Elsevier

Performance Evaluation

Volume 92, October 2015, Pages 40-50
Performance Evaluation

Equilibrium in cloud computing market

https://doi.org/10.1016/j.peva.2015.07.002Get rights and content

Abstract

The emerging market of public and private cloud infrastructure benefits the end users, as it reduces their costs, introduces new efficient services and provides variety of products. End-users primary deal with private clouds or brokers, which serve all the users needs, and if needed, buy extra capacity from public cloud. In this paper we study such a three-level market structure. Our goal is to find Nash equilibrium of prices in this market as well as market influence on the end users. We observe that new resources at public clouds positively affect the market from the end-user perspective. Additionally our observation indicates that the switching cost plays an important role in achieving the optimal point in average market price value, and thus reduction of the switching costs will benefit end-users even more. Thus the results imply that standardization of the interfaces and interoperability between various clouds increases market efficiency.

Introduction

The increasingly perceived vision of cloud computing as utility like electricity or telephony creates great challenges to the development of the emerging market structures and related ecosystems. The history has shown that separation of network and service has increased competition in, former monopoly, energy and mobile-communications industries. When diverse new service companies entered into markets network companies had to cut their fees significantly. Additionally, the introduction of the number portability by the regulators of the telecommunications market has increased competition which resulted in declining customer loyalty and increased churn rates. The markets perform in these industries more efficiently because of increased interoperability and lower switching costs.

The public cloud computing market is still dominated by the services based on proprietary platforms and customer interfaces  [1]. Under these kind of circumstances the customer expose switching costs and lock in to the cloud service provider  [2]. Another significantly observed problem, which hinders the proliferation of cloud computing, is related to trust issues between service providers and their customers  [3]. Software as a Service (SaaS) providers can easily lose their reputation, if the underlying Infrastructure as a Service (IaaS) infrastructure creates Quality of Service (QoS) or privacy related problems.

Hybrid or federated cloud is a promising architecture to the market oriented cloud ecosystems. In this context public cloud with unlimited capacity provides a solution to handle unexpected traffic peaks of variable Internet traffic and private cloud capacity for typical load. It has been discovered that optimal cost structure occurs in certain IaaS applications when 40% computation is in private cloud and 60% in public cloud  [4]. Additionally the hosting of private cloud can be outsourced to a broker, which is connected to the public clouds.

Currently there are significant efforts to standardize customer interfaces of public cloud in order to realize better interoperability between various clouds. In this paper we introduce a game-theoretical model, which describes the behavior of a hybrid cloud market. Additionally based on simulation we explore the effect of interoperability on the market efficiency. In particular we concentrate on the effect of the number of market players, switching cost and pricing.

The rest of the paper is organized as follows. In Section  2 we provide the related work in the field. Section  3 is dedicated to the three-layer market model. In Section  4 we analyze theoretically and study numerically the proposed model. In Section  5 we discuss the impact of switching cost on our model as well as the further development of the model. Finally, Section  6 concludes the paper.

Section snippets

Related work

Real workloads are very heterogeneous, and thus designing an optimal computing cluster is a difficult task. A hybrid cloud is a promising solution to meet the varying computing needs. In this approach the base load can be managed with a private cloud, while the excessive peaks can be redirected to a public cloud. However, the hybrid cloud architecture has a few major design challenges. First of all the load balancing algorithm must be fast, scalable, adaptive and robust  [5]. Secondly, the

Market model

First, we formulate market model which we consider in this work. For that let us introduce three main roles which are present in the cloud market today, namely, (i) end-users, (ii) broker cloud service providers, and (iii) public cloud service providers (see Fig. 1). Public cloud service providers (CSPs) are the big companies which sell their cloud capacity to individual clients or other CSPs. Conventionally, they are assumed to have large enough amount of resources which were provisioned for

Analysis

In this section we introduce the game-theoretical model and prove that it has stable points in terms of Nash equilibrium. Later, the analysis is reduced to two-player game and symmetric games. Finally, numerically, we will study hybrid cloud market behavior based on general examples.

Switching costs

Let us assume that in the cloud computing market there is only one public cloud PuC1. PrCs request for resources from PuC1 if the demand is sufficiently large. Suppose that at some moment a new PuC2 appears on the market (L2<L1, so that the new public cloud is more beneficial for PrCs) and some PrCs prefer to switch from PuC1 to PuC2. Let the equilibrium prices before the change be p (pi for ith PrC). Then we should consider p as an initial profile for the system with a new PuC. We also

Conclusion

As a result we list here our findings. First we have constructed a game-theoretical model for emerging a three-level hybrid cloud market. In this market, users at the bottom are the main recipients for cloud services. Above them are two levels of clouds: (i) public clouds which provide general resources at high capacity and low costs, and (ii) private clouds which provide services to the end-users, and if needed buy extra resources for their services from public clouds. We have found potential

Acknowledgments

The authors would like to thank Yrjö Raivio for his help at an early stage of the article. He provided valuable input for the research. Vladimir Mazalov was supported by the Mathematical Department of Russian Academy of Sciences and Russian Humanitarian Science Foundation (project 15-02-00352).

V. Mazalov is Research Director at the Institute of Applied Mathematical Research, Karelian Research Center, Russian Academy of Sciences. He is also Professor of the Probability Theory Department at Petrozavodsk State University. He finished his Ph.D. studies at the Faculty of Applied Mathematics, Leningrad University in 1979. After that he has mainly worked in research projects funded by the Russian Academy of Sciences, in 1980–1998 at the Chita Institute of Natural Resources, East Siberia

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  • Cited by (9)

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    V. Mazalov is Research Director at the Institute of Applied Mathematical Research, Karelian Research Center, Russian Academy of Sciences. He is also Professor of the Probability Theory Department at Petrozavodsk State University. He finished his Ph.D. studies at the Faculty of Applied Mathematics, Leningrad University in 1979. After that he has mainly worked in research projects funded by the Russian Academy of Sciences, in 1980–1998 at the Chita Institute of Natural Resources, East Siberia and, currently, at the Institute of Applied Mathematical Research, Karelian Research Center. His research interests are related with game theory and stochastic analysis and applications in behavioral biology, networking and economical systems. He was a supervisor of 20 Ph.D. Thesis. He is an editorial board member of International Game Theory Review, International Journal of Mathematics, Game Theory and Algebra, Scientiae Mathematicae Japonicae. He has published more than 100 publications in international conferences, journals and books and been awarded many competitive grants such as SNSF (Switzerland), JSPS (Japan), DAAD (Germany), Swedish Institute and Russian Fund for Basic Research.

    A. Lukyanenko received first M.Sc. degree in 2005 from University of Kuopio (Computer Science), second M.Sc. degree in 2005 from Petrozavodsk State University (Mathematics) and Ph.D. degree (Computer Science) from University of Helsinki in 2010. From 2006 until 2010, he was a researcher at networking group in Helsinki Institute for Information Technology (HIIT). Starting 2010, he is a postdoctoral researcher at Aalto University, in Datacommunication software group. During 2013 he was on research visit to ICSI/UC Berkeley. He worked on problems related to backoff protocols in IEEE802.11, security with host identity protocol (HIP), problems of denial-of-service attacks and reputations in peer-to-peer networks. His research interests include information-centric networking, datacenters architecture, in-network caching mechanisms, and future Internet technologies. During his research, he actively uses game theory, queuing theory and data analysis methods.

    S. Luukkainen took his D.Sc. at Helsinki University of Technology. In the 1990’s he worked in the Technical Research Centre of Finland, where he directed the Multimedia Communications research group. He also has practical managerial experience in technology companies of the telecommunications industry. Currently he is responsible at Aalto university for the Networking Business education program, which combines business and technology studies in the telecommunications field. Mr. Luukkainen’s research interests include technology innovation management and commercialization of new network services.

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