algorithm checks whether themaximum generation is reached If the generation counter 119905is less than the maximum value (MAX GEN) then 119905 is in-creased by 1 and then the algorithm goes to step S1 otherwisethe algorithm terminates
4 Evaluation
In this section we evaluate the effectiveness of proposed algo-rithm The simulation is conducted by the simulator devel-oped on Matlab [15] The simulation of the proposed algo-rithm is conducted with following setting in Table 1
The parameters used in the simulation are listed as fol-lows The initial population is created using a uniform ran-dom distributionThe population size is 15 sdot |119883| where |119883| isthe number of prices each of which corresponds to a serviceThe price is a real number whose range is from 1 to 2 We setthe Pareto fraction as 035 whichmeans the algorithmwill tryto limit the number of individuals in the current population
Table 1 Parameter setting
Parameter ValuesNumber of prices (services) |119883| where |119883| is 3 5 17Initial population Uniform random distributionPopulation size 15 sdot |119883|
Range of price variable (119883) (1 2)Pareto fraction 035StallGenLimit 100Toleratethreshold 1 times 10minus6
MAX GEN 200 sdot |119883|
that are on the Pareto front to 35 percent of the populationsize
In the simulation two conditions are used to determinewhether to stop the algorithm execution In Condition-1 thealgorithm stops when the maximum number of generations(MAX GEN) is reached where theMAX GEN is 200 sdot |119883| InCondition-2 the algorithm stops if the average change in thespread of the Pareto front over the ldquoStallGenLimitrdquo genera-tions is less than the tolerable threshold (TolerateThresold)The algorithm stops when either of the conditions is satisfied
41 Evaluation of Tradeoff Relationship of Two ConflictingObjectives We first simulate the proposed algorithm in thebasic setting which is to decide price variables for three ser-vices for the evaluation of tradeoff relationship of twoconflicting objectives The simulation results are shown inFigure 5 whereObjective 1 is operatorrsquos profit andObjective 2is subscribersrsquo satisfaction per unit of paid price Several frontpoints are plotted in Figure 5 which form the Pareto front ofthe multiobjective optimization theory Each point has twovalues which are the operatorrsquos profit and the subscriberrsquos sat-isfaction As shown in Figure 5 the lower profit implies thehigher satisfaction while the higher profit implies the lowersatisfaction In summary it is impossible to increase the profitand satisfaction at the same time and thus there is tradeoff
The Scientific World Journal 7
0 20 40 60 80 100 1200
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
Figure 5 Results of pricing under two conflicting objectives whereObjective 1 is the operatorrsquos profit and Objective 2 is subscribersrsquosatisfaction
between the two objectives the operatorrsquos profits and sub-scribersrsquo satisfaction
42 Evaluation of Impacts of Raising Prices of Two ConflictingObjectives In this section we study the effectiveness of rais-ing prices of the services We add into (2) an additional vari-able for controlling price raising factor 120575 to have (7) wherethe price raising factor 120575 is 1 12 2
119875 = sum119904isinΩ
119876119904
(120575 sdot 119875119904
) minus sum119894isin119861
119861119894
119862119894
(7)
As shown in Figure 6 the maximum values of profit(Objective 1) of Pareto fronts move to the right if the priceraising factor 120575 is increased It reflects the effectiveness of rais-ing prices to increase the profit
The solutions found by the proposed algorithm are stablesince the results do not fluctuate along the curves as shownin Figure 6 Moreover the effect of raising prices can be easilyobserved in the results For example the maximal profit oforiginal curve (120575 = 1) is 108 and the maximal profit ofadjusted curve (120575 = 2) is 214 as shown in the Figure 6There-fore the maximum profit is almost doubled meaning theeffect of raising price is obvious
43 Evaluation of Impacts of Raising Prices of Two ConflictingObjectives We study in this section the effect of changing ofthemedian value (120573) of the satisfaction of servicesWe set themedian value (120573) as 2 4 12 in order to analyze the corres-ponding results As shown in Figure 7 if 120573 is increased sat-isfaction is decreased This is because a subscriber starts tofeel satisfied only after a lot of resources are allocated to himher for the cases of higher 120573 values
The results show that the difference of satisfactions for dif-ferent subscriber types is obvious by the results found bythe PRPSO algorithm Moreover the characteristics of rela-tionship of operator profit and subscriber satisfaction can be
0 50 100 150 200 2500
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
120575 = 1
120575 = 18
120575 = 2
120575 = 16120575 = 14120575 = 12
Figure 6 Evaluation of the effect of raising prices by adjusting theprice raising factor 120575
0 20 40 60 80 100 1200
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
120573 = 2
120573 = 12
120573 = 4
120573 = 6
120573 = 8120573 = 10
Figure 7 Evaluation of the effect of changing sensitivity of satisfac-tion on services
easily observed based on the results For example in the 120573 =
12 case the satisfaction is almost the same even if the profitreaches the maximum value
44 Evaluation of Efficiency of Finding Pareto Fronts Fourthwe evaluate the qualitymetrics of forming the Praetor front indifferent number of decision variablesThequalitymetrics are(1) the average distance of Pareto front and (2) number ofpoints of Pareto front In general a smaller average distanceindicates that the solutions on the Pareto front are evenly dis-tributedThe average distance is the crowding distance whichis the perimeter of the cuboid formed by using the nearestneighbors as the vertices in the Pareto front please refer tothe paper [5] for more detailsThe number of points of Paretofront indicates the tractability of the Pareto front for a deci-sionmakerWhen the number of points or solutions of Pareto
8 The Scientific World Journal
0
0005
001
0015
002
0025
003
0
50
100
150
200
250
300
350
3 5 7 9 11 13 15 17Number of decision variables
Average of distance
Num
ber p
oint
s of P
aret
o
Number of points of Pareto front
Aver
age o
f dist
ance
Figure 8 Evaluation of the Pareto front in terms of (1) the numberof points of Pareto front and (2) the average of distance where theright-side 119910-axis is the average distance of the Pareto front the left-side 119910-axis is the number of points of the Pareto front and the 119909-axisis the number of decision variables which is the number of prices (orservices)
front are too large then the solutions may be intractable for adecision maker
As shown in Figure 8 the number of points of the Paretofront is increased but the average distance is decreased whenthe number of decision variables is increased It implies thatmore points are included in the Pareto front when the num-ber of decision variables is larger Selecting a pricing solutionfrom a larger set is more intractable for a decision maker fac-ing higher numbers of price variables Hence the decisionmaker needs to carefully make decisions when they face ahigher number of price variables
5 Conclusions
The operators invest huge funds for acquiring the spectrumresources in the LTE network The operator profit and thesubscriber satisfaction are two most important factors Thusit is necessary to consider the operator profit factor and sub-scriber satisfaction factor for pricing resources in the LTEnetworks Howevermost of existing studies only consider theproblem about maximizing operator profitThis paper inves-tigates the pricing resources with profit and satisfaction opti-mization (PRPSO) problem in the LTE network to simulta-neously maximize the operator profit and subscriber satisfac-tion This paper contributes a theoretical framework to helpdecision makers in pricing resources based on the heuristicoptimization algorithmmdashPRPSO algorithm Compared withthe algorithm only solving a single pricing optimization goalthe PRPSO algorithm solves the optimal problem with theconsideration of two important goals which is more helpfulfor making decisions in pricing
The PROSO algorithm has been verified and tested by thesimulations on the basis of convergence and diversity perfor-mance metrics to guarantee the quality of optimal solutionsfound The simulation results show that the difference of sat-isfactions for different subscriber types is obvious Moreover
the characteristics of relationship of the operator profit andthe subscriber satisfaction can also be easily observed basedon the results
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this article
References
[1] F Beltran J AGutierrez and J LMelus ldquoTechnology andmar-ket conditions toward a new competitive landscape in the wire-less access marketrdquo IEEE Communications Magazine vol 48no 6 pp 46ndash52 2010
[2] D Astely E Dahlman A Furuskar Y Jading M Lindstromand S Parkvall ldquoLTE the evolution ofmobile broadbandrdquo IEEECommunications Magazine vol 47 no 4 pp 44ndash51 2009
[3] P Bhat S Nagata L Campoy et al ldquoLTE-advanced an operatorperspectiverdquo IEEE CommunicationsMagazine vol 50 no 2 pp104ndash114 2012
[4] K Coussement and D Van den Poel ldquoChurn prediction in sub-scription services an application of support vector machineswhile comparing two parameter-selection techniquesrdquo ExpertSystems with Applications vol 34 no 1 pp 313ndash327 2008
[5] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast andelitist multiobjective genetic algorithm NSGA-IIrdquo IEEE Trans-actions on Evolutionary Computation vol 6 no 2 pp 182ndash1972002
[6] C-J Huang Y-T Chuang and D-X Yang ldquoImplementation ofcall admission control scheme in next generation mobile com-munication networks using particle swarm optimization andfuzzy logic systemsrdquo Expert Systems with Applications vol 35no 3 pp 1246ndash1251 2008
[7] C-J Huang H-Y Shen and Y-T Chuang ldquoAn adaptive band-width reservation scheme for 4G cellular networks using flex-ible 2-tier cell structurerdquo Expert Systems with Applications vol37 no 9 pp 6414ndash6420 2010
[8] S Dixit S Periyalwar and H Yanikomeroglu ldquoSecondary useraccess in LTE architecture based on a base station centric frame-work with dynamic pricingrdquo IEEE Transactions on VehicularTechnology vol 62 no 1 pp 284ndash296
[9] H Ekstrom ldquoQoS control in the 3GPP evolved packet systemrdquoIEEE Communications Magazine vol 47 no 2 pp 76ndash83 2009
[10] A Ghosh R Ratasuk B Mondal N Mangalvedhe and TThomas ldquoLTE-advanced next-generation wireless broadbandtechnologyrdquo IEEE Wireless Communications vol 17 no 3 pp10ndash22 2010
[11] B Sadiq R Madan and A Sampath ldquoDownlink scheduling formulticlass traffic in LTErdquo Eurasip Journal on Wireless Commu-nications and Networking vol 2009 Article ID 510617 18 pages2009
[13] H Lin M Chatterjee S K Das and K Basu ldquoARC an inte-grated admission and rate control framework for CDMA datanetworks based on non-cooperative gamesrdquo in Proceedings ofthe 9th Annual International Conference on Mobile Computingand Networking (MobiCom rsquo03) pp 326ndash338 ACM September2003
The Scientific World Journal 9
[14] D E Goldberg and J H Holland ldquoGenetic algorithms andmachine learningrdquoMachine Learning vol 3 no 2-3 pp 95ndash991988
where individuals with higher fitness can survive to next gen-eration [14]
In the GA approach the population (a set of individualsor solutions) is randomly generated in the initial step Thenthe population evolves in the generation loop for MAX GENtimes In each generation fundamental operations such asselection crossover and mutation are used to generate indi-viduals into the next generationWhen the generation loop isterminated the solution is made by decoding the best indi-viduals in the decode step
Based on the above steps and based on the nondominatedsorting genetic algorithm II (NSGA-II) algorithm in [5] wedesign the PRPSO algorithm for finding good solutions to thePRPSO problem The basic idea of the NSGA-II algorithm isto find from the solutions of the current and the next gen-erations the optimal front (called Pareto front) which is theset of nondominated feasible solutions (or front points) thatare not dominated by any others It is noted that a solution 119909
is said to dominate another solution119910 if and only if119909 is betterthan 119910 in at least one evaluation of objectives and 119909 is notworse than 119910 in all evaluations of objectives
119873 solutions in the Pareto front are selected to evolve asthe population is assumed to be of size119873 for each generationIf the first-found optimal front (or call the first optimal front)has less than 119873 front points then the second optimal frontshould also be found The second optimal front is the setof nondominated feasible solutions over all populationmem-bers except for those in the first optimal front If the first andthe second optimal fronts totally have less than 119873 membersthen the third optimal front should be found further and soon Not all the front points in the last-found optimal front areselectedThey are in practice selected according to the fitness(ie the nondomination) and the spread of solutions so thatthe optimal front found in the final generationwill have betterconvergence near the true Pareto front It is noted that thenotion of crowding distance is used for evaluating the degreeof spread of solutions
Nowwe introduce how to evaluate an individual of a pop-ulation in the proposed algorithm Each individual (say 119909)in the population has two attributes (1) nondomination 119909rankand (2) crowding distance (119909
119888 dist) where 119909 has rank 1 (or2 3 ) if it belongs to the 1st (2nd 3rd ) optimal front andthe crowding distance is the summation of distances between119909 and two adjacent individuals in every evaluation of objec-tives (please refer to [5] for the details of crowding distancecalculation) A partial order ≺
119899
is defined between two indi-viduals 119909 and 119910 in
In (6) between two individuals or solutionswith differingnondomination ranks we prefer the solution with the lower(better) rank Otherwise if both solutions belong to the samefront then we prefer the solution that is located in a lesscrowded region
The PRPSO algorithm runs generation by generation Ineach generation a front set 119865 = 119865
1
1198652
119865119903
is producedfrom both populations of the current and the previous
OF1
OF2
F3
F2F1
Figure 3 Illustration of a front set 119865 where 119865 = 1198651
1198652
1198653
Each point represents one feasible solution in one front in the 2-dimensional space 119865
1
(resp 1198653
) is best (resp worst) front and thesolutions in 119865
1
1198652
and 1198653
have the nondomination rank of 1 2 and3 respectively
generations where 1198651
1198652
119865119903
are the 1st 2nd 119903thoptimal fronts and 119903 is the maximum number of fronts to beaccommodate in a population of size 119873 (ie |119865
1
| + |1198652
| +
sdot sdot sdot |119865119903minus1
| lt 119873 and |1198651
|+ |1198652
|+ sdot sdot sdot |119865119903minus1
| ge 119873) As shown in theexample in Figure 3 there are three fronts (119865
1
1198652
and 1198653
)produced on the two dimensional space where the twodimensions correspond to the two objective functions OF1and OF2 Front 119865
1
is the set of solutions that are not domin-ated by any others Each solution in front 119865
119894
is not dominatedby any solution in front 119865
119895
for all 119895 gt 119894 ge 1 The optimizationgoals in the PRPSO problem are to maximize the OF1 (ieprofit P defined in (3)) and OF2 (ie satisfactionU definedin (4)) so an optimal front is the farthest from the originpoint
Since the populations are generated from the parents withthe best finesses of the previous generation the goodness ofpopulationswill be improved after some generations In addi-tion the diversity of solutions is kept by the crowding distanceso that the solutionswidely spread In this way when the algo-rithm terminates the returned optimal front 119865
1
will be veryclose to the real Pareto front
The pseudocode of the PRPSO algorithm is shown inAlgorithm 1 Initially the generation counter 119905 is 0 and thepopulation119875
119905
is randomly generated where amember in119875119905
isan individual (or a solution) consisting of the price variablewhich is a vector formultiple service cases An offspring pop-ulation 119876
119905
is set as empty initiallyAs illustrated inAlgorithm 1 in step S1 we set119867
119905
to be theunion of119875
119905
and119876119905
The step S1 is also illustrated in Figure 4 Instep S2 the algorithm evokes the Nondominated Fronts Sort(119867119905
PU) subroutine to sort solutions according to their non-domination ranks to have a front set 119865 = 119865
1
1198652
119865119903
The step S3 is to set the population 119875
119905+1
to be empty andset the counter 119894 to be 1 before the algorithm enters the loop instep S4 The step S4 is to insert the nondominated solutionsinto119875
119905+1
The step S5 is to generate a sorted119865119894
by the crowdingdistance in the descending order The step S6 is to insert themost widely spread (119873 minus |119875
119905+1
|) solutions using the crowdingdistance values in the sorted front 119865
119894
into the 119875119905+1
The step S7 is to create new offspring population 119876
S4 While (1003816100381610038161003816119875119894+11003816100381610038161003816 +
10038161003816100381610038161198651198941003816100381610038161003816 lt 119873) Do 119875
119905+1
= 119875119905+1
cup 119865119894
119894 + +
S5 Crowding Distance Sort(119865119894
)
S6 Insert the first (119873 minus1003816100381610038161003816119875119905+1
1003816100381610038161003816) elements in the sorted 119865119894
into 119875119905+1
S7 119876119905+1
larr GenerateNewPouluation(119875119905+1
)
S8 If (119905 ltMAX GEN)Then 119905 = 119905 + 1Goto S1 Else Return the Pareto front 1198651
Algorithm 1 Pricing resources with profit and satisfaction optimization (PRPSO) algorithm
Crowding distance sort
F1
F2
F1
F2
Ht =
Nondominated fronts sort
F3
middot middot middot
F 9984003
Nso
lutio
ns
Pt
Qt
Pt cup Qt
Figure 4 Procedures of generating new population119875119905+1
from119875119905
and119876119905
where 119875119905
is the parent population and119876119905
is the child population
size of119876119905+1
is119873 In step S8 the algorithm checks whether themaximum generation is reached If the generation counter 119905is less than the maximum value (MAX GEN) then 119905 is in-creased by 1 and then the algorithm goes to step S1 otherwisethe algorithm terminates
4 Evaluation
In this section we evaluate the effectiveness of proposed algo-rithm The simulation is conducted by the simulator devel-oped on Matlab [15] The simulation of the proposed algo-rithm is conducted with following setting in Table 1
The parameters used in the simulation are listed as fol-lows The initial population is created using a uniform ran-dom distributionThe population size is 15 sdot |119883| where |119883| isthe number of prices each of which corresponds to a serviceThe price is a real number whose range is from 1 to 2 We setthe Pareto fraction as 035 whichmeans the algorithmwill tryto limit the number of individuals in the current population
Table 1 Parameter setting
Parameter ValuesNumber of prices (services) |119883| where |119883| is 3 5 17Initial population Uniform random distributionPopulation size 15 sdot |119883|
Range of price variable (119883) (1 2)Pareto fraction 035StallGenLimit 100Toleratethreshold 1 times 10minus6
MAX GEN 200 sdot |119883|
that are on the Pareto front to 35 percent of the populationsize
In the simulation two conditions are used to determinewhether to stop the algorithm execution In Condition-1 thealgorithm stops when the maximum number of generations(MAX GEN) is reached where theMAX GEN is 200 sdot |119883| InCondition-2 the algorithm stops if the average change in thespread of the Pareto front over the ldquoStallGenLimitrdquo genera-tions is less than the tolerable threshold (TolerateThresold)The algorithm stops when either of the conditions is satisfied
41 Evaluation of Tradeoff Relationship of Two ConflictingObjectives We first simulate the proposed algorithm in thebasic setting which is to decide price variables for three ser-vices for the evaluation of tradeoff relationship of twoconflicting objectives The simulation results are shown inFigure 5 whereObjective 1 is operatorrsquos profit andObjective 2is subscribersrsquo satisfaction per unit of paid price Several frontpoints are plotted in Figure 5 which form the Pareto front ofthe multiobjective optimization theory Each point has twovalues which are the operatorrsquos profit and the subscriberrsquos sat-isfaction As shown in Figure 5 the lower profit implies thehigher satisfaction while the higher profit implies the lowersatisfaction In summary it is impossible to increase the profitand satisfaction at the same time and thus there is tradeoff
The Scientific World Journal 7
0 20 40 60 80 100 1200
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
Figure 5 Results of pricing under two conflicting objectives whereObjective 1 is the operatorrsquos profit and Objective 2 is subscribersrsquosatisfaction
between the two objectives the operatorrsquos profits and sub-scribersrsquo satisfaction
42 Evaluation of Impacts of Raising Prices of Two ConflictingObjectives In this section we study the effectiveness of rais-ing prices of the services We add into (2) an additional vari-able for controlling price raising factor 120575 to have (7) wherethe price raising factor 120575 is 1 12 2
119875 = sum119904isinΩ
119876119904
(120575 sdot 119875119904
) minus sum119894isin119861
119861119894
119862119894
(7)
As shown in Figure 6 the maximum values of profit(Objective 1) of Pareto fronts move to the right if the priceraising factor 120575 is increased It reflects the effectiveness of rais-ing prices to increase the profit
The solutions found by the proposed algorithm are stablesince the results do not fluctuate along the curves as shownin Figure 6 Moreover the effect of raising prices can be easilyobserved in the results For example the maximal profit oforiginal curve (120575 = 1) is 108 and the maximal profit ofadjusted curve (120575 = 2) is 214 as shown in the Figure 6There-fore the maximum profit is almost doubled meaning theeffect of raising price is obvious
43 Evaluation of Impacts of Raising Prices of Two ConflictingObjectives We study in this section the effect of changing ofthemedian value (120573) of the satisfaction of servicesWe set themedian value (120573) as 2 4 12 in order to analyze the corres-ponding results As shown in Figure 7 if 120573 is increased sat-isfaction is decreased This is because a subscriber starts tofeel satisfied only after a lot of resources are allocated to himher for the cases of higher 120573 values
The results show that the difference of satisfactions for dif-ferent subscriber types is obvious by the results found bythe PRPSO algorithm Moreover the characteristics of rela-tionship of operator profit and subscriber satisfaction can be
0 50 100 150 200 2500
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
120575 = 1
120575 = 18
120575 = 2
120575 = 16120575 = 14120575 = 12
Figure 6 Evaluation of the effect of raising prices by adjusting theprice raising factor 120575
0 20 40 60 80 100 1200
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
120573 = 2
120573 = 12
120573 = 4
120573 = 6
120573 = 8120573 = 10
Figure 7 Evaluation of the effect of changing sensitivity of satisfac-tion on services
easily observed based on the results For example in the 120573 =
12 case the satisfaction is almost the same even if the profitreaches the maximum value
44 Evaluation of Efficiency of Finding Pareto Fronts Fourthwe evaluate the qualitymetrics of forming the Praetor front indifferent number of decision variablesThequalitymetrics are(1) the average distance of Pareto front and (2) number ofpoints of Pareto front In general a smaller average distanceindicates that the solutions on the Pareto front are evenly dis-tributedThe average distance is the crowding distance whichis the perimeter of the cuboid formed by using the nearestneighbors as the vertices in the Pareto front please refer tothe paper [5] for more detailsThe number of points of Paretofront indicates the tractability of the Pareto front for a deci-sionmakerWhen the number of points or solutions of Pareto
8 The Scientific World Journal
0
0005
001
0015
002
0025
003
0
50
100
150
200
250
300
350
3 5 7 9 11 13 15 17Number of decision variables
Average of distance
Num
ber p
oint
s of P
aret
o
Number of points of Pareto front
Aver
age o
f dist
ance
Figure 8 Evaluation of the Pareto front in terms of (1) the numberof points of Pareto front and (2) the average of distance where theright-side 119910-axis is the average distance of the Pareto front the left-side 119910-axis is the number of points of the Pareto front and the 119909-axisis the number of decision variables which is the number of prices (orservices)
front are too large then the solutions may be intractable for adecision maker
As shown in Figure 8 the number of points of the Paretofront is increased but the average distance is decreased whenthe number of decision variables is increased It implies thatmore points are included in the Pareto front when the num-ber of decision variables is larger Selecting a pricing solutionfrom a larger set is more intractable for a decision maker fac-ing higher numbers of price variables Hence the decisionmaker needs to carefully make decisions when they face ahigher number of price variables
5 Conclusions
The operators invest huge funds for acquiring the spectrumresources in the LTE network The operator profit and thesubscriber satisfaction are two most important factors Thusit is necessary to consider the operator profit factor and sub-scriber satisfaction factor for pricing resources in the LTEnetworks Howevermost of existing studies only consider theproblem about maximizing operator profitThis paper inves-tigates the pricing resources with profit and satisfaction opti-mization (PRPSO) problem in the LTE network to simulta-neously maximize the operator profit and subscriber satisfac-tion This paper contributes a theoretical framework to helpdecision makers in pricing resources based on the heuristicoptimization algorithmmdashPRPSO algorithm Compared withthe algorithm only solving a single pricing optimization goalthe PRPSO algorithm solves the optimal problem with theconsideration of two important goals which is more helpfulfor making decisions in pricing
The PROSO algorithm has been verified and tested by thesimulations on the basis of convergence and diversity perfor-mance metrics to guarantee the quality of optimal solutionsfound The simulation results show that the difference of sat-isfactions for different subscriber types is obvious Moreover
the characteristics of relationship of the operator profit andthe subscriber satisfaction can also be easily observed basedon the results
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this article
References
[1] F Beltran J AGutierrez and J LMelus ldquoTechnology andmar-ket conditions toward a new competitive landscape in the wire-less access marketrdquo IEEE Communications Magazine vol 48no 6 pp 46ndash52 2010
[2] D Astely E Dahlman A Furuskar Y Jading M Lindstromand S Parkvall ldquoLTE the evolution ofmobile broadbandrdquo IEEECommunications Magazine vol 47 no 4 pp 44ndash51 2009
[3] P Bhat S Nagata L Campoy et al ldquoLTE-advanced an operatorperspectiverdquo IEEE CommunicationsMagazine vol 50 no 2 pp104ndash114 2012
[4] K Coussement and D Van den Poel ldquoChurn prediction in sub-scription services an application of support vector machineswhile comparing two parameter-selection techniquesrdquo ExpertSystems with Applications vol 34 no 1 pp 313ndash327 2008
[5] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast andelitist multiobjective genetic algorithm NSGA-IIrdquo IEEE Trans-actions on Evolutionary Computation vol 6 no 2 pp 182ndash1972002
[6] C-J Huang Y-T Chuang and D-X Yang ldquoImplementation ofcall admission control scheme in next generation mobile com-munication networks using particle swarm optimization andfuzzy logic systemsrdquo Expert Systems with Applications vol 35no 3 pp 1246ndash1251 2008
[7] C-J Huang H-Y Shen and Y-T Chuang ldquoAn adaptive band-width reservation scheme for 4G cellular networks using flex-ible 2-tier cell structurerdquo Expert Systems with Applications vol37 no 9 pp 6414ndash6420 2010
[8] S Dixit S Periyalwar and H Yanikomeroglu ldquoSecondary useraccess in LTE architecture based on a base station centric frame-work with dynamic pricingrdquo IEEE Transactions on VehicularTechnology vol 62 no 1 pp 284ndash296
[9] H Ekstrom ldquoQoS control in the 3GPP evolved packet systemrdquoIEEE Communications Magazine vol 47 no 2 pp 76ndash83 2009
[10] A Ghosh R Ratasuk B Mondal N Mangalvedhe and TThomas ldquoLTE-advanced next-generation wireless broadbandtechnologyrdquo IEEE Wireless Communications vol 17 no 3 pp10ndash22 2010
[11] B Sadiq R Madan and A Sampath ldquoDownlink scheduling formulticlass traffic in LTErdquo Eurasip Journal on Wireless Commu-nications and Networking vol 2009 Article ID 510617 18 pages2009
[13] H Lin M Chatterjee S K Das and K Basu ldquoARC an inte-grated admission and rate control framework for CDMA datanetworks based on non-cooperative gamesrdquo in Proceedings ofthe 9th Annual International Conference on Mobile Computingand Networking (MobiCom rsquo03) pp 326ndash338 ACM September2003
The Scientific World Journal 9
[14] D E Goldberg and J H Holland ldquoGenetic algorithms andmachine learningrdquoMachine Learning vol 3 no 2-3 pp 95ndash991988
S4 While (1003816100381610038161003816119875119894+11003816100381610038161003816 +
10038161003816100381610038161198651198941003816100381610038161003816 lt 119873) Do 119875
119905+1
= 119875119905+1
cup 119865119894
119894 + +
S5 Crowding Distance Sort(119865119894
)
S6 Insert the first (119873 minus1003816100381610038161003816119875119905+1
1003816100381610038161003816) elements in the sorted 119865119894
into 119875119905+1
S7 119876119905+1
larr GenerateNewPouluation(119875119905+1
)
S8 If (119905 ltMAX GEN)Then 119905 = 119905 + 1Goto S1 Else Return the Pareto front 1198651
Algorithm 1 Pricing resources with profit and satisfaction optimization (PRPSO) algorithm
Crowding distance sort
F1
F2
F1
F2
Ht =
Nondominated fronts sort
F3
middot middot middot
F 9984003
Nso
lutio
ns
Pt
Qt
Pt cup Qt
Figure 4 Procedures of generating new population119875119905+1
from119875119905
and119876119905
where 119875119905
is the parent population and119876119905
is the child population
size of119876119905+1
is119873 In step S8 the algorithm checks whether themaximum generation is reached If the generation counter 119905is less than the maximum value (MAX GEN) then 119905 is in-creased by 1 and then the algorithm goes to step S1 otherwisethe algorithm terminates
4 Evaluation
In this section we evaluate the effectiveness of proposed algo-rithm The simulation is conducted by the simulator devel-oped on Matlab [15] The simulation of the proposed algo-rithm is conducted with following setting in Table 1
The parameters used in the simulation are listed as fol-lows The initial population is created using a uniform ran-dom distributionThe population size is 15 sdot |119883| where |119883| isthe number of prices each of which corresponds to a serviceThe price is a real number whose range is from 1 to 2 We setthe Pareto fraction as 035 whichmeans the algorithmwill tryto limit the number of individuals in the current population
Table 1 Parameter setting
Parameter ValuesNumber of prices (services) |119883| where |119883| is 3 5 17Initial population Uniform random distributionPopulation size 15 sdot |119883|
Range of price variable (119883) (1 2)Pareto fraction 035StallGenLimit 100Toleratethreshold 1 times 10minus6
MAX GEN 200 sdot |119883|
that are on the Pareto front to 35 percent of the populationsize
In the simulation two conditions are used to determinewhether to stop the algorithm execution In Condition-1 thealgorithm stops when the maximum number of generations(MAX GEN) is reached where theMAX GEN is 200 sdot |119883| InCondition-2 the algorithm stops if the average change in thespread of the Pareto front over the ldquoStallGenLimitrdquo genera-tions is less than the tolerable threshold (TolerateThresold)The algorithm stops when either of the conditions is satisfied
41 Evaluation of Tradeoff Relationship of Two ConflictingObjectives We first simulate the proposed algorithm in thebasic setting which is to decide price variables for three ser-vices for the evaluation of tradeoff relationship of twoconflicting objectives The simulation results are shown inFigure 5 whereObjective 1 is operatorrsquos profit andObjective 2is subscribersrsquo satisfaction per unit of paid price Several frontpoints are plotted in Figure 5 which form the Pareto front ofthe multiobjective optimization theory Each point has twovalues which are the operatorrsquos profit and the subscriberrsquos sat-isfaction As shown in Figure 5 the lower profit implies thehigher satisfaction while the higher profit implies the lowersatisfaction In summary it is impossible to increase the profitand satisfaction at the same time and thus there is tradeoff
The Scientific World Journal 7
0 20 40 60 80 100 1200
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
Figure 5 Results of pricing under two conflicting objectives whereObjective 1 is the operatorrsquos profit and Objective 2 is subscribersrsquosatisfaction
between the two objectives the operatorrsquos profits and sub-scribersrsquo satisfaction
42 Evaluation of Impacts of Raising Prices of Two ConflictingObjectives In this section we study the effectiveness of rais-ing prices of the services We add into (2) an additional vari-able for controlling price raising factor 120575 to have (7) wherethe price raising factor 120575 is 1 12 2
119875 = sum119904isinΩ
119876119904
(120575 sdot 119875119904
) minus sum119894isin119861
119861119894
119862119894
(7)
As shown in Figure 6 the maximum values of profit(Objective 1) of Pareto fronts move to the right if the priceraising factor 120575 is increased It reflects the effectiveness of rais-ing prices to increase the profit
The solutions found by the proposed algorithm are stablesince the results do not fluctuate along the curves as shownin Figure 6 Moreover the effect of raising prices can be easilyobserved in the results For example the maximal profit oforiginal curve (120575 = 1) is 108 and the maximal profit ofadjusted curve (120575 = 2) is 214 as shown in the Figure 6There-fore the maximum profit is almost doubled meaning theeffect of raising price is obvious
43 Evaluation of Impacts of Raising Prices of Two ConflictingObjectives We study in this section the effect of changing ofthemedian value (120573) of the satisfaction of servicesWe set themedian value (120573) as 2 4 12 in order to analyze the corres-ponding results As shown in Figure 7 if 120573 is increased sat-isfaction is decreased This is because a subscriber starts tofeel satisfied only after a lot of resources are allocated to himher for the cases of higher 120573 values
The results show that the difference of satisfactions for dif-ferent subscriber types is obvious by the results found bythe PRPSO algorithm Moreover the characteristics of rela-tionship of operator profit and subscriber satisfaction can be
0 50 100 150 200 2500
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
120575 = 1
120575 = 18
120575 = 2
120575 = 16120575 = 14120575 = 12
Figure 6 Evaluation of the effect of raising prices by adjusting theprice raising factor 120575
0 20 40 60 80 100 1200
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
120573 = 2
120573 = 12
120573 = 4
120573 = 6
120573 = 8120573 = 10
Figure 7 Evaluation of the effect of changing sensitivity of satisfac-tion on services
easily observed based on the results For example in the 120573 =
12 case the satisfaction is almost the same even if the profitreaches the maximum value
44 Evaluation of Efficiency of Finding Pareto Fronts Fourthwe evaluate the qualitymetrics of forming the Praetor front indifferent number of decision variablesThequalitymetrics are(1) the average distance of Pareto front and (2) number ofpoints of Pareto front In general a smaller average distanceindicates that the solutions on the Pareto front are evenly dis-tributedThe average distance is the crowding distance whichis the perimeter of the cuboid formed by using the nearestneighbors as the vertices in the Pareto front please refer tothe paper [5] for more detailsThe number of points of Paretofront indicates the tractability of the Pareto front for a deci-sionmakerWhen the number of points or solutions of Pareto
8 The Scientific World Journal
0
0005
001
0015
002
0025
003
0
50
100
150
200
250
300
350
3 5 7 9 11 13 15 17Number of decision variables
Average of distance
Num
ber p
oint
s of P
aret
o
Number of points of Pareto front
Aver
age o
f dist
ance
Figure 8 Evaluation of the Pareto front in terms of (1) the numberof points of Pareto front and (2) the average of distance where theright-side 119910-axis is the average distance of the Pareto front the left-side 119910-axis is the number of points of the Pareto front and the 119909-axisis the number of decision variables which is the number of prices (orservices)
front are too large then the solutions may be intractable for adecision maker
As shown in Figure 8 the number of points of the Paretofront is increased but the average distance is decreased whenthe number of decision variables is increased It implies thatmore points are included in the Pareto front when the num-ber of decision variables is larger Selecting a pricing solutionfrom a larger set is more intractable for a decision maker fac-ing higher numbers of price variables Hence the decisionmaker needs to carefully make decisions when they face ahigher number of price variables
5 Conclusions
The operators invest huge funds for acquiring the spectrumresources in the LTE network The operator profit and thesubscriber satisfaction are two most important factors Thusit is necessary to consider the operator profit factor and sub-scriber satisfaction factor for pricing resources in the LTEnetworks Howevermost of existing studies only consider theproblem about maximizing operator profitThis paper inves-tigates the pricing resources with profit and satisfaction opti-mization (PRPSO) problem in the LTE network to simulta-neously maximize the operator profit and subscriber satisfac-tion This paper contributes a theoretical framework to helpdecision makers in pricing resources based on the heuristicoptimization algorithmmdashPRPSO algorithm Compared withthe algorithm only solving a single pricing optimization goalthe PRPSO algorithm solves the optimal problem with theconsideration of two important goals which is more helpfulfor making decisions in pricing
The PROSO algorithm has been verified and tested by thesimulations on the basis of convergence and diversity perfor-mance metrics to guarantee the quality of optimal solutionsfound The simulation results show that the difference of sat-isfactions for different subscriber types is obvious Moreover
the characteristics of relationship of the operator profit andthe subscriber satisfaction can also be easily observed basedon the results
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this article
References
[1] F Beltran J AGutierrez and J LMelus ldquoTechnology andmar-ket conditions toward a new competitive landscape in the wire-less access marketrdquo IEEE Communications Magazine vol 48no 6 pp 46ndash52 2010
[2] D Astely E Dahlman A Furuskar Y Jading M Lindstromand S Parkvall ldquoLTE the evolution ofmobile broadbandrdquo IEEECommunications Magazine vol 47 no 4 pp 44ndash51 2009
[3] P Bhat S Nagata L Campoy et al ldquoLTE-advanced an operatorperspectiverdquo IEEE CommunicationsMagazine vol 50 no 2 pp104ndash114 2012
[4] K Coussement and D Van den Poel ldquoChurn prediction in sub-scription services an application of support vector machineswhile comparing two parameter-selection techniquesrdquo ExpertSystems with Applications vol 34 no 1 pp 313ndash327 2008
[5] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast andelitist multiobjective genetic algorithm NSGA-IIrdquo IEEE Trans-actions on Evolutionary Computation vol 6 no 2 pp 182ndash1972002
[6] C-J Huang Y-T Chuang and D-X Yang ldquoImplementation ofcall admission control scheme in next generation mobile com-munication networks using particle swarm optimization andfuzzy logic systemsrdquo Expert Systems with Applications vol 35no 3 pp 1246ndash1251 2008
[7] C-J Huang H-Y Shen and Y-T Chuang ldquoAn adaptive band-width reservation scheme for 4G cellular networks using flex-ible 2-tier cell structurerdquo Expert Systems with Applications vol37 no 9 pp 6414ndash6420 2010
[8] S Dixit S Periyalwar and H Yanikomeroglu ldquoSecondary useraccess in LTE architecture based on a base station centric frame-work with dynamic pricingrdquo IEEE Transactions on VehicularTechnology vol 62 no 1 pp 284ndash296
[9] H Ekstrom ldquoQoS control in the 3GPP evolved packet systemrdquoIEEE Communications Magazine vol 47 no 2 pp 76ndash83 2009
[10] A Ghosh R Ratasuk B Mondal N Mangalvedhe and TThomas ldquoLTE-advanced next-generation wireless broadbandtechnologyrdquo IEEE Wireless Communications vol 17 no 3 pp10ndash22 2010
[11] B Sadiq R Madan and A Sampath ldquoDownlink scheduling formulticlass traffic in LTErdquo Eurasip Journal on Wireless Commu-nications and Networking vol 2009 Article ID 510617 18 pages2009
[13] H Lin M Chatterjee S K Das and K Basu ldquoARC an inte-grated admission and rate control framework for CDMA datanetworks based on non-cooperative gamesrdquo in Proceedings ofthe 9th Annual International Conference on Mobile Computingand Networking (MobiCom rsquo03) pp 326ndash338 ACM September2003
The Scientific World Journal 9
[14] D E Goldberg and J H Holland ldquoGenetic algorithms andmachine learningrdquoMachine Learning vol 3 no 2-3 pp 95ndash991988
Figure 5 Results of pricing under two conflicting objectives whereObjective 1 is the operatorrsquos profit and Objective 2 is subscribersrsquosatisfaction
between the two objectives the operatorrsquos profits and sub-scribersrsquo satisfaction
42 Evaluation of Impacts of Raising Prices of Two ConflictingObjectives In this section we study the effectiveness of rais-ing prices of the services We add into (2) an additional vari-able for controlling price raising factor 120575 to have (7) wherethe price raising factor 120575 is 1 12 2
119875 = sum119904isinΩ
119876119904
(120575 sdot 119875119904
) minus sum119894isin119861
119861119894
119862119894
(7)
As shown in Figure 6 the maximum values of profit(Objective 1) of Pareto fronts move to the right if the priceraising factor 120575 is increased It reflects the effectiveness of rais-ing prices to increase the profit
The solutions found by the proposed algorithm are stablesince the results do not fluctuate along the curves as shownin Figure 6 Moreover the effect of raising prices can be easilyobserved in the results For example the maximal profit oforiginal curve (120575 = 1) is 108 and the maximal profit ofadjusted curve (120575 = 2) is 214 as shown in the Figure 6There-fore the maximum profit is almost doubled meaning theeffect of raising price is obvious
43 Evaluation of Impacts of Raising Prices of Two ConflictingObjectives We study in this section the effect of changing ofthemedian value (120573) of the satisfaction of servicesWe set themedian value (120573) as 2 4 12 in order to analyze the corres-ponding results As shown in Figure 7 if 120573 is increased sat-isfaction is decreased This is because a subscriber starts tofeel satisfied only after a lot of resources are allocated to himher for the cases of higher 120573 values
The results show that the difference of satisfactions for dif-ferent subscriber types is obvious by the results found bythe PRPSO algorithm Moreover the characteristics of rela-tionship of operator profit and subscriber satisfaction can be
0 50 100 150 200 2500
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
120575 = 1
120575 = 18
120575 = 2
120575 = 16120575 = 14120575 = 12
Figure 6 Evaluation of the effect of raising prices by adjusting theprice raising factor 120575
0 20 40 60 80 100 1200
002
004
006
008
01
012
014
016
018
02 Pareto fronts
Objective 1
Obj
ectiv
e 2
120573 = 2
120573 = 12
120573 = 4
120573 = 6
120573 = 8120573 = 10
Figure 7 Evaluation of the effect of changing sensitivity of satisfac-tion on services
easily observed based on the results For example in the 120573 =
12 case the satisfaction is almost the same even if the profitreaches the maximum value
44 Evaluation of Efficiency of Finding Pareto Fronts Fourthwe evaluate the qualitymetrics of forming the Praetor front indifferent number of decision variablesThequalitymetrics are(1) the average distance of Pareto front and (2) number ofpoints of Pareto front In general a smaller average distanceindicates that the solutions on the Pareto front are evenly dis-tributedThe average distance is the crowding distance whichis the perimeter of the cuboid formed by using the nearestneighbors as the vertices in the Pareto front please refer tothe paper [5] for more detailsThe number of points of Paretofront indicates the tractability of the Pareto front for a deci-sionmakerWhen the number of points or solutions of Pareto
8 The Scientific World Journal
0
0005
001
0015
002
0025
003
0
50
100
150
200
250
300
350
3 5 7 9 11 13 15 17Number of decision variables
Average of distance
Num
ber p
oint
s of P
aret
o
Number of points of Pareto front
Aver
age o
f dist
ance
Figure 8 Evaluation of the Pareto front in terms of (1) the numberof points of Pareto front and (2) the average of distance where theright-side 119910-axis is the average distance of the Pareto front the left-side 119910-axis is the number of points of the Pareto front and the 119909-axisis the number of decision variables which is the number of prices (orservices)
front are too large then the solutions may be intractable for adecision maker
As shown in Figure 8 the number of points of the Paretofront is increased but the average distance is decreased whenthe number of decision variables is increased It implies thatmore points are included in the Pareto front when the num-ber of decision variables is larger Selecting a pricing solutionfrom a larger set is more intractable for a decision maker fac-ing higher numbers of price variables Hence the decisionmaker needs to carefully make decisions when they face ahigher number of price variables
5 Conclusions
The operators invest huge funds for acquiring the spectrumresources in the LTE network The operator profit and thesubscriber satisfaction are two most important factors Thusit is necessary to consider the operator profit factor and sub-scriber satisfaction factor for pricing resources in the LTEnetworks Howevermost of existing studies only consider theproblem about maximizing operator profitThis paper inves-tigates the pricing resources with profit and satisfaction opti-mization (PRPSO) problem in the LTE network to simulta-neously maximize the operator profit and subscriber satisfac-tion This paper contributes a theoretical framework to helpdecision makers in pricing resources based on the heuristicoptimization algorithmmdashPRPSO algorithm Compared withthe algorithm only solving a single pricing optimization goalthe PRPSO algorithm solves the optimal problem with theconsideration of two important goals which is more helpfulfor making decisions in pricing
The PROSO algorithm has been verified and tested by thesimulations on the basis of convergence and diversity perfor-mance metrics to guarantee the quality of optimal solutionsfound The simulation results show that the difference of sat-isfactions for different subscriber types is obvious Moreover
the characteristics of relationship of the operator profit andthe subscriber satisfaction can also be easily observed basedon the results
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this article
References
[1] F Beltran J AGutierrez and J LMelus ldquoTechnology andmar-ket conditions toward a new competitive landscape in the wire-less access marketrdquo IEEE Communications Magazine vol 48no 6 pp 46ndash52 2010
[2] D Astely E Dahlman A Furuskar Y Jading M Lindstromand S Parkvall ldquoLTE the evolution ofmobile broadbandrdquo IEEECommunications Magazine vol 47 no 4 pp 44ndash51 2009
[3] P Bhat S Nagata L Campoy et al ldquoLTE-advanced an operatorperspectiverdquo IEEE CommunicationsMagazine vol 50 no 2 pp104ndash114 2012
[4] K Coussement and D Van den Poel ldquoChurn prediction in sub-scription services an application of support vector machineswhile comparing two parameter-selection techniquesrdquo ExpertSystems with Applications vol 34 no 1 pp 313ndash327 2008
[5] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast andelitist multiobjective genetic algorithm NSGA-IIrdquo IEEE Trans-actions on Evolutionary Computation vol 6 no 2 pp 182ndash1972002
[6] C-J Huang Y-T Chuang and D-X Yang ldquoImplementation ofcall admission control scheme in next generation mobile com-munication networks using particle swarm optimization andfuzzy logic systemsrdquo Expert Systems with Applications vol 35no 3 pp 1246ndash1251 2008
[7] C-J Huang H-Y Shen and Y-T Chuang ldquoAn adaptive band-width reservation scheme for 4G cellular networks using flex-ible 2-tier cell structurerdquo Expert Systems with Applications vol37 no 9 pp 6414ndash6420 2010
[8] S Dixit S Periyalwar and H Yanikomeroglu ldquoSecondary useraccess in LTE architecture based on a base station centric frame-work with dynamic pricingrdquo IEEE Transactions on VehicularTechnology vol 62 no 1 pp 284ndash296
[9] H Ekstrom ldquoQoS control in the 3GPP evolved packet systemrdquoIEEE Communications Magazine vol 47 no 2 pp 76ndash83 2009
[10] A Ghosh R Ratasuk B Mondal N Mangalvedhe and TThomas ldquoLTE-advanced next-generation wireless broadbandtechnologyrdquo IEEE Wireless Communications vol 17 no 3 pp10ndash22 2010
[11] B Sadiq R Madan and A Sampath ldquoDownlink scheduling formulticlass traffic in LTErdquo Eurasip Journal on Wireless Commu-nications and Networking vol 2009 Article ID 510617 18 pages2009
[13] H Lin M Chatterjee S K Das and K Basu ldquoARC an inte-grated admission and rate control framework for CDMA datanetworks based on non-cooperative gamesrdquo in Proceedings ofthe 9th Annual International Conference on Mobile Computingand Networking (MobiCom rsquo03) pp 326ndash338 ACM September2003
The Scientific World Journal 9
[14] D E Goldberg and J H Holland ldquoGenetic algorithms andmachine learningrdquoMachine Learning vol 3 no 2-3 pp 95ndash991988
Figure 8 Evaluation of the Pareto front in terms of (1) the numberof points of Pareto front and (2) the average of distance where theright-side 119910-axis is the average distance of the Pareto front the left-side 119910-axis is the number of points of the Pareto front and the 119909-axisis the number of decision variables which is the number of prices (orservices)
front are too large then the solutions may be intractable for adecision maker
As shown in Figure 8 the number of points of the Paretofront is increased but the average distance is decreased whenthe number of decision variables is increased It implies thatmore points are included in the Pareto front when the num-ber of decision variables is larger Selecting a pricing solutionfrom a larger set is more intractable for a decision maker fac-ing higher numbers of price variables Hence the decisionmaker needs to carefully make decisions when they face ahigher number of price variables
5 Conclusions
The operators invest huge funds for acquiring the spectrumresources in the LTE network The operator profit and thesubscriber satisfaction are two most important factors Thusit is necessary to consider the operator profit factor and sub-scriber satisfaction factor for pricing resources in the LTEnetworks Howevermost of existing studies only consider theproblem about maximizing operator profitThis paper inves-tigates the pricing resources with profit and satisfaction opti-mization (PRPSO) problem in the LTE network to simulta-neously maximize the operator profit and subscriber satisfac-tion This paper contributes a theoretical framework to helpdecision makers in pricing resources based on the heuristicoptimization algorithmmdashPRPSO algorithm Compared withthe algorithm only solving a single pricing optimization goalthe PRPSO algorithm solves the optimal problem with theconsideration of two important goals which is more helpfulfor making decisions in pricing
The PROSO algorithm has been verified and tested by thesimulations on the basis of convergence and diversity perfor-mance metrics to guarantee the quality of optimal solutionsfound The simulation results show that the difference of sat-isfactions for different subscriber types is obvious Moreover
the characteristics of relationship of the operator profit andthe subscriber satisfaction can also be easily observed basedon the results
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this article
References
[1] F Beltran J AGutierrez and J LMelus ldquoTechnology andmar-ket conditions toward a new competitive landscape in the wire-less access marketrdquo IEEE Communications Magazine vol 48no 6 pp 46ndash52 2010
[2] D Astely E Dahlman A Furuskar Y Jading M Lindstromand S Parkvall ldquoLTE the evolution ofmobile broadbandrdquo IEEECommunications Magazine vol 47 no 4 pp 44ndash51 2009
[3] P Bhat S Nagata L Campoy et al ldquoLTE-advanced an operatorperspectiverdquo IEEE CommunicationsMagazine vol 50 no 2 pp104ndash114 2012
[4] K Coussement and D Van den Poel ldquoChurn prediction in sub-scription services an application of support vector machineswhile comparing two parameter-selection techniquesrdquo ExpertSystems with Applications vol 34 no 1 pp 313ndash327 2008
[5] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast andelitist multiobjective genetic algorithm NSGA-IIrdquo IEEE Trans-actions on Evolutionary Computation vol 6 no 2 pp 182ndash1972002
[6] C-J Huang Y-T Chuang and D-X Yang ldquoImplementation ofcall admission control scheme in next generation mobile com-munication networks using particle swarm optimization andfuzzy logic systemsrdquo Expert Systems with Applications vol 35no 3 pp 1246ndash1251 2008
[7] C-J Huang H-Y Shen and Y-T Chuang ldquoAn adaptive band-width reservation scheme for 4G cellular networks using flex-ible 2-tier cell structurerdquo Expert Systems with Applications vol37 no 9 pp 6414ndash6420 2010
[8] S Dixit S Periyalwar and H Yanikomeroglu ldquoSecondary useraccess in LTE architecture based on a base station centric frame-work with dynamic pricingrdquo IEEE Transactions on VehicularTechnology vol 62 no 1 pp 284ndash296
[9] H Ekstrom ldquoQoS control in the 3GPP evolved packet systemrdquoIEEE Communications Magazine vol 47 no 2 pp 76ndash83 2009
[10] A Ghosh R Ratasuk B Mondal N Mangalvedhe and TThomas ldquoLTE-advanced next-generation wireless broadbandtechnologyrdquo IEEE Wireless Communications vol 17 no 3 pp10ndash22 2010
[11] B Sadiq R Madan and A Sampath ldquoDownlink scheduling formulticlass traffic in LTErdquo Eurasip Journal on Wireless Commu-nications and Networking vol 2009 Article ID 510617 18 pages2009
[13] H Lin M Chatterjee S K Das and K Basu ldquoARC an inte-grated admission and rate control framework for CDMA datanetworks based on non-cooperative gamesrdquo in Proceedings ofthe 9th Annual International Conference on Mobile Computingand Networking (MobiCom rsquo03) pp 326ndash338 ACM September2003
The Scientific World Journal 9
[14] D E Goldberg and J H Holland ldquoGenetic algorithms andmachine learningrdquoMachine Learning vol 3 no 2-3 pp 95ndash991988
