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Much effort has been made to provide a Cloud Computing (CC) autonomic management. Thus, related works are discussed and the need of a full autonomic model with stakeholders is presented. Moreover, this paper introduces a full model of cloud environment to support decision making in autonomic systems. This model is based on an economic utility view of cloud computing, control theory and autonomic computing. It innovates by introducing the concept of conjuncture and imaginary elements (essential elements to forecast and to a non-stationary model). Mathematical modeling is used to formally define a model and a model implementation overview is given.
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Decision-Theoretic Model to Support Autonomic Cloud Computing
Alexandre Augusto Flores, Rafael de Souza Mendes, Gabriel Beims Bräscher, Carlos Becker Westphall, Maria
Elena Villareal
Department of Informatics and Statistics
Federal University of Santa Catarina
Florianopolis, Brazil
e-mail: alexandre.flores@posgrad.ufsc.br; rafaeldesouzamendes@gmail.com; brascher@lrg.ufsc.br; westphal@inf.ufsc.br;
maria@lrg.ufsc.br
Abstract Much effort has been made to provide a Cloud
Computing (CC) autonomic management. Thus, related works
are discussed and the need of a full autonomic model with
stakeholders is presented. Moreover, this paper introduces a
full model of cloud environment to support decision making in
autonomic systems. This model is based on an economic utility
view of cloud computing, control theory and autonomic
computing. It innovates by introducing the concept of
conjuncture and imaginary elements (essential elements to
forecast and to a non-stationary model). Mathematical
modeling is used to formally define a model and a model
implementation overview is given.
Keywords-cloud computing; autonomic computing; decision-
theoretic planning; cloud model.
I. INTRODUCTION
The widespread use of computing devices has introduced
a drastic change in the way that computing is produced,
distributed and consumed. A strong trend is the concept of
cloud computing (CC), which is basically a paradigm that
deals with economical activity of production, distribution
and consumption of computing. According to Kephart et al.
[1], the difficulty of managing computer systems goes
beyond managing software isolates. The CC dynamic
integrates heterogeneous environments and introduces new
levels of complexity, outperforming the levels of human
capacity [2]. The result is a demand by autonomics clouds.
Although many works propose the automation of CC
management, none of them has a model that represents all
the stakeholders involved.
This work presents a new CC view based on economy,
and utility leading to a useful approach to cloud
management. Using a holistic definition, we propose a model
to CC management derived from our model introduced in
[3]. This generic model can be used to subsidize many
decision-making processes and is presented using a
mathematical modeling of principal elements and their
relationship with eachother.
This paper is organized as follows. Section II addresses
the relevant literature and presents our view of CC. Section
III presents CC needs for autonomic management based on
related works. Section IV describes our proposed model with
mathematical representations and presents a simplified class
diagram. Finally, we draw conclusions and suggest
possibilities for future research.
II. LITERATURE REVIEW
A. Cloud Computing definition
In this section, we will introduce three CC definitions
chronologically. Those references brief our view of the
evolution of CC definition over the last years.
Foster et al. [4] have an interesting definition for CC: a
widely distributed computing paradigm driven by
economies of scale, in which a pool of abstracted,
virtualized, dynamically-scalable, managed computing
power, storage, platforms, and services are delivered on
demand to external customers over the Internet.
Fosters definition is relevant mainly for two reasons:
Firstly, he defines CC as a paradigm, and secondly,
understands the economic influence at cloud
Furthermore, Buyya et al. [5] have a more complete view
which recognizes CC as a paradigm for delivering
computing resources as an utility, like gas and water.
Later, the National Institute of Standards and Technology
(NIST) [6] defines CC as:
Cloud computing is a model for enabling ubiquitous,
convenient, on-demand network access to a shared pool of
configurable computing resources (e.g., networks, servers,
storage, applications, and services) that can be rapidly
provisioned and released with minimal management effort
or service provider interaction. This cloud model is
composed of five essential characteristics, three service
models, and four deployment models.
The five essential characteristics stated by NIST are: on
demand self-service, broad network access, resource
pooling, rapid elasticity and measurable service.
As demonstrated, CC definition has changed in the last
years from an economic view to a pragmatic and limited
understanding. NIST definition is an attempt to allow
comparisons between services. However, they recognize the
limitation and state that the service and deployment models
defined form a simple taxonomy that is not intended to
prescribe or constrain any particular method.
Because we see the CC phenomenon more like Foster et
al [4] and Buyya et al. [5], our view of CC is:
the economic activity that focuses on mass production,
distribution and consumption of computing. This computing
has abstracted logical and physical resources and
218Copyright (c) IARIA, 2015. ISBN: 978-1-61208-398-8
ICN 2015 : The Fourteenth International Conference on Networks
prominent commercial frontiers between the stakeholders
who produce and consume it.
B. Autonomic Computing
The autonomic computing (AC) concept is based in the
human autonomic nervous system that governs our heart
rate and body, thus freeing our conscious brain from the
burden of dealing with these and many other low-level, yet
vital, functions [1]. The overall goal of Autonomic
Computing is the creation of self-managing systems; these
are proactive, robust, adaptable and easy to use.
Figure 1. IBM's MAPE-K reference model for autonomic control [6]
A fundamental element that figure in AC bibliography is
the MAPE-K con trol cycle (Figure 1), that consists in
Monitor, Analyze, Plan, Execute and Knowledge elements.
For an autonomic system, as shown in [7], to be able to
perform self-management, four main abilities must be
present: self-configuration, self-optimization, self-protection
and self-healing. To achieve these objectives a system must
be both self-conscious and environment-conscious, meaning
that it must have knowledge of the current state of both
itself and its operating environment.
Huebscher et al. [7] define four degrees of autonomicity
which can be used to classify autonomic managers and give
us the focus, architecturally, that it has been applied. Those
elements are:
Support: focuses on one particular aspect or component
of architecture to help improve the performance of the
complete architecture using autonomicity.
Core: the self-management function involves the core
application. It is a full end-to-end solution.
Autonomous: it is also a full end-to-end solution, but the
system is more intelligent and it’s able to self-adapts to the
environment.
Autonomic: this is the most complete level where the
interest is in higher-level human based goals like service-
level agreements (SLAs), service-level objectives (SLOs) or
business goals are taken into account.
C. Control Theory
Control theory uses engineering and mathematics to deal
with the beh avior of dynamic systems. The objective of a
control system is to make de output y behave in a desired
way by manipulating the plant (system) input u [8].
Therefore, we present the first four steps to design a
control system, stated by Skogestad [8]:
1. study the system plant to be controlled and obtain
initial information about the control objectives;
2. model the system and simplify the model if
necessary;
3. analyze the resulting model determine its properties;
4. decide which variables are to be controlled outputs;
Those steps will be mentioned furthermore as the Design
Process (DP).
Control Theory often uses transfer functions as a
representation, in terms of spatial or temporal frequency, of
the relation between the input and output of a linear system.
On the other hand, to model complex systems, such as a
multi-objetive system, Modern Control Theory often uses a
state approach instead of transformation. The systems state
is a set of values representing environm ent.
CC environment management can be classified as a
multi-objective multivariable control problem in a time-
discrete system. We can assume the dynamics of the CC
system to be controlled by several actors where each of the
actors has the aim of optimizing its results along the
trajectory determined by vectors of control parameters
chosen by all players together [9]. A stochastic approach
can be used resulting in a Stochastic Multiplayer Game
(SMG).
In this class of problem, Nash, Pareto and Stackelberg
optimization principles are often used with cooperative and
non-cooperative game-theoretic models. To deal with
complex systems control, another known strategy is to use
Markov Decision Process (MDP) to select the best sequence
of actions to been taking. Now we revise those concepts.
1) Nash Equilibrium
Nash equilibrium, proposed by John Nash [10], describes
a situation where no player can increase his payoff by
unilaterally switching to a different strategy.
2) Pareto optimal
The Pareto optimal is achieved only when a player can
become better off in the game without making any other
individual worst off.
3) Stackelberg games
A Stackelberg game solution is formulated to model a
leader-follower joint optimization problem as a two-level
optimization problem between two decision makers.
The upper-level decision maker (leader) announces his
decisions to the lower level (follower). Next, follower
makes his own decisions and then feeds decisions back to
the leader. This implicates in a mathematical program that
contains sub-optimization problems as its constraints [11].
4) Markov Decision Process
MDP is a discrete time stochastic control process. MDP
provides a mathematical modeling using decision epochs,
actions, system states, transitions functions and functions
rewards or cost functions.
Broadly speaking, MDP encodes the interaction between
an agent and its environment where every action takes the
219Copyright (c) IARIA, 2015. ISBN: 978-1-61208-398-8
ICN 2015 : The Fourteenth International Conference on Networks
system to a new state with a certain probability (determined
by the transition functions). Choosing an action generates a
reward or a cost determinate by reward function.
Policies are prescriptive of which action to take under any
circumstance at every future decision epoch. The agent
objective is to choose the best sequence of action (policy)
under optimum criteria [12].
III. CLOUD COMPUTING CONTROL NEEDS
In this section, we review and show how the scientific
community is dealing with autonomic computing to manage
Clouds. Firstly, works related to the need of a full autonomic
model are presented. Secondly, the need for stakeholders in
our model is explained.
A. Full autonomic model
When Sharma [2] designs and implements a system to
automate the process of deployment and reconfiguration of
the cloud management system, he recognizes that capacity
estimation of a distributed systems is a hard challenge. He
also states that this challenge is intensified by the fact that
software components behave differently in each hardware
configuration.
Assuming that we cannot predict how software will
perform in any particular hardware, cloud manager be
dynamic enough to adapt to these differences. Despite
Sharma [2] recognizing this, his approach involves only
elasticity performed by nodes allocation based on SLOs,
monitoring and forecast.
In [13], autonomic energy-aware mechanisms for self
managing changes in the state of resources is developed to
satisfy SLAs/SLOs and achieve energy efficiency. Unlike
[2], this work focuses on power consumption. It also
introduces a more complete model, involving not only
physical machines and Virtual Machines (VMs), but
expanding on it with customers and a service allocator
(interface between the Cloud infrastructure and consumer).
Fitó et al. [14] propose an innovative model of self-
management of Cloud environments driven by Business-
Level Objectives. The aim is to ensure successful alignment
between business and IT systems, extending business-driven
IT [15]. In this work, typical IT events and risks during the
operation of Cloud providers, such as SLAs or SLOs
violations, are not dealt with.
However, Beloglazov [13] shows that many optimization
techniques are contradictory. To this end, two techniques are
considered: one aimed at the consolidation of VMs and
increasing the amount of physical resources in cases of
workload peaks; and the other at de-consolidating VMs in
cases of node overheating incorporating additional
constraints.
Therefore, when the presented models are implemented
in ad-hoc approaches, they aim to satisfy only a few users or
autonomic computing objectives. As demonstrated, in many
cases the models have different granularity levels (hardware
level, service levels and business goals). These models
cannot be integrated naturally and as a result it is difficult to
achieve full management of the Cloud environment.
Palmieri et al. [16] have presented a rich application of
game theory to schedule tasks on machines in a multi user
environment. They use a temporal model based on time slots
to promote each agent interaction scene, but do not consider
uncertainty. The game-theoretic approach supports the
synergy of agents objectives in a non-stationary way.
To improve overall system performance, Palmieri et al.
[16] introduce a peer-to-peer negotiation method, without a
central regulator, that influences agent decisions about its
strategies. However, this model is limited by granularity of
decisions. Their model is limited because it involves only
tasks and schedule.
Thus, we believe that cloud computing needs a full
model at the autonomic level as presented by Huebscher et
al. [7]. The model is a base for decision-making. A broad,
generic, and extensible model can be used with many
decision-making processes and can help researchers find the
best techniques.
The cloud model must be broad enough to involve all
cloud components, stakeholders and their goals. Thereby, it
will allow a global understanding permitting the system
manager to be able to pay attention to all cloud variables and
seek synergy between them. By generic we mean that it must
work in any CC system. Extensible characteristic can be
understood in two ways: firstly in terms of system variables,
the system must deal with undefined variables; and secondly
recognising that it is not a final model and specifics scenarios
may require new components.
B. Stakeholder
The first step stated in the DP creates the necessity to
obtain information about the control objectives. Autonomic
computing goals are some control objectives for a CC
autonomic manager. Others control objectives are relative
and are different in many works, such as [17] [18] [19].
In [20], the following objectives are used for resource
allocation and re-provisioning and are represented as use
cases:
Acceleration: This use case explores how clouds can be
used as accelerators to reduce the application time to
conclude by, for example, using cloud resources to exploit an
additional level of parallelism.
Conservation: This use case investigates how clouds can
be used to conserve allocations, within the appropriate
runtime and budget constraints.
Resilience: This use case investigates how clouds can be
used to handle the unexpected..
Another example of objectives can be obtained for [13].
A high-level architecture for supporting energy-efficient
service allocation in a Green Cloud is proposed. Energy-
efficient service allocation is one objective in this work.
Sharma [2] presents two approaches on decisions for
dynamic provisioning: cloud provider centric and customer-
centric. Cloud provider centric approaches attempt to
maximize revenue, while a customer centric approach
attempts to minimize the cost of renting servers.
Taking into account Sharma [2], we believe that the
objectives presented by Kim et al. [20] and by Beloglazov et
al. [13] are relative in what concerns autonomic computing.
220Copyright (c) IARIA, 2015. ISBN: 978-1-61208-398-8
ICN 2015 : The Fourteenth International Conference on Networks
This relativism refers to the scope, time and user perspective,
or stakeholder.
Stakeholder is a broader concept than users or actors. The
term stakeholder involves not only users and cloud
consumers, but it also involves the cloud itself, the cloud
provider and related parties.
Thereby, we have established the following definition for
management of CC as an activity of configuring manageable
computational resources to meet and reconcile the interests
of various stakeholders, maintaining and increasing the flow
of value through the cloud over time.
Thus, we understand that what many authors call
objectives, in order to have a complete management at an
autonomic level, should be treated as stakeholders’ interests.
IV. PROPOSAL
In this section, we present our proposed model and his
building process. Aiming to construct a cloud control model
that really automates the whole system, we propose a model
using as reference the mathematical modeling of Control
Theory.
Resulting model of this process is the basis for decision
process in CC and it supports the plan phase of MAPE-K.
Essential elements of this model are: Stakeholders; Interests;
Cloud state; Actions; Events; Conjuncture and Imaginaries
elements. Those elements will be presented in the next
sections followed by an implementation overview.
A. Essencials elements
1) The Cloud State
The cloud state is a representation of cloud in a specific
moment. It represents a static view, just like photography of
the Cloud domain. In Markov decision process and in
control theory a state is often represented as a tuple of
monitored variables and stationary set of all possible states
is . However, in CC, the set of all possible states at time
can be different at the time  because monitored
variables in a Cloud change in time, creating different sets
of possible states.
The controlled variables stated at step 4 of DP are a sub
set of monitored variables. Those are represented as
dimensions ( ) in our model. So is the finite set of all
monitored variables at time. For example, (1) represents
the resulting set of: CPU of physical machine one (, its
memory ( ) and its state ( ); CPU of virtual
machine one () and its memory (); and the router
usage ().

(1)
The dimension index  represents all possible values of
a dimension at time , where  . The relation of
and  is a bijective function (). So  can
be represented as a set of sets (2), wh ere the first element
() is the index of first dimension at time , which
represents , line 2 is  and represents, and so
on. This relation is represented by function 







(2)
The set of possible states consists of the cartesian product
of each set in  . The consequence is that each
element in is a tuple , where is one
element of , is one element of  and so on. Thus, we
can represent the as (3).

(3)
2) Stakeholders and Interests
As explained before, ad-hoc objectives are not sufficient
to deal with the CC management problem. So, in our model
we use a stakeholder interests approach.
The aforementioned acceleration objective, achieved
through the allocation of new VMs, is translated in our
model as interest of a stakeholder in a state with new VMs.
This interest could induce the allocation of more VMs. In
this case we can also observe that our model can represent
the interests of all involved parties, and the manager could
balance the interests using Stackelberg games principles and
search for a Pareto optimum or a Nash equilibrium.
Allocating more VMs may be interesting for a cloud
consumer; however, it can be detrimental to the whole
system if, for example, the environment is already
overloaded.
Economic problems are normally modeled using a utility
function which represents the usefulness of something at a
particular time. Extrapolating this concept, we propose an
interest function (5) that gives the interest of a stakeholder
in a particular state at time t.
As result, (4) returns where is a real number between
 and  (. So zero represents a
neutral interest, positive numbers represent real interest in a
particular state and negative numbers represents a non-
interest.
We also define a function (5) that maps all
dimensions that a stakeholder () can change, where is set
of all stakeholders at time and .

(5)
3) Actions and Events
Once we have introduced the concept of stakeholders,
interests and the cloud state, we present the action that allows
the connection between these concepts. The stakeholders can
affect and change cloud state directly, through actions, and
indirectly, through their interests that are passed to the
system manager and that can be translated into actions.
221Copyright (c) IARIA, 2015. ISBN: 978-1-61208-398-8
ICN 2015 : The Fourteenth International Conference on Networks
Control theory usually chooses a configuration to get the
system to a better state. Therefore, MDPs and SMGs usually
understand that an action leads to a new state. In [3], we had
good adherence to management needs using MDP and
actions, but we refined that model and conclude that cloud
state can change in an unexpected way because of
unpredicted events.
Stakeholders or the system manager can take an action
and lead the system to a new desired state with a certain
probability, given by function (6).

(6)
Events are similar to actions and can also change the
cloud state. The main difference between them is that events
are not planned or even carried out by a stakeholder. An
event can be a hardware problem, a software failure or even
a power outage, for example.
In addition, the set of all possible actions and events are
not stationary, resulting in and . This is because some
of them only make sense in some specific state. For example,
the action of turning on a server only exists if the server is
off at that time. The same occurs with events, a fault in
software, for example, can only happen if the software is
installed and running. So events and actions are related to
states as:
 and
(7)
.
(8)
4) Cost fuction
Every action has a related cost. The cost implies in a
reduction of a stakeholder interest. Cost function can be
defined as (9).
(9)
5) Conjuncture and Imaginary Elements(Future)
Here, we define our concept of model conjuncture and its
natural derivation, the imaginary elements.
a) Conjuncture
Conjuncture represents the system’s structure at a
particular time. When new structure elements are added or
removed, the conjuncture changes. That is why this element
is so important, as what is true in an environment that has,
for example, 1 server and 2 VMs, may not be true when the
environment grows and has 100 servers and 1000 VMs.
So, for the presented elements we postulate the
conjuncture at time as:
.
(10)
Other elements can be added to (10) because we are
dealing only with essential elements.
b) Imaginary Elements
The following example demonstrates the need of
imaginary elements: The environment has one cloud
provider and one server. The server at workload peaks uses
all available resources and satisfies the SLAs for all
consumers. If we give more resources to one of the users, the
SLAs will be compromised. The question is: should the
system add new resources? Given this, a system manager can
infer Nash equilibrium and not allocate more resources.
However, a human manager, in that situation, will analyze
the whole system, including business goals, and predict new
cloud consumers and new demand in the future. So he could
identify other needs and have a better plan.
The greatest advantage that a human manager has over
autonomic management algorithms is the capacity of human
beings to speculate about the future environment. So in order
to develop a good plan it is necessary to choose appropriate
future actions, based not only on present interests, but
possible future interests that may be generated as a
consequence of any of these actions.
So, our model can map future imaginary elements,
supposing a new conjuncture so that the autonomic manager
can take it in to account.
6) Implementation overview
The following implementation overview aims to better
explain our model. In Figure 2, a class diagram depicts our
proposed model.
Figure 2. Class Diagram
As shown in (10), conjuncture is the system's core. It has
a relationship with dimensions and their possible values,
stakeholders, states, actions and events. Although
conjuncture class can contain all of them, directly, it is not
the only nor the best way to design the system with all
elements contained in one class.
222Copyright (c) IARIA, 2015. ISBN: 978-1-61208-398-8
ICN 2015 : The Fourteenth International Conference on Networks
Following Figure 2, conjuncture associates directly with
events, as they come from an unknown source. Also, it must
contain stakeholders, which define a set of controlled
dimensions and their actions. Finally, it maps states,
indirectly, using all the dimensions from the monitored
environment, considering possible states as an aggregate of
dimensions. Consequentially, all states can be generated
from arranged combinations of possible values in every
dimension.
With all sets of components defined, half of the system is
modeled. However, the functions, as previously described,
by (4), (5), (6) and (9) are not yet defined.
V. CONCLUSION
Based on the view of CC presented, it was possible to
base the management model for decision-making on a
perspective of public utility management and not only on a
data center management perspective.
The presented model gives a solid mathematical base to
research political behaviors of CC. Also, using the
formalisms that were researched, this work introduced CC
management as a multi-player game with high level
objectives (Pareto optimal and Nash equilibrium) and
presented holistic interests independent of CC architecture
or implementation.
Finally, this work presented a new concept of
“imagination, essential for a human-like CC management.
For future work CloudSim will be extended to simulate
and validate the proposed model and to compare the results
with other solutions. CloudSim is a framework to simulation
of emerging CC infrastructures and management services.
Following, a multi-strategy approach will be developed.
Usin g Nash equilibrium, Pareto optima, max satisfaction
and others in the simulator will be able to choose the best
one to implement.
At least, possibilities for future research are:
Implement a pilot of proposed model using results
obtain ed from simulation;
Improve the model, if necessary;
Extend the pilot.
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223Copyright (c) IARIA, 2015. ISBN: 978-1-61208-398-8
ICN 2015 : The Fourteenth International Conference on Networks
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