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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
$ 0.00
$ 20.00
$ 40.00
$ 60.00
2009 2014
$ 13.10
$ 40.50
billions
Worldwide SaaS Market Size
Source: IDC
25.3% CAGR Through 2014
Clients
SaaS
Provider
IaaS Provider
Request for Cloud
ERP Service
Cloud ERP
Response
Process/Reject
Cloud CRM
Other
Software
Application
Admission
Control
Scheduling
Platform Layer
Application Layer
Request/Response on VMs Schedule on VMs
VM
VM
ServersDatacenter
m =
E[R1]
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][ ii REm =
S =
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sn
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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
Vp = Vij ´si ´sj
j
å
i
å
• 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