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Pricing Model of Cloud Computing Service with Partial

Multihoming

Zhang Rui

1

, Tang Bing-yong

1 1

.Glorious Sun School of Business and Managment, Donghua University, Shanghai 200051,

China

E-mail:rui5028369@mail.dhu.edu.cn

Abstract

Currently the articles about pricing strategy and business operation of cloud computing are rare, and most of these articles focus on the discussion of the prices given by industry leaders or the improvement in these prices, which cannot reflect market supply and demand as well as customers’ needs. By using the theory of two-sided markets, this paper analyzes the pricing model and operating strategy of cloud computing with partial multihoming, and compares with previous studies to explore the impact of partial multihoming on carriers’ strategy. The results show that when users and developers are partial multihoming, carriers will eventually occupy the same market shares, but the market shares are expanded; the number of multihoming users (or developers) would increase by the enhancing of the cross-side network effect or the decreasing of the services or resources differentiation among various cloud computing services; the behavior of partial multihoming may reduce the prices and profits of carriers. So in commercial operation, carriers should take measures to reduce the number of multihoming customers.

Keywordscloud computing service, partial multihoming, pricing

1. Introduction

In the recent decade, cloud computing has been flourishing in the world. As a new utility computing mode, its core is to submit computing resources, storage resources, and network resources expressed in the form of virtualization and automated through the internet. The emergence of cloud computing has changed the traditional way that IT resources have used, and combined grid computing, virtualization technology, SaaS and other technologies together.

Compared with the traditional computing modes, cloud computing has the following advantages: (1) With a “pay-as-you-go” economic model, customers only need to pay for the services or resources that they just need and use, and save carriers’ capital investment and operating expenses; (2) These services and resources on cloud are provided by third-party companies, which can be used by customers anywhere and anytime [1]. So it attracts plenty of great tycoons such as Google, IBM, Microsoft, SUN, which expand into the new market. So are a number of small and medium-sized enterprises. Currently, government, research institutions and industry leaders are eager to adopt cloud computing to solve the problems in computing and storage [2]. There is no doubt that cloud computing is the development direction of the next generation internet technology. Cloud computing will change the traditional business method, and bring a huge commercial value. However, its success in business largely depends on the rational pricing mechanism [3].

So far, every cloud computing carrier has its own pricing scheme. Amazon AWS use tiered pricing to charge their customers. For example, Amazon EC2 provides customers with the VM service at the price of 1 dollar per hour over a period of time [4]. Google App Engine and FlexScale select a pricing model of

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pay per use to charge services and resources, i.e. customers need to pay for the use of service which is based on units with fixed prices. Subscription price as the most commonly pricing model in SaaS, means that customers sign a contract based on a fixed price and a constant period of time to use the services and resources on cloud, such as annual fee or monthly rent. In addition, Amazon EC2 has recently adopted a new dynamic pricing-“spot instance pricing” (current auction price), which would adjust to the changes in market supply and demand [5]. However, fixed pricing is always the dominant form of cloud computing pricing today. Customers (including users and providers) prefer to accepting and using fixed pricing model because of its simplicity and convenience. Nevertheless, for high-value services, it is necessary to find a more suitable pricing model, which can reflect the changes in supply and demand. In trying to address the above problems, this paper attempts to use the theory of platform economics and the pricing model of two-sided markets to build the dynamic pricing of cloud computing services, in order to reflect market changes, and maximize the expected revenues of carriers and the expected utilities of customers.

In the previous works [6,7], we addressed the pricing model of cloud computing in Hotelling model and singlehoming customers. In this work, we extend the analysis to consider the setting, where customers are partial multihoming, i.e. some customers purchased more than one cloud computing service.

The remainder of this paper is organized as follows: in section 2, we summarize related work. In section 3, we present a dynamic pricing model with partial multihoming based on Hotelling specification. Section 4 discusses the main factors that affect the pricing model, the behavior of partial multihoming, and its influences on carriers’ prices and revenues. Finally, section 5 concludes the paper.

2. Related work

With the rapid development of cloud computing, scholars also put more attention into it, and many studies have been made. These studies involve the concepts and key technologies of cloud computing, the construction of cloud, cloud security and other aspects. And there also exist a lot of literatures about the innovation and practical of cloud computing. In recent years, there is a major new trend to study the business value and pricing strategies on cloud computing.

Yeo, et al. [8] point out that fixed pricing has been unable to meet different customers’ needs, and dynamic pricing can not only satisfy customers but also bring high profits for carriers. Christof, et al. [9] present a cloud business model Framework, which can be divided into three layers as the technical layers in cloud. Zhu et al. [10] argue that distinguishing from the previous computing paradigms, cloud computing creates a new business model and a remarkable commercial value. In addition to the analysis of existing pricing models of cloud computing, many other scholars meet the problems of the existing pricing models by giving the improved models. Hadji, et al. [11] hold that the pricing model of cloud computing should be enable to maximize carriers’ revenue as well as customers’ utilities. And they also propose a theoretical model based on Stackelberg game and a Stackelberg/Nash equilibrium solution. Mihailescu, et al. [12] propose a dynamic pricing model on federated clouds by considering the forces of demand and supply. They also draw that dynamic pricing can increase the success rate of business deals by comparing the static pricing model with the dynamic model. Few researchers have studied Amazon spot price traces and built improved models around that. Buyya, et al. [13] analyze one year price history of Amazon’s spot instances in four data centers of Amazon’s EC2, and build a statistical model to capture the spot prices in the data centers. Sowmya, et al. [14] use the game theory to build a pricing model in a spot market and analyze real time data from Amazon EC2 market to validate the model. However, there are some drawbacks of spot instance, such as untruthful bidding and unfair resource allocation. In regard to these problems, Wang, et al. [15] propose a computationally efficient auction-style pricing mechanism which can ensure the balanced distribution of resources, and improve carrier's overall revenues.

3. The model

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This model is based on our previous study [6], which regards cloud computing service as a two-sided market, and the two sides are divided into two types: users and developers. Those models are built by Hotelling specification. However, the previous study only considers that users and developers are singlehoming, i.e. one user or one developer only chooses one cloud computing service to purchase. But in an actual market, each cloud computing carriers exhibited differences in services or products. And if the price is reasonable and favorable enough to users, some users hope for contacting with more developers and get more services by purchasing more than one cloud computing service. And developers also want to get more users to trade. So some users and developers would join two or more clouds, i.e. users and developers are partial multihoming.

This paper takes account of charging users and developers a registration fee, which is similar to subscription price. But subscription price is often made by carriers. And the pricing model of this paper is a dynamic pricing model, which reflects the situation of market supply and demand.

This model is based on the model of Armstrong [16].

Suppose there is a cloud computing market which fully covered users (denoted by 1) and developers (denoted by 2). And there exist two cloud computing services in the market, denoted by cloud A and B. Cloud A is located at 0 and cloud B is located at 1. p1i and p2i are the registration fees of users and

developers on cloud i (i = A, B). According to their own needs, preferences and economic strength, users and developers select one or more cloud computing services to purchase. Users and developers are both uniformly distributed on the linear city. t, k > 0 are the transportation costs which also describe the services or resources differentiation. Suppose n1i users and n2i developers are singlehoming on cloud i,

as well as n10 users and n20 developers are mulithoming on cloud i. So we can get the fact:

n n0 n = = , . (1)

Utility for some user who is located at a distance xi from cloud i (i = A, B) and is singlehoming on cloud i is defined as follow:

1i = (n2i n20) p1i txi, (2)

where α> 0 is the cross-side network effect parameter by developers to users on the same cloud, which describes the attraction of developers for users. Likewise, β> 0 is the cross-side network effect parameter by users to developers on the same cloud.

Expression (2) indicates that when a user only choose cloud i, he will got the cross-side network effect by developers, as well as the transportation cost and the registration fee. The cross-side network effect is equal to the cross-side network effect parameter by developers to users multiplied by the number of developers on cloud i, including multihoming and singlehoming.

The same as stated above, utility for a user who chooses both cloud A and B (i.e. multihoming) is given by:

1

0= p

1 p1 t. (3)

Before the equilibrium analysis, we give the following assumptions:

Assumption 1 t < 𝛼 and k < 𝛽.

Assumption 1 ensures that users and developers are both multihoming. According to expression (3), users and developers can be multihoming only when the differentiation between the two clouds is less than the attractive force between users and developers.

Assumption 2[17] 8tk <α2 β2 6αβ.

Assumption 2 is the necessary and sufficient condition for market equilibrium.

Assumption 3[17] t f1<α+β

2 < 𝑡 f1 and k f2< α+β

2 < k f2.

Assumption 3 ensures that the number of multihoming users falls somewhere between 0, , and so do developers.

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represents the number of singlehoming users on cloud i, i.e. xi= n1i. So putting (2) and (3) together, we can get the following equation:

tn10 n20= t p1 p1 . (4)

For developers in the cloud market, it can also be got:

n10 kn20= k p2 p2 . (5)

Putting (4) and (5) together, the number of multihoming users and developers are given by:

{ n10= k kt k p1 p1 p2 p2 kt , n20= t kt p1 p1 t p2 p2 kt (6)

So the number of singlehoming users and developers on cloud A are given by:

{ n1 = kt k kp1 p2 kt , n2 = kt t p1 tp2 kt (7)

With expression (1), we can also have n1 and n2.

The profit function of cloud i is expressed as:

i= (p 1 i f

1)(n1i n10) (p2i f2)(n2i n20), (8)

where the fixed cost f = , remains constant, which is spent by cloud carriers for each user or developer in a trading. Without loss of generality, let f =f = 0.

Putting expression (7) into the profit function, differentiating the resulting function with respect to the prices and setting the first order condition equal to 0, we can get the symmetric prices:

{ p1 = p1 = kt t 2 kt , p2 = p2 = kt k 2 kt (9)

The prices are similar to the case of singlehoming, that is, the two cloud carriers charge users or developers for the same prices when they are partial multihoming.

And putting (9) into (7), the number of singlehoming users and developers on cloud A and B are

{ n1 = n1 = n10 = kt k kt kt kt , n2 = n2 = n20 = kt t kt kt kt (10)

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i= kt t 2 kt [ kt k kt kt kt ] kt k 2 kt [ kt t kt kt kt ] (11)

4. Discussion

In section 3, the paper describes the pricing model of cloud computing with partial multihoming. And in this section, it would analysis the pricing model and the influence of partial multihoming on the model.

For simplicity, let α=β and t = k. So the prices charged by cloud carriers are translated into:

p1 = p1 = p2 = p2 = p =

α t α

t α (12)

Based on assumption 3, we find that the two clouds are of a price for users or developers, which are similar to the case of singlehoming. And the impacts of the cross-side network effect and transportation cost on the price level are also the same.

Proposition 1 If users and developers are partial multihoming, the prices are inversely proportional to the cross-side network effect, and are directly proportional to the transportation cost.

The optimal market shares of two cloud computing services are:

{ n1 = n1 = n2 = n2 = t2 α2 t α t α , n10= n20= α t t α t α t α (13)

It proves that when the cloud market is in equilibrium, the two clouds would win the same number of users (or developers), which is more than half of users (or developers).

Proposition 2 If users and developers are partial multihoming, the prices of users (or developers) charged by the two clouds are the same; and the two cloud carriers have the same and more than half of users (or developers).

Then, by expression (13), it can get that there are +α 2 +α

α 2 α users (or developers) who are multihoming.

Enhancing the cross-side network effect or decreasing the degree of difference among cloud computing services can increase the number of multihoming users (or developers) in the market.

Proposition 3 In a competition market with partial multihoming, +α 2 +α

α 2 α users (or developers) are

multihoming; and the number of multihoming users (or developers) rises proportionately to the cross-side network effect, and is in inverse proportion to the transportation cost.

In addition, the carriers’ profit is translated into:

= = = α2t t α

t α t α 2 (14)

We can get

α< 0 and > 0. It turns out that the profits cloud carriers gained rise with the increasing

of the differentiation level of services, and reduce with the enhancing of the cross-side network effect. Thus, cloud carriers can improve their profits by increasing differentiation with competitors.

The following part of this section will analyze the effect of partial multihoming on the pricing strategy in the competitive market.

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First of all, the effect of partial multihoming is reflected in two sides-the scale of users and developers. In the case of singlehoming, the two cloud carriers equally split the market shares. According to proposition 1 and proposition 2, in the case of partial multihoming, the carriers also have the same market shares. But they get +α 2 +α

α 2 α users (or developers) raise.

Secondly, compare the prices and carriers’ profits between the case of singlehoming and partial multihoming. According to the reference [6], when users and developers are singlehoming, the registration fee is p = t α and the carriers’ profit is = t α. Compare the two kinds of prices and profits, p p =2 α

2 α > 0 and

=[ +α α ] α +α 2 α > 0.

Proposition 4 In a competition cloud computing market, the prices for users and developers in the case of singlehoming are higher than those in the case of partial multihoming, as well as the carriers’ profits.

Section 1 of the paper has mentioned that users and developers in cloud computing service market would choose to purchase more than one cloud. And one of the reasons is that the price is reasonable and acceptable. Proposition 4 is fully in line with the fact. Only when the price is low enough, customers will shift from purchasing one cloud to choosing more clouds. Proposition 4 also shows that the behavior of partial multihoming cloud reduce the carriers’ profits. That is to say, carriers can obtain more profits when users and developers are singlehoming. This is also in accord with the fact. In commercial operation of cloud computing service, carriers would tend to take various ways to prevent multihoming, which is known as the exclusive behaviors [18].

5. Conclusion

Over the past decade, cloud computing has won tremendous success. As the commercial implementation of other utility computing, such as grid computing, parallel computing and distributed computing, cloud computing has its own economic attributes. Currently some scholars have begun the study of commercial operation and pricing strategy on cloud. Based on the former references, the paper studies the pricing model and business operating strategy of cloud computing service by using the theory of two-sided markets, and analyzes the impact of partial multihoming on the prices and profits. The study indicates that partial multihoming can expand the market shares carriers have, and there exist α 2 +α +α 2 α users and developers to purchase more than one cloud computing service; the increasing of the cross-side network effect or the decreasing of differentiation among cloud can enlarge the number of multihoming users (or developers); partial multihoming would lead to a lower prices and profits. As stated above, the carriers’ profits in the case of singlehoming are more than those in the case of partial multihoming. So in order to obtain higher profits, cloud carriers need to take measures to restrain the behavior of multihoming.

 Cloud carriers sign a contract with the customer who want use their services or resources, and tie him down to the contract.

 By improving the features of their services and products, cloud carriers can widen the gap with others, retain customer by maintaining customer satisfaction and improving customer loyalty.

Acknowledgements

This paper is supported by National Key Technology Research and Development Program of the Ministry of Science and Technology of China under Grant No. 2012BAH19F04 and the Fundamental Research Funds for the Central Universities under Grant No. 12D10818.

References

[1] Armbrust M, Fox A, Griffith R, et al. A view of cloud computing[J]. Communications of the ACM, 2010, 53(4): 50-58.

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[2] Sharma B, Thulasiram R K, Thulasiraman P, et al. Pricing cloud compute commodities: a novel financial economic model[C]. Proceedings of the 2012 12th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (ccgrid 2012). IEEE Computer Society, 2012: 451-457. [3] Christof W, Arun A, Benjamin B, et al. Cloud computing - a classification, business models, and

research directions[J]. Business Models & Information Systems Engineering, 2009, 5: 391-399. [4] Amazon Web Services.http://aws.amazon.com/cn/. 2013/6/16.

[5] Xu H, Li B. Maximizing revenue with dynamic cloud pricing: The infinite horizon case[C]. Communications (ICC), 2012 IEEE International Conference on IEEE, 2012: 2929-2933.

[6] Zhang R, Tang B Y. Comparison of three different pricing models for cloud computing services[J].

Advances in Information Sciences and Service Sciences, 2013, 5(4): 379-386.

[7] Zhang, R, Song, X L, Tang, B Y. (2013) Pricing Strategy of Cloud Computing Based on Two-Part Tariff. In: Journal of Natural Science of Heilongjiang University. 30(2): 1-7.

[8] Yeo C. S., Venugopal S., Chu X., et al. Autonomic metered pricing for a utility computing service[J].

Future Generation Computer Systems, 2010, 26(8): 1368-1380.

[9] Christof W, Arun A, Benjamin B, et al. Cloud computing - a classification, business models, and research directions[J]. Business Models & Information Systems Engineering, 2009, 5: 391-399. [10] Zhu J, Fang X, Guo Z, et al. IBM cloud computing powering a smarter planet[M]. Cloud

Computing. Springer Berlin Heidelberg, 2009: 621-625.

[11] Hadji M, Louati W, Zeghlache D. Constrained Pricing for Cloud Resource Allocation[C]. Network Computing and Applications (NCA), 2011 10th IEEE International Symposium on. IEEE, 2011: 359-365.

[12] Mihailescu M, Teo Y M. Dynamic Resource Pricing on Federated Clouds[C]. Proceedings of the 2010 10th IEEE/ACM International Conference on Cluster, Cloud and Grid Computing. Washington, DC: IEEE Computer Society, 2010: 513-517.

[13] Javadi B, Thulasiramy R K, Buyya R. Statistical modeling of spot instance prices in public cloud environments[C]. Utility and Cloud Computing (UCC), 2011 Fourth IEEE International Conference on. IEEE, 2011: 219-228.

[14] Sowmya K, Sundarraj R P. Strategic Bidding for Cloud Resources under Dynamic Pricing Schemes[C]. Cloud and Services Computing (ISCOS), 2012 International Symposium on. IEEE, 2012: 25-30.

[15] Wang Q, Ren K, Meng X. When cloud meets eBay: Towards effective pricing for cloud computing[C]. INFOCOM, 2012 Proceedings IEEE. IEEE, 2012: 936-944.

[16] Armstrong M. Competition in two-sided markets[J]. The RAND Journal of Economics, 2006, 37(3): 668-691.

[17] Zhang K, Li X Y. Competitive model in two-sided markets with partial overlapping operations[J]. Systems Engineering-Theory & Practice, 2010, 30(6): 961-970.

[19] Ji Hanlin. Research of Pricing Strategy of Two-Sided Markets[D]. Fudan University, Shanghai, 2006.

References

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