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The rapid growth in popularity of cloud computing and increased competition in cloud market have significantly changed the requirements for the quality of services provided.In order to provide the high quality of service and to increase the profit of cloud providers we suggest that providers should form and put on the market a certain set of cloud services based on cloud services demand.In this paper we recommend SaaS-providers to use the basic principles proposed by Markowitz to generate the optimal portfolio of cloud services.

INTRODUCTION

The process of cloud service providing is based on three-tiered architecture. The key role in this structure belongs to the cloud service provider. He offers a certain set of ready-to-use solutions – SaaS-applications that work on virtual platforms to his clients. The second tier is client, who buys these services. The third tier is infrastructure vendor who leases the hardware, operating systems, system software and middleware to SaaS-providers.

BACKGROUND

• In this section we want to formulate cloud services portfolio formation problem, applying Markowitz portfolio theory. We assume that this approach can result in the increase in providers’ profits and ensure higher quality of servicing. To illustrate the method, we suppose that service provider has n services at his disposal and can form a certain portfolio of the services available. Each service has an expected return of Ri. Expected returns can be given or calculated using historical returns on services.

• Returns of all services in the portfolio form the vector of expected returns:

where - expected return on service i.• We suppose that si – the amount of capital to be invested in the service

i, portfolio of services can be represented as following vector:

• Given this, now we are going to find a vector of service weights that minimizes the risk of the portfolio:

MARKOWITZ’S PORTFOLIO THEORY APPLICATION FOR CLOUD SERVICE OPTIMIZATION

Table 3. Historical Data on Returns for the Services

Table 4. Covariance Matrix

CONTACTS

Function cov from the standard function library of MATLAB allows computing covariance matrix that shows degree of dependence between services profitability rates.

CONCLUSIONS• Each portfolio that lies on efficient frontier is acceptable for the

service provider because its expected return reaches maximum within given level of risk and its risk reaches minimum within given level of expected return.

• Selection of a certain portfolio from this efficient set depends on provider’s individual risk assessment that we have mentioned before. For instance, provider may decide to select the optimal portfolio that provides highest profitability or he can pick the portfolio that has the lowest risks.

Victor Romanov1, Alexandra Varfolomeeva1, Eugeniya Blinnikova1

Department of Computer Science, Russian Plekhanov University of Economics, Moscow, Russian Federation

The Cloud Services Portfolio Optimization based on Markowitz’s Model

2009 2014$ 0.00

$ 10.00$ 20.00$ 30.00$ 40.00$ 50.00

$ 13.10

$ 40.50

billions

Worldwide SaaS Market SizeSource: IDC

25.3% CAGR Through 2014

Service Number Service Name

Service 1 HRM

Service 2 Document Management

Service 3 Task Management

Service 4 CRM

Service 5 Finance and Accounting

№ Week Service-1 Service-2 Service-3 Service-4 Service-5

1 20,34 33,17 14,72 27,54 77,87

2 13,28 26,23 12,83 24,89 74,12

3 29,34 35,56 13,55 24,67 68,13

4 12,12 36,78 13,12 35,37 59,22

5 23,16 34,49 14,12 37,76 74,12

6 14,12 34,13 12,57 35,34 75,17

7 18,56 23,19 12,45 38,38 74,12

8 12,45 35,56 13,12 34,13 68,13

9 13,12 36,78 11,17 23,19 58,23

10 18,34 34,56 13,12 35,56 74,12

11 13,28 34,13 29,34 36,78 68,13

12 29,34 23,19 12,12 34,56 58,23

13 19,34 35,56 23,16 23,67 76,32

14 13,28 36,78 14,12 32,68 74,12

15 29,34 34,56 29,34 67,45 68,13

16 17,12 34,13 12,12 45,34 75,11

17 23,16 23,19 23,16 44,12 75,11

18 15,28 35,56 14,18 34,72 74,12

19 27,34 36,78 12,11 37,98 68,13

20 18,34 34,56 14,23 34,67 58,23

Cov Service 1 Service 2 Service 3 Service 4 Service 5

Service 1 36,4222 -6,8449 6,2102 20,8489 -2,7674

Service 2 -6,8449 22,6962 -0,5139 -4,2428 -3,1838

Service 3 6,2102 -0,5139 31,8966 26,5280 4,9002

Service 4 20,8489 -4,2428 26,5280 95,2534 2,2138

Service 5 -2,7674 -3,1838 4,9002 2,2138 43,7845

Service 1

Service 2

Service 3

Service 4

Service 5

m (expected

return)Risk

Port 1 0,2566 0,4113 0,1444 0 0,1877 33,8352 2,6281

Port 2 0,2073 0,4150 0,0170 0,0363 0,3244 41,8592 2,8583

Port 3 0,0250 0,3377 0 0,0661 0,5712 53,8951 3,9921

Port 4 0 0,1885 0 0,0304 0,7811 61,9190 5,1697

Port 5 0 0 0 0 1 69,9430 6,6170

# Components of ERP-system

Traditional company SaaS-provider

1 Manufacturing Manufacturing of goods

Processing of incoming queries

2 Inventory Goods Data

3 Suppliers Supply of required raw materials

Infrastructure vendors

4 Customers Consumers of manufactured goods SaaS-clients

5 Marketing Marketing of goods Service marketing

6 Profit Profit from selling goods

Profit from providing services

Table 1. Comparison of Traditional Company with Cloud Service Provider

• Harry Markowitz introduced the theory of formulating the optimal investment portfolio in 1952.

• In his article Markowitz suggested probabilistic formalization of risk and return associated with particular asset, thus formulating portfolio construction problem in strict mathematical terms.

• He was the first who proposed portfolio diversification and suggested how investors could reduce standard deviation of portfolios’ profitability by choosing assets that have different price changing mechanism.

Table 2. List of the Services Provided

• Traditional Markowitz model imposes two constraints:1. The capital of the service provider should be fully invested (sum of services weights

equals 1)2. Minimization problem is to find a portfolio that has minimum variance for the given

expected return

Fig.1. Markowitz Efficient Frontier

Table 5. The List of Portfolios from the Efficient Set of Portfolios.

Implying frontcon function without arguments we plotted an efficient frontier that is shown on Figure 1. Portfolios that lay on this efficient frontier illustrate the efficient set of portfolios.

{victorromanov1, aovarfolomeeva, ij.9393}@gmail.com