An Off-line Analytical Approach to Identify Suitable Management

Policies for Autonomic Cloud Architecture

Marwah Alansari and Behzad Bordbar

School of Computer Science, University of Birmingham, Birmingham, U.K.

Keywords:

Coloured Petri-Nets, Autonomic Cloud Platform, Management Policies, Rules-set, Formal Analysis, Cost

Analysis, Modelling.

Abstract:

Delivering cloud services with better quality-of- service demands infrastructures which are autonomic and

self- manageable. In particular, there is a clear scope for developing automated methods for enforcing suitable

management policies that would run such infrastructures. An example of a management policy is the one that

governs the triggering of migration of virtual machines to manage energy consumption. Although there is

extensive research on developing novel methods of implementing such policies in an autonomic manner, the

identiﬁcation of suitable policies in terms of cost reduction has received less attention. This requires an analy-

sis of two given sets of policies to identify which one is more suitable. This paper presents a method involving

Coloured Petri Nets for an ofﬂine modelling and analysis of an autonomic cloud platform which executes

sets of policies. We use traces of execution in Petri Nets for calculating minimum cost associated to each set

of policies. Petri Net models can generate inﬁnite traces because of the appearance of loops. However, as

migration of virtual machines entails cost, many of the inﬁnite traces will not result in the identiﬁcation of the

minimal cost. This paper presents an analytical method using Integer Programming to ﬁnd the minimum cost

of energy consumption for a given policy. We evaluated our approach with the help of an energy management

case study.

1 INTRODUCTION

Delivering cloud services with better quality-of-

service demands infrastructures which are autonomic

and self- manageable. Manual methods for managing

the deployed cloud services would not beneﬁt cloud

providers to achieve their objectives because of the

large size of cloud-infrastructure, as well as the regu-

lar changes in business requirements. Therefore, there

are some autonomic management techniques making

a use of rule-based systems as suggested in (Borgetto

et al., 2012; ?; Alansari and Bordbar, 2013). Such

frameworks have been used for automatically trigger-

ing a dynamic action, such as the live-migration of

a virtual machine, by using different types of man-

agement policies. The management policies can use

constraints, or can be time based, or a combination of

both types (Alansari and Bordbar, 2014).

Autonomic cloud platforms which are governed

by such a combination of policies are very complex

because of the interacting rule sets. These rule sets

may involve a comparison between monitored param-

eters with given threshold values, and also may use

a set of Boolean constraints (Alansari and Bordbar,

2014). Therefore, studying the effectiveness of man-

agement policies in terms of cost saving and iden-

tifying the most appropriate policy before execution

is difﬁcult. Thus, a model-based approach using the

Coloured Petri Nets (CPN) technique is proposed in

(Alansari and Bordbar, 2014). The proposed method

is aimed at deﬁning a formal model for an autonomic

cloud platform which includes a migration action as

a dynamic action. The formal description model for

both cloud platform and policy is denoted as the CPN

Cloud. Each generated CPN Cloud model is simu-

lated to produce a set of traces of execution for 24

hours. At each sampled trace, the Cost Calculating

Method (SM) for computing the costs of both energy

consumption and the migration of a virtual machine

(VM) is applied to assess the overall cost of a policy

(Alansari and Bordbar, 2014).

We investigated some of CPN Cloud models pro-

duced by modelling approach suggested in (Alansari

and Bordbar, 2014). We noticed that the traces

of executions for such models might have complex

structures and might also include various loops. As

232

Alansari, M. and Bordbar, B.

An Off-line Analytical Approach to Identify Suitable Management Policies for Autonomic Cloud Architecture.

In Proceedings of the 6th International Conference on Cloud Computing and Services Science (CLOSER 2016) - Volume 2, pages 232-239

ISBN: 978-989-758-182-3

a result, the Cost Calculating Method proposed in

(Alansari and Bordbar, 2014), does not consider com-

plex cases. Hence, in this paper, we extend the off-

line cost analysis approach developed in (Alansari and

Bordbar, 2014) to consider the time intervals. This

can be achieved by formulating a set of equations of

Integer Programming solved by the Modiﬁed Simplex

algorithm (FrontlineSolvers, 2015). The purpose is to

provide comprehensive cost estimation values which

cover all the possible cases that might be found in a

trace generated from a CPN Cloud model. Further-

more, we solved the problem of including loop traces

inside traces of execution. This can be accomplished

by proposing a theory which relates the migration cost

to the loop traces. The objective of this theory is to

ﬁnd the loop traces that would be discarded during

the process of the cost calculation.

The paper is organised as follows; Section 2 in-

cludes an overview of Coloured Petri Nets (CPN) and

the investigated related work in computing optimal

cost from Petri-nets models. Section 3 presents a sce-

nario for an autonomic cloud platform. The mod-

elling concept for cloud platform and policies is ex-

plained in Section 4. The description of the problem

addressed in this paper is expressed in Section 4.1.

Section 5 presents the proposed method for calculat-

ing the cost using Integer Programming. Section 6

contains the evaluation of the proposed solution us-

ing the scenario presented in Section 3. Finally, the

conclusion is presented in Section 7.

2 BACKGROUND AND RELATED

WORK

2.1 Coloured Petri-Nets (CPNs)

Petri Nets (PNs) are graphical and mathematical lan-

guages used for modelling a wide range of systems.

Through the years, several representations and exten-

sions to the classical Petri Nets have been introduced.

One of the existing Petri Net types is the Coloured

Petri Nets (CPN) (Jensen and Kristensen, 2009) (Cal-

lou et al., 2008).

In CPN, any model consists of a set of places

represented as circles and a set of transitions repre-

sented as bars. Places and transitions are connected

by arrows which contain expressions. Furthermore,

in CPN models some transitions may have guards,

which are conditional expressions used to increase the

control of ﬁring transitions. The guards are written

between square brackets. In addition, a CPN model

has a set of tokens, which in CPN context are called

the colour set, with a data type similar to the place

type. In order to execute the model, there must be

a set of initial markings, which represent the values

of the tokens at each place before running the model

(For more information about CPN formal representa-

tion see (Jensen and Kristensen, 2009)).

2.2 Computing the Optimal Total Cost

in Petri-Nets

Calculating the optimal cost has been studied in var-

ious researches for different types of Petri Net mod-

els particularly in Priced Time Petri Net (PTPN) and

Time Petri Net (TPN). As stated in a study by Ab-

dulla and Mayr (Abdulla and Mayr, 2009), the cost

to reach a ﬁnal marking from an initial marking is

computable if non-negative cost values are associated

with places and transitions in both PTPN and TPN.

They provide a mathematical formula for computing

the total cost along a path in the reachability graph

which is denoted as Cost(M

→ M

) (Abdulla and

Mayr, 2009)(Abdulla and Mayr, 2011). In (Abdulla

and Mayr, 2009) and (Abdulla and Mayr, 2011), the

minimal reachable cost in PTPN and TPN is com-

putable if it is transformed to a cost threshold prob-

lem. As a result, we conclude that the optimal cost

can be computed in PTPN if it becomes bounded,

contains set of reachable ﬁnal markings and also is

associated with cost thresholds variables.

In (Li and Hadjicostis, 2011), the optimal cost

is estimated by using a recursive algorithm for com-

puting the cost at each node in the produced trellis.

Then, the node that has the least cost is determined

at each level in the graph (Li and Hadjicostis, 2011).

The recursive algorithm proposed in (Li and Hadji-

costis, 2011) can be useful to compute the minimal

cost in some Petri Net models. However, the algo-

rithm would not suitable for computing the minimum

cost from the reachability graph generated from CPN

Cloud models studied in our research. The reason

is that our CPN Cloud model is a dynamic platform

which has unﬁxed cost values along the markings.

3 A SCENARIO FOR AN

AUTONOMIC MANAGEMENT

IN CLOUD PLATFORM

Let us consider a cloud platform consisting of four

private hosts located in different locations and one

public host, as seen in Figure 1. Two private hosts

are located in Europe, whereas the remaining are in

Asia. Furthermore, the platform also has some Ama-

An Off-line Analytical Approach to Identify Suitable Management Policies for Autonomic Cloud Architecture

233

Table 1: Rules-set templates for expressing Time-based Rules for both Policy A and Policy B.

Time-based Policy A Time-based Policy B

• RuleSet 1: (Applied between Private Hosts)

– When Private Host(x) can accept Migrated VM and Time is

after 10.00 and Private Host(y) can migrate VM

then

Allow only one VM to be migrated between Private Host(x)

and Private Host(y) every ∆

time

• RuleSet 2:( Applied between Private Host and Public Host)

– When Public Host(x) can accept Migrated VM and Time is

after 10.00 and Private Host(y) can Migrate

then

Allow VM to be Migrated to Public Host(x) every ∆

time

• RuleSet 3: ( Applied at Public Host )

– When Time is after 10.00 at Public Host(x)

then

Allow VM to be Migrated to Private Hosts from Pub-

lic Host(x) every ∆

time

• RuleSet 4: (Applied between Private Hosts)

– When Private Host(x) can accept Migrated VM and Time is

between 16.00 and 7.00 and Private Host(y) can migrate VM

then

Allow only one VM to be migrated between Private Host(x)

and Private Host(y) every ∆

time

• RuleSet 5:( Applied between Private Host and Public Host)

– When Public Host(x) can accept Migrated VM and Time is

between 16.00 and 23.00 and Private Host(y) can Migrate

then

Allow VM to be Migrated to Public Host(x) every ∆

time

• RuleSet 6: ( Applied at Public Host )

– When Time is after 23.00 at Public Host(x)

then

Allow VM to be Migrated to Private Hosts from Pub-

lic Host(x) every ∆

time

Figure 1: A scenario for an autonomic management via trig-

gering virtual machine migration in a cloud platform.

zon instances, which are located in the USA. All hosts

in the platform are allowed to only migrate one VM

to available hosts at a time. The running virtual ma-

chines in the platform are used for executing com-

putational applications submitted by cloud consumers

(Alansari and Bordbar, 2014). The cloud provider that

owns this architecture is willing to restrict the live mi-

gration action among the hosts using different sets of

policies. All the policies are composed of constraints

and time-based rule sets. The constraint policies are

applied at the hosting node level which analyse the

status of the node using measurement values such as

SLA Violation Rate, Resource Consumption and En-

ergy Consumption. The following is an example of a

constraints policy used in the scenario:

1. RuleSet 1:

When Violation Rate is High or CPU Usage is High or CPU Usage is

Low

then Migrate Smallest VM Running in Host

2. RuleSet 2:

When Violation Rate is Normal and CPU Usage is Normal

then Accept Migrated VM

Moreover, in this scenario, there are two types of

time- based policies that might be used by the cloud

provider. Policy A uses random time constraints that

allow the trigger of the migration action at any time

after 10:00 between all the hosting nodes. Policy B

has ﬁxed time constraints which only permit the mi-

gration during the off-peak time which will be be-

tween 16:00 and 7:00 among private hosts, and from

16:00 to 23:00 between private and public nodes. Ta-

ble 1 is a sample of a rule set used for expressing time

intervals in both Policy A and Policy B.

Before executing policies explained in Table 1 in

real cloud platform, such policies can be modelled

and be analysed in terms of saving energy consump-

tion cost via Coloured Petri Nets (CPN). Brieﬂy, the

approach of using Coloured Petri Nets for modelling

cloud infrastructure with policies will be explained in

Section 4.

4 COLOURED PETRI-NETS FOR

MODELLING MANAGEMENT

POLICIES

Figure 2 is a model of the CPN Cloud for the sce-

nario explained in Section 3. In this CPN model,

places can be represented as hosts for running virtual

machines. Dynamic migration action is modelled as

transitions between places which are in blue colour.

In addition, constraint policies can be a part of inter-

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234

Figure 2: The Coloured Petri Nets model for the scenario.

nal transitions occurring at places, which are referred

to as monitoring transitions. These monitoring transi-

tions are ﬁred periodically with a time delay referred

to as @MointoringTime. The monitoring transitions

appear in grey colour in Figure 2. On the other hand,

the time-based policy is modelled as a guard at each

migration transition. Examples of time-based policies

are those explained in Section 3.

The proposed CPN Cloud model in (Alansari and

Bordbar, 2014) has become a tool that can be used to

assess policies in terms of cost savings. The compar-

ison depends on simulating the Coloured Petri Nets

model to partially generate traces of execution. Then,

the cost is computed by applying the modiﬁed Cost

Calculation Method proposed in (Abdulla and Mayr,

2013) which is considered a simple method. The

outcome of such an approach is obtaining the esti-

mated total cost of energy consumption and migration

cost from a single trace σ from the sampled graph.

This calculation method is applied to all traces in the

graph (Alansari and Bordbar, 2014)(a detailed expla-

nation about the Cost Calculation Method is provided

in (Alansari and Bordbar, 2014)).

4.1 The Description of the Problem

From CPN Cloud model that is presented in Figure 2,

we partially generated a reachability graph. A sam-

ple of such graph are shown in Figure 3. In Figure

3, these traces represent the possible execution during

24 hours which is generated using CPN Tool (Jensen

and Kristensen, 2009). Focusing on the highlighted

trace, any single trace can be described in a format as

presented on the right hand side of Figure 3. In a trace

σ, the squares represent the markings which can be ei-

ther a marking resulting from triggering a monitoring

transition or a marking generated from ﬁring a migra-

tion transition. These markings contain the computed

cost values for all running hosting nodes in a cloud

platform. In addition, the trace σ also has arrows

which are annotated with (t

, θ

). In this form, the

notation θ

represents the time unit for ﬁring a transi-

tion. Formally, the trace can be described as follows:

σ := M

,θ

)

−→ M

,θ

)

−→ M

,θ

)

−→ . . .

n−1

,θ

n−1

)

−→ M

0 ≤ θ

≤ θ

. . . ≤ θ

n−1

< 24 (1)

As mentioned in the previous section, by applying

the Cost Calculation Method in (Alansari and Bor-

dbar, 2014), we can obtain the estimated cost val-

ues which are Energy Consumption and Migration

Costs. However, there are some CPN Cloud models

that have migration transitions restricted to time in-

tervals, such as the model of the CPN Cloud for the

scenario explained in Section 3. This means that in a

trace σ, a migration transition t

is ﬁred with a time

delay d

which is between the allowed time-interval

Mini

, D

Maxi

]. The Simple Cost Calculation Method

relies on using CPN simulator to select the time de-

lay for ﬁring a migration transition. However, in case

of using time-interval [D

Mini

, D

Maxi

] for ﬁring a mi-

gration transition t

, there is a time delay d

where the

cost of energy consumption between the marking M

and M

i+1

can be the minimum. As a results, the Sim-

ple Cost Calculation Method explained in (Alansari

and Bordbar, 2014), is extended to compute the min-

imum energy consumption cost between the mark-

ings. This can be achieved by ﬁnding the optimal or

near-optimal time delays for ﬁring migration actions

in traces associated with time-intervals.

5 THE IMPROVED COST

CALCULATION METHOD (IM)

Our solution starts by computing both Energy Cost

and Migration Cost at each marking M

in a trace

σ using both Equation 3 and Equation 5 mentioned

in our previous research in (Alansari and Bordbar,

2014). Then, we formulate a set of Integer Program-

ming equations for obtaining the minimum energy

consumption cost.

5.1 Computing the Overall Cost in the

Trace

Lets consider that the generated trace σ has the fol-

lowing format:

σ := M

,θ

)

−−−→

,θ

)

−−−→

,θ

)

−−−→

. . .

n−l

n−1

,θ

n−1

)

−−−−−−→

n−1

0 ≤ θ

≤ θ

. . . ≤ θ

n−1

< 24 (2)

An Off-line Analytical Approach to Identify Suitable Management Policies for Autonomic Cloud Architecture

235

Figure 3: A sample of a reachability graph (left hand-side) and a sample of a trace extracted (right-hand-side).

which each M

is a marking resulted from ﬁring t

with a delay time unit d

. Each M

happens at time

. To compute the total cost in trace σ such that each

ti is ﬁred with time delay d

which has the minimum

ECost(M

), we deﬁne the following objective func-

tion:

OverallCost(σ) = Minimize(

n−1

∑

i=0

∗ ECost(M

)

+ TCost(t

)) (3)

subject to the following constraints:

1. In case the ﬁring transition t

is a migration tran-

sition, then:

Mini

≤ d

≤ D

Maxi

2. In case t

is a monitoring transition, then:

= @MonitoringTime ≤ 24.

3. θ

i+1

= d

+ θ

≤ 24

4. θi , θ

i+1

, d

> 0, θ

< θ

i+1

5. θ

= 0 and θ

= 24

6. d

, θ

i+1

, θ

are integers

In our solution, we consider computation for a day

(i.e., 24 hours). Yet, the computation can be easily

adjusted for days, weeks or seasons. Both D

Mini

and

Maxi

are integer values extracted from the manage-

ment policy used to limit the variable d

. The variable

@MonitoringTime represents the delay-time unit for

monitoring transitions which will be assigned in CPN

Cloud model before extracting the traces. θ

is the

time for ﬁring the transitions in a trace σ and θ

i+1

the next time unit after ﬁring a transition t

. In this

method, we assume that each ﬁred monitoring transi-

tion has no cost. As a result, in Equation 3, the ob-

tained cost value for any monitoring transition will be

equal to 0.

The value of OverallCost(σ) is obtained using

Modiﬁed Simplex Algorithm uses the Branch and

Bound Method (FrontlineSolvers, 2015). The objec-

tive is to ﬁnd the feasible integer values for time-delay

. Since the CPN Cloud model considers discrete

time not continuous time. Using such algorithm, the

total cost along σ can be computed by ﬁning the best

time-delay d

for ﬁring each migration transition t

. In

case Modiﬁed Simplex does not ﬁnd a feasible solu-

tion in a trace σ, we assign for each d

the value D

mini

5.2 A Special Case: Handling Traces

with Loops

In the previous section, we mentioned a method of

calculating the minimal cost for a given ﬁnite trace

σ consisting of transitions ﬁred using time-intervals.

However, it is possible that some traces involve peri-

odic behaviours which appear in these traces as loops.

This is depicted in Figure 4, from the trace shown in

the ﬁgure, inﬁnite traces can be obtained by repeating

the loop involving the markings M

, M

and M

It is possible for each given number of iterations of

the loop to obtain a trace and apply the method of the

previous section to calculate the minimum cost. The

trace would repeat the markings involved in the loop.

Clearly, the length of the traces can increase as we

can include an arbitrary number of repetitions of each

loop. At ﬁrst glance, it might be the case that we need

to identify the minimal cost over an inﬁnite number of

traces. However, with each iteration on a loop, there

are associated costs with the traces. This is because

the migration of the virtual machine accumulates cost.

For a sufﬁciently large number of migration costs, the

Figure 4: An example of a trace with a loop.

CLOSER 2016 - 6th International Conference on Cloud Computing and Services Science

236

trace will be large enough to be discarded from the

calculation, when we are looking for a solution with a

minimal cost.

Lemma 1. Assume that σ is a trace of execution such

that σ has a loop. i.e. σ has the following sub-

sequence:

λ = M

k−1

,θ

k−1

)

−−−−−−→

k−1

,θ

)

−−−→

k+1

. . .

l−1

,θ

l−1

)

−−−−−−→

l−1

such that M

= M

k−1

and Cost(σ) ≥

N × LoopCost(λ) in which N is the num-

ber of repetitions of the sequence (∗) and

LoopCost(λ) =

∑

i=k

TCost(t

)

Sketch of The Proof: The amount of energy as-

soicated with λ consists of the amount of energy con-

sumed of running virtual machines at all hosts in CPN

Cloud model. (i.e.) The cost at M

where k − 1 ≤

i ≤ l − 1 plus the cost of the migration when the

transitions t

k−1

, . . . , t

l−1

are ﬁred. LoopCost(λ) =

∑

i=k

TCost(t

) captures only the cost migration. If

there are N repetitions of the loop, we end up with

N × LoopCost(λ) with at least the cost assoicated

with migration for N iterations of the loop.

Theorem 1. Assume L represents the set of all loops

with at least one migration transition with a non-

negative cost. Suppose C

min

= min{LoopCost(λ)|λ ∈

L} repeating the smallest value for all the cost of mi-

gration within a loop. Suppose that σ

is an arbitrary

ﬁnite trace of execution starting from the initial mark-

ing and executing for 24 hours. If q is the smallest

number that q ×C

min

≥ TCost(σ

), then the minimum

cost will be

Min{Cost(σ)|σ is a trace with at most q

repetitions of each loop} (4)

Proof. For any trace σ with more than q repetitions

of a loop L, the cost of σ will be grater than or equal

Cost(σ

). Hence, traces will be discarded as it will

result in a minimum cost of energy.

Using the above theorem, we need to calculate

the minimum cost with the help of a ﬁnite number

of traces. As a result, if any graph resulting from the

CPN Cloud model consists of a set of traces includ-

ing loops, a ﬁnite set of traces executing the loops

should be generated. This can be done by repeating

the loops N repetitions. Then, the cost is computed

using the Improved Method explained in Section 5.

In addition, the cost of migration for traces with loops

should be considered. We stop computing the cost for

traces consisting of loops when the cost values be-

come greater than the cost of a trace with the smallest

repetition number for the loop sequence.

Figure 5: The sequence of execution graph for CPN model

for Policy A.

6 THE EVALUATION OF THE

METHOD

The proposed solution is evaluated by analysing and

comparing a number of modelled policies in the CPN

Cloud model. The CPN tool(Jensen and Kristensen,

2009) is used to generate Coloured Petri Net models

for all tested policies mentioned in Section 3. Then,

a set of sequence of executions for each model is cre-

ated. The cost of energy consumption and the migra-

tion cost which are associated with the markings are

also computed during the process of generating the

sequence graphs using the ML Function in the CPN

tool. After that, Integer Programming equations are

formulated and solved using the Modiﬁed Simplex al-

gorithm (FrontlineSolvers, 2015) which is provided

in Microsoft Excel Software. Both the modelling and

analysis processes were done on a Samsung laptop

which has 2.40GHz Intel(R) Core(TM) processor and

6GB memory.

We used the CPN tool to create the models for

Policy A and Policy B. The workload for the models

is simulated to be generated randomly using the ML

function. The traces of execution graphs for the mod-

els are shown in Figure 5 and Figure 6. In all graphs,

the values inside the markings are the cost of energy

consumption for four private hosts. The time intervals

which are applied at each migration transition are lo-

cated at the edges between the markings. We notice

that the graph in Figure 5 has two traces containing

loop traces. For the loop traces, we applied the theo-

rem explained in Subsection 5.2. We noticed that the

overall cost values for each of the traces with loops

are higher than similar traces without executing the

loop sub-traces. Therefore, we discard all the loop

An Off-line Analytical Approach to Identify Suitable Management Policies for Autonomic Cloud Architecture

237

Figure 6: The sequence of execution graph for CPN model

for Policy B.

traces generated in the graph of Policy A from our

calculation.

6.1 Results and Discussion

The graphs shown in Figure 5 and Figure 6, there are

18 traces generated. We applied the Cost Calculation

Method explained in Section 5 to all generated traces.

We obtained the minimum cost of Energy Consump-

tion, Total Migration Cost and Optimal Overall Cost

at each generated trace for all the graphs. To com-

pare both Energy Consumption and The Overall Cost

for all the policies, we selected 18 traces from each

generated graph ignoring all the loop traces. The de-

tailed results produced from the analysis method are

displayed in Figure 7 and Figure 8.

Figure 7 illustrates the Optimal Energy Consump-

tion Cost for 18 traces generated from each of the

traces of execution graphs presented in Figures 5 and

6. Generally, the ﬁgures show that each trace for Pol-

icy B has an Optimized Energy Consumption Cost

value which is less than the traces in Policy A, since

Policy A allows the migration to be triggered at any

time using random time intervals. In contrast, the mi-

gration action in Policy B is restricted to the off-peak

time which is from 16:00 until 21:00 mapped as [8-

24] in some of the traces of the graph of Policy B

(See Figure 6).

Figure 7, we can analyse the cost of each trace

for each policy individually. For instance, we can see

that trace σ

has the lowest Optimized Energy Con-

sumption Cost among traces of Policy A. Whilst trace

has the least Optimized Energy Consumption Cost

Figure 7: The optimal energy consumption cost for 18

traces from the sequence of execution graphs.

Figure 8: The optimal overall cost for 18 traces from the

sequence of execution graphs.

among the traces of Policy B which is nearly 0.26. In

addition, we can notice that there are some traces of

Policy A that have nearly the same cost values which

are reasonably high such as σ

, σ

and σ

Figure 8 presents the Optimal Overall Cost af-

ter accumulating the Migration Cost values of each

trace to its Optimized Energy Consumption Cost. We

found that there are changes in cost values since some

traces required the triggering of migration transitions

which means their migration costs are high. As a re-

sult, the ﬁgures for each trace of execution for both

Policy A and Policy B are roughly similar.

6.2 Comparing the Improved Method

with the Simple Method

To study the effectiveness of the proposed method

on the computed cost values, we compared this

method with the Simple Method proposed method in

(Alansari and Bordbar, 2014). For all traces of both

Policy A and Policy B graphs the Simple Method are

applied. During this process, we ignored the Migra-

tion Cost values computed from both methods be-

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238

Figure 9: A comparison between the two methods of calcu-

lating the cost energy consumption in traces.

cause these values are ﬁxed. On the other hand, we

focused on the computed Energy Consumption Cost

values from both methods. As shown in Figure 9 that

the Improved Method produces averages of Energy

Consumption Cost for both Policy A and Policy B

which are lower than the values given by the Simple

Method. Thus, the Improved Method is more accurate

in estimating the cost of Energy Consumption which

can be suitable for analysis of some types of manage-

ment policies. However, if the objective is to speed

up the process of calculating the cost, or if time de-

lays are not of much concern to cloud providers, then

the Simple Method can be applicable in such types of

management policies.

7 CONCLUSION

Management policies that would be executed in a

cloud platform can be assessed in terms of Energy

Cost saving before execution via Coloured Petri Nets.

By using the Improved Cost Calculation Method sug-

gested in this paper, the estimated energy consump-

tion and the migration costs can be obtained. The

Improved Cost Calculation Method provides a deep

analysis for both cost values which are extracted from

the traces of execution graph of CPN Cloud models.

The method uses a set of Integer Programming equa-

tions which are solved via the Modiﬁed Simplex al-

gorithm. The objective is to ﬁnd traces which have

minimum energy cost values and the best time for ﬁr-

ing migration actions during 24 hours. Coloured Petri

Nets can be a powerful tool for modelling and anal-

ysis of autonomic Cloud platforms and management

policies. If Cloud CPN models are combined with the

off-line cost analysis method suggested in this paper,

various set of policies can be assessed before real im-

plementation.

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An Off-line Analytical Approach to Identify Suitable Management Policies for Autonomic Cloud Architecture

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