Prcng Model of Cloud Computng Servce wth Partal Multhomng Zhang Ru 1 Tang Bng-yong 1 1.Glorous Sun School of Busness and Managment Donghua Unversty Shangha 251 Chna E-mal:ru528369@mal.dhu.edu.cn Abstract Currently the artcles about prcng strategy and busness operaton of cloud computng are rare and most of these artcles focus on the dscusson of the prces gven by ndustry leaders or the mprovement n these prces whch cannot reflect market supply and demand as well as customers needs. By usng the theory of two-sded markets ths paper analyzes the prcng model and operatng strategy of cloud computng wth partal multhomng and compares wth prevous studes to explore the mpact of partal multhomng on carrers strategy. The results show that when users and developers are partal multhomng carrers wll eventually occupy the same market shares but the market shares are expanded; the number of multhomng users (or developers) would ncrease by the enhancng of the cross-sde network effect or the decreasng of the servces or resources dfferentaton among varous cloud computng servces; the behavor of partal multhomng may reduce the prces and profts of carrers. So n commercal operaton carrers should take measures to reduce the number of multhomng customers. Keywords:cloud computng servce partal multhomng prcng 1. Introducton In the recent decade cloud computng has been flourshng n the world. As a new utlty computng mode ts core s to submt computng resources storage resources and network resources expressed n the form of vrtualzaton and automated through the nternet. The emergence of cloud computng has changed the tradtonal way that IT resources have used and combned grd computng vrtualzaton technology SaaS and other technologes together. Compared wth the tradtonal computng modes cloud computng has the followng advantages: (1) Wth a pay-as-you-go economc model customers only need to pay for the servces or resources that they just need and use and save carrers captal nvestment and operatng expenses; (2) These servces and resources on cloud are provded by thrd-party companes whch can be used by customers anywhere and anytme [1]. So t attracts plenty of great tycoons such as Google IBM Mcrosoft SUN whch expand nto the new market. So are a number of small and medum-szed enterprses. Currently government research nsttutons and ndustry leaders are eager to adopt cloud computng to solve the problems n computng and storage [2]. There s no doubt that cloud computng s the development drecton of the next generaton nternet technology. Cloud computng wll change the tradtonal busness method and brng a huge commercal value. However ts success n busness largely depends on the ratonal prcng mechansm [3]. So far every cloud computng carrer has ts own prcng scheme. Amazon AWS use tered prcng to charge ther customers. For example Amazon EC2 provdes customers wth the VM servce at the prce of 1 dollar per hour over a perod of tme [4]. Google App Engne and FlexScale select a prcng model of
pay per use to charge servces and resources.e. customers need to pay for the use of servce whch s based on unts wth fxed prces. Subscrpton prce as the most commonly prcng model n SaaS means that customers sgn a contract based on a fxed prce and a constant perod of tme to use the servces and resources on cloud such as annual fee or monthly rent. In addton Amazon EC2 has recently adopted a new dynamc prcng- spot nstance prcng (current aucton prce) whch would adjust to the changes n market supply and demand [5]. However fxed prcng s always the domnant form of cloud computng prcng today. Customers (ncludng users and provders) prefer to acceptng and usng fxed prcng model because of ts smplcty and convenence. Nevertheless for hgh-value servces t s necessary to fnd a more sutable prcng model whch can reflect the changes n supply and demand. In tryng to address the above problems ths paper attempts to use the theory of platform economcs and the prcng model of two-sded markets to buld the dynamc prcng of cloud computng servces n order to reflect market changes and maxmze the expected revenues of carrers and the expected utltes of customers. In the prevous works [67] we addressed the prcng model of cloud computng n Hotellng model and snglehomng customers. In ths work we extend the analyss to consder the settng where customers are partal multhomng.e. some customers purchased more than one cloud computng servce. The remander of ths paper s organzed as follows: n secton 2 we summarze related work. In secton 3 we present a dynamc prcng model wth partal multhomng based on Hotellng specfcaton. Secton 4 dscusses the man factors that affect the prcng model the behavor of partal multhomng and ts nfluences on carrers prces and revenues. Fnally secton 5 concludes the paper. 2. Related work Wth the rapd development of cloud computng scholars also put more attenton nto t and many studes have been made. These studes nvolve the concepts and key technologes of cloud computng the constructon of cloud cloud securty and other aspects. And there also exst a lot of lteratures about the nnovaton and practcal of cloud computng. In recent years there s a major new trend to study the busness value and prcng strateges on cloud computng. Yeo et al. [8] pont out that fxed prcng has been unable to meet dfferent customers needs and dynamc prcng can not only satsfy customers but also brng hgh profts for carrers. Chrstof et al. [9] present a cloud busness model Framework whch can be dvded nto three layers as the techncal layers n cloud. Zhu et al. [1] argue that dstngushng from the prevous computng paradgms cloud computng creates a new busness model and a remarkable commercal value. In addton to the analyss of exstng prcng models of cloud computng many other scholars meet the problems of the exstng prcng models by gvng the mproved models. Hadj et al. [11] hold that the prcng model of cloud computng should be enable to maxmze carrers revenue as well as customers utltes. And they also propose a theoretcal model based on Stackelberg game and a Stackelberg/Nash equlbrum soluton. Mhalescu et al. [12] propose a dynamc prcng model on federated clouds by consderng the forces of demand and supply. They also draw that dynamc prcng can ncrease the success rate of busness deals by comparng the statc prcng model wth the dynamc model. Few researchers have studed Amazon spot prce traces and bult mproved models around that. Buyya et al. [13] analyze one year prce hstory of Amazon s spot nstances n four data centers of Amazon s EC2 and buld a statstcal model to capture the spot prces n the data centers. Sowmya et al. [14] use the game theory to buld a prcng model n a spot market and analyze real tme data from Amazon EC2 market to valdate the model. However there are some drawbacks of spot nstance such as untruthful bddng and unfar resource allocaton. In regard to these problems Wang et al. [15] propose a computatonally effcent aucton-style prcng mechansm whch can ensure the balanced dstrbuton of resources and mprove carrer's overall revenues. 3. The model In ths secton we descrbe our dynamc prcng model n detal.
Ths model s based on our prevous study [6] whch regards cloud computng servce as a two-sded market and the two sdes are dvded nto two types: users and developers. Those models are bult by Hotellng specfcaton. However the prevous study only consders that users and developers are snglehomng.e. one user or one developer only chooses one cloud computng servce to purchase. But n an actual market each cloud computng carrers exhbted dfferences n servces or products. And f the prce s reasonable and favorable enough to users some users hope for contactng wth more developers and get more servces by purchasng more than one cloud computng servce. And developers also want to get more users to trade. So some users and developers would jon two or more clouds.e. users and developers are partal multhomng. Ths paper takes account of chargng users and developers a regstraton fee whch s smlar to subscrpton prce. But subscrpton prce s often made by carrers. And the prcng model of ths paper s a dynamc prcng model whch reflects the stuaton of market supply and demand. Ths model s based on the model of Armstrong [16]. Suppose there s a cloud computng market whch fully covered users (denoted by 1) and developers (denoted by 2). And there exst two cloud computng servces n the market denoted by cloud A and B. Cloud A s located at and cloud B s located at 1. p 1 and p 2 are the regstraton fees of users and developers on cloud ( = A B). Accordng to ther own needs preferences and economc strength users and developers select one or more cloud computng servces to purchase. Users and developers are both unformly dstrbuted on the lnear cty. t k > are the transportaton costs whch also descrbe the servces or resources dfferentaton. Suppose n 1 users and n 2 developers are snglehomng on cloud as well as n 1 users and n 2 developers are multhomng on cloud. So we can get the fact: n n n = =. (1) Utlty for some user who s located at a dstance x from cloud ( = A B) and s snglehomng on cloud s defned as follow: 1 = (n 2 n 2 ) p 1 tx (2) where α > s the cross-sde network effect parameter by developers to users on the same cloud whch descrbes the attracton of developers for users. Lkewse β > s the cross-sde network effect parameter by users to developers on the same cloud. Expresson (2) ndcates that when a user only choose cloud he wll got the cross-sde network effect by developers as well as the transportaton cost and the regstraton fee. The cross-sde network effect s equal to the cross-sde network effect parameter by developers to users multpled by the number of developers on cloud ncludng multhomng and snglehomng. The same as stated above utlty for a user who chooses both cloud A and B (.e. multhomng) s gven by: 1 = p 1 p 1 t. (3) Before the equlbrum analyss we gve the followng assumptons: Assumpton 1 t < α and k < β. Assumpton 1 ensures that users and developers are both multhomng. Accordng to expresson (3) users and developers can be multhomng only when the dfferentaton between the two clouds s less than the attractve force between users and developers. Assumpton 2 [17] 8tk < α 2 β 2 6αβ. Assumpton 2 s the necessary and suffcent condton for market equlbrum. Assumpton 3 [17] t f 1 < α+β < t f 2 1 and k f 2 < α+β < k f 2 2. Assumpton 3 ensures that the number of multhomng users falls somewhere between and so do developers. Turn to the equlbrum analyss. Accordng to the Hotellng specfcaton we have 1 = 1. x also
represents the number of snglehomng users on cloud.e. x = n 1. So puttng (2) and (3) together we can get the followng equaton: For developers n the cloud market t can also be got: tn 1 n 2 = t p 1 p 1. (4) n 1 kn 2 = k p 2 p 2. (5) Puttng (4) and (5) together the number of multhomng users and developers are gven by: n 1 = k k p 1 p 1 p 2 p 2 n 2 = t p 1 p 1 t p 2 p 2 So the number of snglehomng users and developers on cloud A are gven by: (6) Wth expresson (1) we can also have n 1 and n 2. The proft functon of cloud s expressed as: n 1 = k kp 1 p 2 n 2 = t p 1 tp 2 (7) = (p 1 f 1 )(n 1 n 1 ) (p 2 f 2 )(n 2 n 2 ) (8) where the fxed cost f = remans constant whch s spent by cloud carrers for each user or developer n a tradng. Wthout loss of generalty let f = f =. Puttng expresson (7) nto the proft functon dfferentatng the resultng functon wth respect to the prces and settng the frst order condton equal to we can get the symmetrc prces: p 1 = p 1 = t 2 p 2 = p 2 = k 2 (9) The prces are smlar to the case of snglehomng that s the two cloud carrers charge users or developers for the same prces when they are partal multhomng. And puttng (9) nto (7) the number of snglehomng users and developers on cloud A and B are n 1 = n 1 = n 1 = n 2 = n 2 = n 2 = k t (1) And the proft of cloud amounts to
= t 2 [ 2 k [ k t ] ] (11) 4. Dscusson In secton 3 the paper descrbes the prcng model of cloud computng wth partal multhomng. And n ths secton t would analyss the prcng model and the nfluence of partal multhomng on the model. For smplcty let α = β and t = k. So the prces charged by cloud carrers are translated nto: p 1 = p 1 = p 2 = p 2 = p = α t α t α (12) Based on assumpton 3 we fnd that the two clouds are of a prce for users or developers whch are smlar to the case of snglehomng. And the mpacts of the cross-sde network effect and transportaton cost on the prce level are also the same. Proposton 1 If users and developers are partal multhomng the prces are nversely proportonal to the cross-sde network effect and are drectly proportonal to the transportaton cost. The optmal market shares of two cloud computng servces are: t 2 α 2 n 1 = n 1 = n 2 = n 2 = t α t α n 1 = n 2 = α t t α t α t α (13) It proves that when the cloud market s n equlbrum the two clouds would wn the same number of users (or developers) whch s more than half of users (or developers). Proposton 2 If users and developers are partal multhomng the prces of users (or developers) charged by the two clouds are the same; and the two cloud carrers have the same and more than half of users (or developers). Then by expresson (13) t can get that there are users (or developers) who are multhomng. Enhancng the cross-sde network effect or decreasng the degree of dfference among cloud computng servces can ncrease the number of multhomng users (or developers) n the market. Proposton 3 In a competton market wth partal multhomng users (or developers) are multhomng; and the number of multhomng users (or developers) rses proportonately to the cross-sde network effect and s n nverse proporton to the transportaton cost. In addton the carrers proft s translated nto: = = = α 2 t t α t α t α (14) 2 We can get < and >. It turns out that the profts cloud carrers ganed rse wth the ncreasng α of the dfferentaton level of servces and reduce wth the enhancng of the cross-sde network effect. Thus cloud carrers can mprove ther profts by ncreasng dfferentaton wth compettors. The followng part of ths secton wll analyze the effect of partal multhomng on the prcng strategy n the compettve market.
Frst of all the effect of partal multhomng s reflected n two sdes-the scale of users and developers. In the case of snglehomng the two cloud carrers equally splt the market shares. Accordng to proposton 1 and proposton 2 n the case of partal multhomng the carrers also have the same market shares. But they get users (or developers) rase. Secondly compare the prces and carrers profts between the case of snglehomng and partal multhomng. Accordng to the reference [6] when users and developers are snglehomng the regstraton fee s p = t α and the carrers proft s = t α. Compare the two knds of prces and profts p p = 2 α 2 α > and = [ +α α ] α Proposton 4 In a competton cloud computng market the prces for users and developers n the case of snglehomng are hgher than those n the case of partal multhomng as well as the carrers profts. Secton 1 of the paper has mentoned that users and developers n cloud computng servce market would choose to purchase more than one cloud. And one of the reasons s that the prce s reasonable and acceptable. Proposton 4 s fully n lne wth the fact. Only when the prce s low enough customers wll shft from purchasng one cloud to choosng more clouds. Proposton 4 also shows that the behavor of partal multhomng cloud reduce the carrers profts. That s to say carrers can obtan more profts when users and developers are snglehomng. Ths s also n accord wth the fact. In commercal operaton of cloud computng servce carrers would tend to take varous ways to prevent multhomng whch s known as the exclusve behavors [18]. 5. Concluson Over the past decade cloud computng has won tremendous success. As the commercal mplementaton of other utlty computng such as grd computng parallel computng and dstrbuted computng cloud computng has ts own economc attrbutes. Currently some scholars have begun the study of commercal operaton and prcng strategy on cloud. Based on the former references the paper studes the prcng model and busness operatng strategy of cloud computng servce by usng the theory of two-sded markets and analyzes the mpact of partal multhomng on the prces and profts. The study ndcates that partal multhomng can expand the market shares carrers have and there exst users and developers to purchase more than one cloud computng servce; the ncreasng of the cross-sde network effect or the decreasng of dfferentaton among cloud can enlarge the number of multhomng users (or developers); partal multhomng would lead to a lower prces and profts. As stated above the carrers profts n the case of snglehomng are more than those n the case of partal multhomng. So n order to obtan hgher profts cloud carrers need to take measures to restran the behavor of multhomng. Cloud carrers sgn a contract wth the customer who want use ther servces or resources and te hm down to the contract. By mprovng the features of ther servces and products cloud carrers can wden the gap wth others retan customer by mantanng customer satsfacton and mprovng customer loyalty. Acknowledgements >. Ths paper s supported by Natonal Key Technology Research and Development Program of the Mnstry of Scence and Technology of Chna under Grant No. 212BAH19F4 and the Fundamental Research Funds for the Central Unverstes under Grant No. 12D1818. References [1] Armbrust M Fox A Grffth R et al. A vew of cloud computng[j]. Communcatons of the ACM 21 53(4): 5-58.
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