Wi-Fi or Femtocell: User Choice and Pricing Strategy of Wireless Service Provider

Transcription

1 Wi-Fi or Femtocell: User Choice ad Pricig Strategy of Wireless Service Provider Yajiao Che, Qia Zhag Departmet of Computer Sciece ad Egieerig Hog Kog Uiversity of Sciece ad Techology {cheyajiao, Abstract Wi-Fi ad femtocell are two competig ad complemetary techologies for deliverig broadbad wireless Iteret access services. For the Wireless Service Provider (WSP) who ows both Wi-Fi ad femtocell etwork, pricig for the coexisted heterogeeous etwork is a critical yet challegig problem due to differet features of the two techologies: Wi-Fi is based o wireless local area etwork (WLAN), whose time delay is highly depedet o cocurret i-service users; femtocell is based o cellular techology, which provides guarateed Quality of Service (QoS). I this paper, we cosider a moopolist WSP who operates both Wi-Fi ad femtocell etwork withi a certai area, ad offers correspodig services to a fixed pool of users. Users ca freely choose either service that icurs less cost, which is a weighted sum of service price ad time delay. Users with differet sesitivity for price ad time delay ted to choose differet services. The major objective of WSP is to maximize its profit, which is the reveue from both services. We first aalyze user distributio uder differet Wi-Fi ad femtocell price combiatio, the study the optimal pricig strategy for WSP. Fially, we use simulatio to evaluate the ifluece of Wi- Fi etwork quality o the WSP s utility ad user distributio. I. INTRODUCTION Ever icreasig demad for faster ad more coveiet wireless commuicatio has triggered a series of ew techologies. Wi-Fi ad femtocell are two major ways to provide users with high-speed mobile Iteret access. Sice Wi-Fi ad femtocell are based o differet stadards, they have differet features. Femtocell service provides guarateed QoS (time delay), thaks to the exclusive licesig ad cetralized schedulig, while the time delay of Wi-Fi service is highly depedet o the umber of cocurret i-service users (due to cotetios ad iterferece geerated by sharig the same ulicesed bads) [2]. Users with differet QoS requiremets thus have differet prefereces over these two services. How to maage the Wi-Fi ad femtocell services so that maximum profits ca be achieved remais a challegig problem for WSPs. I this paper, we cosider a moopolist WSP who rus both Wi-Fi ad femtocell etwork, ad provides correspodig services to a fixed pool of users, who are free to choose either service (as show i Fig.1). The reveue of WSP is the sum of service fee charged from users who choose either Wi-Fi or femtocell service. Sice Wi-Fi ad femtocell are two competig services, the umber of users who choose Wi-Fi service will ot oly be affected by Wi-Fi s price ad time delay, but also affected by femtocell s price ad time delay, Fig. 1. Illustratio of Mobile Service Model. vice versa. More users will choose Wi-Fi (femtocell) service if Wi-Fi (femtocell) charges lower price ad has shorter time delay, also if femtocell (Wi-Fi) charges relatively higher price ad has loger time delay. I additio, the time delay of Wi-Fi relies o the umber of users choosig Wi-Fi service: the more Wi-Fi users, the more cogested the Wi-Fi etwork becomes, ad the loger the time delay for Wi-Fi service. WSP has to be fully aware of the impact of Wi-Fi ad femtocell service prices o users choice i order to lauch optimal pricig strategy which yields maximum profit. The competitive ad complemetary relatioship of Wi-Fi ad 3G techology (for which femtocell is a represetative) is surveyed i [2]. I [5], the authors built a pricig competitio model betwee Wi-Fi ad WiMAX, i which the two services are provided by differet operators, which is differet from our moopolistic WSP model. I additio, the paper [5] did t aalyze users choice whe facig differet service prices ad time delays. I [3] [4], the authors studied the iteractio betwee a Wi-Fi service provider ad a cliet ad aalyzed the pricig equilibrium uder differet utility fuctios. Refereces [7] [6] joitly cosidered spectrum allocatio ad pricig strategies for service provider. Femtocell pricig schemes is studied by [8]. Users differet preferece for QoS is take ito cosideratio. Referece [1] aalyzed optimal pricig ad spectrum allocatio for moopolist WSP who ows both femtocell ad macrocell services ad tries to maximize its profit. However, these papers did ot address the pricig issue for heterogeeous etwork where both Wi-Fi ad femtocell are available. I this paper, we first derive the user distributio uder differet Wi-Fi ad femtocell price combiatios. We cosider a fixed umber of ratioal wireless users who choose the service that icurs least cost. Some users are more pricesesitive whose decisio will be more easily iflueced by price differece. Some users care more about time delay ad are willig to pay higher prices to avoid traffic cogestio /13/$ IEEE 4502

2 We joitly cosider the prices ad time delays of both Wi-Fi ad femtocell services as they all have a ifluece o users choice. We compute best pricig strategies ad correspodig maximum profit for WSP. The mai cotributios of the paper are as follows: We propose a cocrete ecoomic framework for aalyzig coexisted heterogeeous Wi-Fi ad femtocell etworks, which addresses fudametal Wi-Fi ad femtocell service diversity. We aalyze user behavior, joitly cosiderig the ifluece of service price ad time delay of both Wi-Fi ad femtocell etworks. We coduct simulatios to study the impact of Wi-Fi etwork quality o the WSP s utility ad user distributio. The results show that if the icrease of Wi-Fi users does ot cause much loger time delay, the WSP ca obtai higher utility ad more users will choose Wi-Fi etwork. While higher Wi-Fi service price leads to fewer Wi- Fi users, the umber of femtocell users also decreases because Wi-Fi time delay is shorteed due to fewer users, makig the femtocell service less advatageous. The rest of the paper is orgaized as follows. First, we itroduce the detailed system model i sectio II. After that, we aalyze user distributio i sectio III. I sectio IV, we compute WSP s optimal strategies ad correspodig profit. I sectio V, we evaluate our model from various aspects through simulatio. We fially summarize our work i sectio VI. II. SYSTEM MODEL We cosider a moopolist WSP who provides Wi-Fi ad femtocell services to ed users 12. There are a total umber of users i the covered area, who are free to toggle betwee Wi-Fi ad femtocell services 3. We assume that WSP charges a flat rate of per user who chooses Wi-Fi service ad p f per user who chooses femtocell service. Let f deote the umber of users who will choose femtocell service ad w deote the umber of users who will choose Wi-Fi service. Users cost comprises of two parts: 1) service cost: for Wi-Fi service ad p f for femtocell service; 2) time delay cost: defied as the time eeded to fiish a typical task 4 usig either Wi-Fi or femtocell service. Let t w ad t f deote the average time delay for Wi-Fi service ad femtocell service respectively. Differet users have differet valuatio for moey ad time. We use γ to represet users sesitivity towards service price. γ [0,γ max ] ca be viewed as the characterizatio of user 1 We assume that the deploymet costs of Wi-Fi ad femtocell etworks are fixed costs which are suk ad will ot affect the pricig strategy of the WSP, so we exclude it from the aalysis. 2 I order to focus o the competitive ad complemetary relatioship of Wi-Fi ad femtocell, we oly cosider the geographic areas where users ca access both services. Areas which are covered by either oe service but ot the other (thus users do ot have multiple choices) are out of the scope of this paper. To further ivolve the macrocell etwork is our future directio. 3 With the techology such as Soft Sim by Apple, users ca switch betwee services without costs. 4 It is flexible to defie a typical task, for example, to upload/dowload 1MB file, to lauch a search egie webpage. type. The cumulative distributio fuctio of γ is Γ ad Γ(γ 0) = 0, Γ(γ γ max )=1are satisfied. A user of type γ is willig to pay price p for a reductio of γp time delay (the user treats the price p ad time delay γp as equivalet). The higher γ is, the more sesitive the user towards moey, ad he is willig to edure loger time delay. Sice femtocell belogs to cellular etwork ad provides guarateed QoS, we assume that t f is fixed regardless of umber of i-service users. However, Wi-Fi is based o the IEEE stadards, operatig o ulicesed bad ad providig best-effort service. Whe the umber of users icreases, the cotetio ad iterferece icreases, resultig i loger time delay. We assume that t w =Φ( w ) is a o-decreasig fuctio of w. For a type γ user, if choosig femtocell service, the equivalet time delay cost is c γ f = γp f + t f ; (1) if choosig Wi-Fi service, the equivalet time delay cost is c γ w = γ +Φ( w ). (2) Each user has a reserve cost c 5 0. Users are ratioal ad utility drive, choosig the service that gives them most beefits, amely, least cost. A type γ user s service choice is as follows: Femtocell service, if c γ f <cγ w,c γ f <c 0 Wi-Fi service, if c γ f >cγ w,c γ w <c 0 (3) No service, otherwise The utility of WSP is the sum of reveue from femtocell service ad Wi-Fi service : p f f + w. (4) III. USER DISTRIBUTION I this sectio, we derive the user distributio, give that the prices of Wi-Fi ad femtocell services ad p f are aouced by WSP ad observed by ed users. For simplicity, we assume that the depedecy of t w o w is liear, i.e., t w =Φ( w )= w, i which is a costat parameter represetig by how much the time delay icreases whe a additioal user jois the Wi- Fi etwork. To better uderstad users choice, we itroduce three critical user type. Idifferet to femtocell ad o service user type. There exists a critical user type γ1 th, whose is idifferet to choosig femtocell service or o service at all. It satisfies γ th 1 p f + t f = c 0 γ th 1 = c 0 t f p f. (5) 5 We assume the same reserve cost for femtocell ad Wi-Fi services, which idicates that users do ot differetiate the Iteret access service provided by either femtocell or Wi-Fi techology. 4503

3 Fig. 2. User Distributio whe p f <. Users of type γ < γ1 th prefer femtocell service to o service. Idifferet to Wi-Fi ad o service user type. There exists a critical user type γ2 th, who is idifferet to choosig Wi-Fi service or o service at all. It satisfies γ2 th + t w = c 0 γ2 th = c 0 t w (6) Users of type γ<γ2 th prefer Wi-Fi service to o service. Idifferet to Wi-Fi ad femtocell service user type. There exists a critical user type γ3 th, who is idifferet to choosig Wi-Fi service or femtocell service. It satisfies γ3 th + t w = γ3 th p f + t f γ3 th = t f t w. (7) p f Here, it is possible that γ 3 0. If >p f, users of type γ>γ3 th prefer femtocell service to Wi-Fi service; otherwise, users of type γ<γ3 th prefer femtocell service to Wi-Fi service. Propositio 1: Give the Wi-Fi ad femtocell service price as ad p f respectively, the user distributio are as follows: 1) Whe (c 0 t f ) t f γ max,p f (γmax + )(c 0 t f ) (8) the umber of Wi-Fi users ad femtocell users are: c 0 γ max +, f =0 (9) 2) Whe (c 0 t f ) t f γ max,p f (γmax + )(c 0 t f ) or (c 0 t f ) t f γ max,p f, (10) the umber of Wi-Fi users ad femtocell users are: t f γ max ( p f )+ f = γ max [ c 0 + p (11) f t w t f p f p f ( p f ) ] 3) Whe (c 0 t f ) t f γ max,p f (γmax + )(c 0 t f ) (12) Fig. 3. User Distributio whe p f. the umber of Wi-Fi users ad femtocell users are: (p f )c 0 + t f γ max (p f ) + p f f = (t (13) w t f ) γ max (p f ) Proof: 1) If p f <, it ca be easily derived that γ2 th = p f γ1 th +(1 p f )γ3 th so there are oly two possibilities: γ1 th γ2 th γ3 th or γ3 th γ2 th γ1 th. γ1 th γ2 th γ3 th as show i the upper subfigure i Fig.2. I this case, o users are willig to choose the femtocell service, ad f =0. c 0 γ max (14) + I order to satisfy that γ1 th γ2 th γ3 th, ad p f have to satisfy that (c 0 t f ) t f γ max, p f (γmax + )(c 0 t f ) γ th 3 γ th 2 γ th 1 as show i the lower subfigure i Fig.2. We first assume that γ 3 > 0 ad derive the umber of users choosig Wi-Fi service as follows: t f γ max (15) ( p f )+ We ca check that t w <t f,soγ 3 > 0 is true. The umber of users choosig femtocell service is: f = γ 1 γ 3 γ max = γ max [ c 0 + p f t w t f p f p f ( p f ) ] I order to satisfy that γ3 th γ2 th γ th satisfy that (16) 1, p f has to p f mi{, (γmax + )(c 0 t f ) } 2) If p f >, it ca be easily derived that γ1 th = γ2 th +(1 )γ3 th p f p f so there are oly two possibilities: γ2 th γ1 th γ3 th or γ3 th γ1 th γ2 th. γ2 th γ1 th γ3 th as show i the upper subfigure i Fig.3. I this case, o users are willig to choose 4504

4 the Wi-Fi service, ad 0. However, it ca be checked that γ 3 = t f /(p f ) < 0. Soγ2 th γ1 th γ3 th actually will ot happe. γ3 th γ1 th γ2 th as show i the lower subfigure i Fig.3. We first assume that γ 3 > 0 ad derive the umber of users choosig Wi-Fi service as follows: γ 2 γ 3 γ max = γ max [c 0 t w t w t f p f ] (p f )c 0 + t f γ max (p f ) + p f (17) To guaratee that γ 3 > 0, it must be satisfied that (c 0 t f )/(t f γ max ). We also check that whe p f >, γ3 th γ1 th γ2 th is always true. I this case, the umber of users choosig femtocell service is f = γ 3 γ max = (t w t f ) γ max (18) (p f ) If (c 0 t f )/(t f γ max ), γ 3 < 0, the o users will choose femtocell service, f =0. The umber of users choosig Wi-Fi service is: c 0 γ max (19) + Combie the results of the above aalysis, we ca get the user distributio i Propositio 1. IV. REVENUE MAXIMIZATION FOR WSP I this sectio, we cosider the pricig strategy of WSP, which is costraied by,p f p f p 6 f. Propositio 2: The optimal pricig strategy ad optimal utility for WSP is as follows: If (c 0 t f )/(t f γ max ), the optimal pricig strategy for WSP is =,p f (γmax + )(c 0 t f ) Ad the optimal utility for WSP is U WSP = c 0 γ max + If (c 0 t f )/(t f γ max ), the optimal pricig strategy for WSP is,p f (γmax + )(c 0 t f ) Ad the optimal utility for WSP is UWSP = (c 0 t f ) γ max 6 The upperboud of the price ca be the restrictio from the govermet o the highest price that the WSP ca charge. The lowerboud of the price ca be the cost of providig the service, below which the WSP receives egative et profit. Proof: 1) Whe coditio (8) is satisfied. The WSP s utility is: c 0 γ max + = c 0 γ max + So the utility of WSP is a icreasig fuctio of. The optimal Wi-Fi price is p w = ad the highest possible U WSP is c 0 /(γ max + ). 2) Whe coditio (10) is satisfied. The WSP s utility is: γ max (c t f 0 γ max ( p f )+ ) The first derivative of U WSP with regard to p f is U WSP 2 t f = p f [γ max ( p f )+] 2 0 So the utility of WSP is icreasig with p f. - Whe (c 0 t f )/(t f γ max ),p f = (γ max + )(c 0 t f )/( ). The WSP s u- tility becomes: c 0 γ max + U WSP is icreasig with, so the optimal Wi-Fi price is p w = ad the highest possible U WSP is c 0 /(γ max + ). - Whe (c0 t f ) t f γ,p max f =. The WSP s utility becomes: γ max (c 0 t f ) So the utility of WSP is irrelevat of, ad the highest possible U WSP is (c 0 t f )/γ max. 3) Whe coditio (12) is satisfied. The WSP s utility is: γ max (c 0 t f ) So the utility of WSP is irrelevat of p f ad as log as coditio (12) is satisfied, ad the highest possible U WSP is (c 0 t f )/γ max. Accordig to the aalysis above, there are two highest possible value for U WSP : (c 0 t f )/γ max ad c 0 /(γ max + ). By comparig these two values ad their costraits, we ca get the optimal pricig strategy for WSP as i Propositio 2. V. SIMULATION RESULTS The parameter values used i the simulatios are listed i Table I. Whe is small, the time delay of Wi-Fi etwork is short, give the same umber of Wi-Fi users. Therefore, whe icreases, fewer users will choose Wi-Fi service due to icreased time delay as show i Fig.5 ad Fig.6. O the cotrary, more users will choose femtocell service istead as show i Fig.7. Icreasig idicates worseed Wi-Fi 4505

5 Utility of WSP U WSP Number of Wi Fi users w Number of Wi Fi users w =0.6 =0.65 = Fig. 4. Utility of WSP U WSP versus. TABLE I SIMULATION PARAMETERS Parameter Descriptio Value Total umber of users 1 t f Femtocell time delay 1.5 γ max Upperboud of user type 1 c 0 Reserve cose 2 Upperboud of 1 lowerboud of Number of femtocell users f =0.6 =0.65 = Fig. 7. Number of femtocell users f versus whe t f γ max /((c 0 t f )). service quality, so the utility of WSP decreases due to user dissatisfactio as show i Fig.4. The reaso why Fig.5 resembles the left part of Fig.4 is: whe t f γ max /((c 0 t f )), if WSP adopts the optimal pricig strategy i Propositio 2, the umber of femtocell users will be zero as idicated by Propositio 1, so the reveue of WSP is the Wi-Fi service price ( ) multiplies the umber of users choosig Wi-Fi service. Whe t f γ max /((c 0 t f )), the prices of Wi- Fi ad femtocell ca be ay value chose from the rages [, ] ad [(γ max +)(c 0 t f )/( ), p f ], without affectig the reveue of WSP. However, the price combiatio does affects the user distributio. I Fig.6 ad Fig.7, we fixed the femtocell service price as 0.9 ad vary Wi-Fi service price. Whe Wi-Fi service price icreases, the umber of users choosig Wi-Fi service decreases as expected sice users prefer low price to high price (as show i Fig.6). Surprisigly, the umber of femtocell service also decreases (as show i Fig.7). This is because fewer Wi-Fi users leads to shorter Wi- Fi time delay, makig femtocell s guarateed time delay less attractive to users. Fig. 5. Number of Wi-Fi users w versus whe t f γ max /((c 0 t f )). Fig. 6. Number of Wi-Fi users w versus whe t f γ max /((c 0 t f )). VI. CONCLUSION I this paper, we propose a ecoomic framework for coexisted heterogeeous Wi-Fi ad Femtocelll etworks. We study the ifluece of users differet sesitivity for price ad time delay o the demad of Wi-Fi ad femtocell services. We derive user distributio, based o which derivig WSP s optimal strategy ad maximum profit. The simulatio results show that improvemet of Wi-Fi etwork (reduce the parameter so that Wi-Fi time delay decreases) cotributes to higher reveue for WSP. The umber of Wi-Fi users is reversely related to Wi-Fi service price as expected, while surprisigly, the umber of femtocell users is also reversely related to Wi-Fi service price. The reaso is that the time delay of Wi-Fi service is reduced due to fewer users, which makes femtocell service less attractive. VII. ACKNOWLEDGEMENT The research was support i part by grats from RGC uder the cotracts CERG , HKUST grat SRFI11FYT01, the grat from Huawei-HKUST joit lab, the Natioal Natural Sciece Foudatio of Chia uder Grats No ad 973 project 2013CB32900X. REFERENCES [1] Y. Che, J. Zhag, P. Li, ad Q. Zhag. Optimal pricig ad spectrum allocatio for wireless service provider o femtocell deploymet. I ICC, IEEE. [2] W. Lehr ad L. McKight. Wireless iteret access: 3g vs. wifi? Telecommuicatios Policy, 27(5-6): , [3] J. Musacchio ad J. Walrad. Game theoretic modelig of wifi pricig. I The aual Allerto Coferece o Commuicatio Cotrol ad Computig, volume 41, pages Citeseer, [4] J. Musacchio ad J. Walrad. Wifi access poit pricig as a dyamic game. TON, IEEE/ACM, 14(2): , [5] D. Niyato ad E. Hossai. Competitive pricig i heterogeeous wireless access etworks: Issues ad approaches. TON, IEEE/ACM, 22(6):4 11, [6] S. Segupta ad M. Chatterjee. A ecoomic framework for dyamic spectrum access ad service pricig. TON, IEEE/ACM, 17(4): , [7] S. Segupta, M. Chatterjee, ad S. Gaguly. A ecoomic framework for spectrum allocatio ad service pricig with competitive wireless service providers. I DySPAN, 2007, pages [8] N. Shetty, S. Parekh, ad J. Walrad. Ecoomics of femtocells. I GLOBECOM, 2009, pages