A CBR MAC/FAC Approach for Cloud Management

Eric K

ubler, Miriam Herold and Mirjam Minor

Goethe University, Frankfurt am Main 60325, Germany

Keywords:

BPMN, CBR, Cloud Management.

Abstract:

In modern working world, efﬁciency is important. This includes the execution of workﬂows. Cloud comput-

ing offers is costumers, pay as you go pricing models which can be used to improve the cost efﬁciency of

workﬂows execution. To beneﬁt form this pricing model, a smart cloud management concept to assign tasks

to cloud resources is required. Simple solutions struggle with over-, and under-provisioning problems or lack

the needed ﬂexibility. In this paper we present our CBR approach with MAC/FAC similarity function and

experiments for task placements in cloud computing. Therefore we implemented a prototype and compared

the results with the results of human experts.

1 INTRODUCTION

In todays working world, efﬁciency is a key element

for success. Cloud computing offers nearly inﬁnite re-

sources on-demand on a pay as you go pricing model

(Mell and Grance, 2011). Cloud computing can help

to improve the cost efﬁciency of a company by reduc-

ing their applications’ demand for buying and hosting

hardware. However, a smart approach for cloud man-

agement is necessary to handle the cloud resource ef-

fective. Further, the working processes can be opti-

mized to save resources. A way to achieve this goal

is the use of workﬂows that organize the processes.

A workﬂow is deﬁned by the Workﬂow Management

Coalition (Workﬂow Management Coalition, 1999) as

”the automation of a business process, in whole or

part, during which documents, information or tasks

are passed from one participant to another for ac-

tion, according to a set of procedural rules”. A task,

also called activity is deﬁned as follows: ”A process

[...] consists of one or more activities, each com-

prising a logical, self-contained unit of work within

the process. An activity represents work, which will

be performed by a combination of resource (speciﬁed

by participant assignment) and/or computer applica-

tions (speciﬁed by application assignment)” (Work-

ﬂow Management Coalition, 1999, p. 14). The com-

bination of cost efﬁciency and process efﬁciency is a

logical step that has led to a new business model. This

model is known under different names: Workﬂow as

a Service (WFaaS) (Cushing et al., 2012), Business

Process as a Service (BPaaS) (Accorsi, 2011) or Busi-

ness Integration as a Service (BIaS) (Chang et al.,

2012). The basic idea that is common for the three

models is to execute workﬂows in a cloud. The execu-

tion of a workﬂow in a cloud means that the cloud pro-

vides the workﬂow with resources and software that

are required to complete the tasks of the workﬂow.

While BIaS targets on integrating existing cloud ser-

vices, WFaaS and BPaaS take a workﬂow as a start-

ing point. BPaaS puts a slightly stronger focus on

integrating human work than WFaaS. Gartner deﬁne

BPaaS as ”the delivery of business process outsourc-

ing (BPO) services that are sourced from the cloud

and constructed for multitenancy. Services are often

automated, and where human process actors are re-

quired, there is no overtly dedicated labor pool per

client. The pricing models are consumption-based

or subscription-based commercial terms. As a cloud

service, the BPaaS model is accessed via Internet-

based technologies.” (Gartner, 2019). An example for

BPaaS is the provision of employee surveys includ-

ing virtual machines with an installed opinion polling

and analytics software with human actors who design

a survey. An example for WFaaS is the deployment

of a web server with a certain web service that ren-

ders images for a scenario such as automatical sum-

marisation of video surveillance data. Each task has

speciﬁc requirements that need to be fulﬁlled. For

instance, a task that renders images has a high de-

mand for CPU power, but less for disk storage and

requires a web services that renders images. In this

work, a cloud node denotes a set of (virtual) hard-

ware and software. The assignment of a task to a

120

Kübler, E., Herold, M. and Minor, M.

A CBR MAC/FAC Approach for Cloud Management.

DOI: 10.5220/0008165001200129

In Proceedings of the 11th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2019), pages 120-129

ISBN: 978-989-758-382-7

ﬁtting cloud node is called a task placement. It is

not efﬁcient, to start a new cloud node for each new

task. On the other hand, the optimization of a task

placement can be reduced to the bin packing prob-

lem if the tasks should be assigned to a ﬁnite set of

cloud nodes. Consequently, a smart approach is re-

quired to decide whether and when a new node is re-

quired or whether a task can be assigned to an exist-

ing node. It is challenging to ﬁnd a feasible solution

that avoids over- and under-provisioning and matches

all requirements. In addition, time restrictions might

occur for tasks that have a time-out timer or where

humans are involved who become frustrated if they

have to wait for too long. It is therefore essential that

the approach is fast, which disqualiﬁes long running

optimization algorithms. In this paper, we investigate

whether Case-based Reasoning (CBR) provides a fea-

sible solution for the task placement problem. The

idea of CBR is that similar problems have similar so-

lutions (Aamodt and Plaza, 1994). The approach of

using CBR for workﬂow execution in a cloud is not

new. One of the earliest works in this ﬁeld is from

Maurer et al. (Maurer et al., 2013). They apply CBR

to implement automatic cloud management. Aamodt

and Plaza describe a case as follows: ”In CBR ter-

minology, a case usually denotes a problem situation.

A previously experienced situation, which has been

captured and learned in a way that it can be reused in

the solving of future problems” (Aamodt and Plaza,

1994). A problem situation in our approach is a task

placement with over- or under-provisioning problems,

missing requirements, or unused resources. A case

comprises a task placement with problems, such as

violated Service Level Agreements (SLAs), missing

web services or unused resources. A case also com-

prise a solution that contains another task placement

that solves the problems from the previous task place-

ment. A sample solution is a newly started VM with

the missing web service, the shutdown of the unused

resources or the increasing of the resources to avoid

future SLA violations. We introduce a MAC/FAC ap-

proach for case retrieval. MAC/FAC is a synonym for

”many are called, few are chosen”. The basic idea of

MAC/FAC (Forbus et al., 1995) is to collect in a ﬁrst

(fast) step promising candidates and determine their

exact similarity values in a second step. The advan-

tage of this approach is that the number of cases for

which the similarity function has to be calculated can

be reduced. In a workshop paper (K

ubler and Minor,

2019), we discussed which problems can occur and

propose a MAC/FAC similarity function. In this work

we empirically investigate the feasibility the similar-

ity function for task placements. Now we have imple-

mented the MAC/FAC function, different workﬂows

from the music mastering domain, executed some in-

stances of the workﬂows and added (based on the real

measured values) some artiﬁcially created cases to the

case base. We report on experiments with two hu-

man experts who ranked the usefulness of the solu-

tions. We compare the results with our MAC/FAC

similarity approach and discuss the beneﬁts of the

MAC and the FAC component. The CBR approach

will be embedded into our Workﬂow Cloud Frame-

work (WFCF) which was recently implemented and

tested with an rule based approach (K

ubler and Mi-

nor, 2018). WFCF is a connector based integration

framework to integration workﬂow management tools

with cloud computing.

2 RELATED WORK

A wide-spread approach to compute the similarity be-

tween two graphs is to determine the edit-distance

(Cushing et al., 2012; Minor et al., 2007). As shown

in section 3 our case is an attributed forest (or could be

a tree, if we add an underlying hardware-root-node)

with labeled nodes, and therefore the edit-distance

could be a possible solution. However, as shown

in (Zeng et al., 2009), the determination of an edit-

distance for graphs is NP-complete. Another way is

to determine the similarity of complex cases as de-

scribed in (Lopez De Mantaras et al., 2005). The

problem of structural similarity is the high compu-

tational effort. Instead of indexing vocabularies as

suggested by the authors, we use the MAC/FAC ap-

proach (Forbus et al., 1995). This should be a more

ﬂexible approach, where the main factor for similar-

ity are the executed tasks and the problems in the

case. An MAC/FAC approach for workﬂows was in-

troduced in (Bergmann and Stromer, 2013). Further,

as stated in (Armbrust et al., 2010), a good balance be-

tween over- and under-provisioning of resources is a

challenging issue that is an important aspect for cloud

computing in general (Baun et al., 2011). The sim-

plest methods provide resources in a static way. Such

systems do not adjust themselves to a new situation

causing under- or over-provisioning (Shoaib and Das,

2014). There are several other works in the literature

that addresses the problem of resource provisioning

in the cloud with different approaches (Shoaib and

Das, 2014; Pousty and Miller, 2014; Quiroz et al.,

2009; Bala and Chana, 2011; Rodriguez and Buyya,

2017). However, these approaches have the problem

that the provisioning is either very static, does not

make use of the capabilities of a cloud, or that the ap-

proaches are not implemented yet and therefore rather

theoretically. Other approaches aim at a deeper inte-

A CBR MAC/FAC Approach for Cloud Management

121

gration of clouds and workﬂows (Wang et al., 2014;

Korambath et al., 2014). They deeply integrate work-

ﬂow and cloud technology, reducing the occurrence of

over-provisioning and under-provisioning. However,

they strongly depend on the used cloud and workﬂow

management tools. Therefore, they are very limited

in their options to exchange either the used cloud or

workﬂow management tool or both. This leads tho a

high risk of vendor lock-in, that should be avoided.

3 SIMILARITY OF TASK

PLACEMENTS

In this section we describe the structure of our cases,

the MAC/FAC method and the similarity function for

our cases.

3.1 Case Representation

As mentioned before, a task placement is the assign-

ment of the currently active tasks to cloud resources.

Fig. 1 gives an example. In this example, the tasks

Task2 and Task3 are active, where Task1 is already

done. Task3 is assigned to a container named CON2

where Task2 is assigned to a VM named V M2 and

Task4 is assigend to CON3. Assigned means that

CON2, CON3 and V M2 host the software that the

tasks needs to execute, for example a web service or

an Ofﬁce Suite. The task calls the web service, or the

user uses a remote desktop connection to work with

the Ofﬁce Suite.

Figure 1: A simple illustration of a task placement with a

task assigned to a VM and another to a VM.

3.2 Relevance of Case Parts for

Retrieval

Next, we discuss what should be important for the

similarity of two task placements. A task placement

has plenty of parameters that could be considered for

the similarity. In this work, we consider a cloud node

either as a virtual machine (VM), or a container. Both

have a set of resources, this can include, but is not

limited to, CPU, GPU, memory, disc storage, net-

work capacity and different kinds of installed soft-

ware. For comparison, even two cloud nodes with

the same set of resources (same CPU, installed soft-

ware etc.) could considered as different, if the re-

source utilization is different. For example, a cloud

node with 4GB of memory and a utilization of 100%

of the memory, should be more similar to a node with

4GB memory and 90% utilization than a node with

4GB memory and a utilization of 10%. Though, a

VM and a container share some attributes, it makes

a difference if a node is a VM or a container. For

example, a container can be migrated relatively easy

from one VM to another, even if the VMs are hosted

on different cloud providers. This is not so easy and

sometimes even impossible for an entire VM. So the

solution for a VM can not be always the migration to

an other host, this is possible for a container. In this

case, it is necessary to propagate the new URL or IP

address to the workﬂow. Therefore, to compare two

cloud nodes, it is important to distinguish whether it

is a VM or container, to know the set of resources and

the utilization of the hardware resources. The driv-

ing force of the task placements are the tasks. With-

out any task, there is generally no need for any cloud

node. To determine the cloud resources required for

a task, we introduced in one of our previous works

the concept of task characteristics in cloud computing

ubler and Minor, 2016). In short, the idea is to label

tasks with its needs and give a hint of the foreseeable

resource usage. In our current work, we extend the

idea of characteristics so that for example the charac-

teristic ”compute intensive” now has a value of 0 to 4

to indicate how intensive the task uses the CPU and

not just a binary value of 0 or 1 to determine whether

the task is compute intensive or not. Other character-

istics that determine if a task is long or short running,

were replaced by a values that contain the minimal,

maximal and average execution time. Another impor-

tant aspect should be the problems that a placement

has. As mentioned before, this could be for example

violations of Service Level Agreements (SLA) or the

violation of internal constraints for example that there

should be no cloud node active that is not in use.

KMIS 2019 - 11th International Conference on Knowledge Management and Information Systems

122

3.3 MAC/FAC Approach

It is clear that this can lead to many parameters to

compare for similarity. And at this point we even

haven’t discussed the similarity of sets of tasks and

sets of cloud nodes. For performance reason, we

use the MAC/FAC Principle as introduced in (Forbus

et al., 1995), to distribute the effort. The idea is to col-

lect fast a set of few promising case candidates (MAC

step) and investigate the similarity of the candidates

in more detail in a second step (FAC step). As men-

tioned before, the most important aspect for similarity

are the tasks. Therefor in the MAC step we compare

the currently active tasks of the problem case with the

currently active tasks in cases stored in the case base.

The currently active tasks is represented by a set of

vectors. Since tasks are Vectors (which include the

values for the task characteristics, the name and so

on), the hamming distance or the euclidean distance

can be used to determine similarity. But in this case,

we have to consider the similarity between two sets

of vectors. There are some metrics for deﬁning the

similarity between two sets, for example the Haus-

dorff metric (Huttenlocher et al., 1993) or the sum of

minimum distances (Eiter and Mannila, 1997). The

problem with these heuristics is, that it is very easy

to create a case where the similarity is very high but

the sets are by intuition very dissimilar. For exam-

ple in one set are only equal tasks. This could be for

example a set with only a single type of image render-

ing tasks and the other set contains different tasks but

one rendering task and a mapping did map all render-

ing task of the ﬁrst tasks to the single rendering tasks

of the second set, then the similarity would be 1 for

these two sets. of course, this is not desired. Another

option is not to use a metric for building a single map-

ping, but to build all possible mappings for the vectors

and chose the mapping with the minimum weight like

the Kuhn-Munkers algorithm (Kuhn, 1955; Munkres,

1957). Though, this method is very compute intensive

as mentioned in (Agrawal et al., 1993).

Our solution for a fast approach that is not that

much vulnerable for special cases, uses an intersec-

tion of the task sets to determine the similarity. Let

and T

be a Set of Tasks, then is the function

sim

, T

) =

∩ T

∪ T

. The beneﬁt of this func-

tion is, that it covers the difference between the size

of the sets, as well as the actually equal tasks. This

will help in the FAC step to ﬁnd more relevant task

placements in a reasonable amount of time. Be-

side the tasks, it is important to consider the prob-

lems that a task placement has. As mentioned be-

fore, this could be SLA or constraint violations. The

SLAs and constraints are stored in a a vector, are

ordered by name and contains the number of viola-

tions for each SLA or constraint. We call this an

SLA vector or Problem Vector. To compare two SLA

vectors, we ﬁrst make sure that both vectors have

the same parameters, which means the same SLAs

and constraints. Let slav

an SLA vector with the

sla slav

= SLA1

, SlA2

and slav

= SlA2

, SLA3

with the values SLA1

= 1, SLA2

= 3, SLA2

2, SLA3

= 1. In a ﬁrst step we add in both SLA vec-

tors the missing parameters but set their value to 0.

The new vectors are slav

= SLA1, SlA2, SLA3

and

slav

= SLA1

, SlA2, SLA3 with SLA1

= 1, SLA1

0, SLA2

= 3, SLA1

= 2, SLA3

= 1, SLA3

= 0.

Now we can compute the euclidean distance between

two SLA vectors. Let q

∈ SLA1 and p

∈ SLA2,

than is the euclidean distance for the SLA vectors

sla

(p, q) =

∑

i=1

− p

)

. The similarity function

is now sim

sla

(slav

, slav

) =

1+d

sla

(slav

,slav

)

. The

MAC step is a combination of the similarity of the

current active tasks, and the problems, therefore we

chose an aggregated similarity function sim

mac

sim(T P

,T P

)

=(T

)+sim

sla

(slav

,slav

)

, where T P

and

T P

are task placements with T

, slav

∈ T P

and

, slav

∈ T P

. Depending on the test results, we

may add some weights to the components of the sim-

ilarity function, but for now we consider the tasks and

the problems as equally important.

After a fast determination of promising candi-

dates, the FAC step compares the candidates with the

current problem situation in more detail. Here is the

placement of the tasks, the resources of the cloud

nodes and their utilization important, as well as the

question, which tasks are to be executed next.

3.4 Similarity of Tasks in Placements

As shown before in Fig. 1, a task placement can be

seen as a tree, if all VMs and containers that are not

related to a VM, are assigned to an abstract ”hard-

ware” node, as shown in Fig. 2. This tree is unordered

and labeled, where the labels are the resources that a

cloud node contains. Graph isomorphism is NP com-

plete as well known, but to compute the edit distance

between two unordered labeled trees is also NP com-

plete, as shown in (Zhang, 1996).

The problem is not easier, if we alter the tree and

add new nodes with null values for the labels, to get a

more generalized structure as shown in 3.

Instead we compare the vector of tasks and their

related cloud nodes. We call this a task cloud vector.

Such a vector contains a task, a container and a VM.

As mentioned earlier, it is important not to compare

A CBR MAC/FAC Approach for Cloud Management

123

Figure 2: Task placement as tree with hardware as the root

and the tasks as leafs.

Figure 3: Task placement as tree with the hardware as root

and abstract nodes for a more generalized model.

containers with VMs.

A task within the task cloud vector is represented

by a sub-vector of parameters with their values, the

characteristics and a set of tasks that could be ex-

ecuted next. The idea of this set is to consider

the next tasks for a foresight of the workload that

coming next. Therefore we use once again the eu-

clidean distance to determine the similarity between

the two characteristic vectors and the similarity for

intersection for the next tasks. Let TASK1, TASK2

are set of tasks and t1, t2 are vectors of charac-

teristics with t1 ∈ TASK1, t2 ∈ TASK2. The eu-

clidean distance is then deﬁned as d

tasks

(t1, t2) =

∑

i=1

(t2

−t1

)

. Let tn1 ∈ TASK1, tn2 ∈ TASK1

the set with the next task. The similarity func-

tion is now sim

ntask

, T

) =

1+d

task

(t1,t2)

|tn1∩tn2|

|tn1∪tn2|

As shown below, we need a distance function for a

special algorithm. Therefore we build the distance

function with d

ntask

(TASK1, TASK2) = |TASK1 ∪

TASK2| − |TASK1 ∩ TASK2|.

A cloud node contains its hardware resources, the

utilization of the hardware resources and additional

software or information, which are stored as a set of

tags. Let cn = (r, u, tag) describe a cloud node, r is

a vector of hardware resources (for example 4 cpu

cores, 16GB Memory ect), u is a vector of resource

utilization in percentage and tag is a set of tags (for

example tag = windows8, tomcat7, jre7). For the dis-

tance between the resources, we use once again the

euclidean distance d

(r1, r2), as well as for the uti-

lization d

(u1, u2). The similarity functions is then

again sim

(r1, r2) =

1+d

(r1,r2)

and sim

(u1, u2) =

1+d

(u1,u2)

. To determine the similarity of the set of

tags we build the intersection and compare it with the

merged sets: sim

tags

(tag1, tag2) = |tag1 ∪tag2|−|tag1 ∩tag2|.

Figure 4: Task placement as paths.

The overall distance function for two

task cloud vectors is d

tcv

(tcv1, tcv2) =

d(tags1, tags2) + d

(u1, u2) + d

(r1, r2) +

ntask

(t1, t2). Similar to the MAC step we might add

weights in the future.

3.5 Similarity of Entire Task

Placements

After deﬁning the similarity for two

task cloud vectors, the next step is do deﬁne the sim-

ilarity between two sets of vectors. For this we have

chosen the Kuhn-Munkers algorithm (also called

Hungarian algorithm) as described in (Kuhn, 1955;

Munkres, 1957). This algorithm builds a minimum

weight mapping for bipartite graphs, our in this case

between two sets of vectors, where the edge weight

is the distance between two task cloud vectors. In

a ﬁrst step a distance matrix must be built, that

KMIS 2019 - 11th International Conference on Knowledge Management and Information Systems

124

contains the distance from each task cloud vector in

the ﬁrst set to each task cloud vector in the second

set. The Kuhn-Munkers algorithm requires a square

matrix. If the two sets have a different number of

vectors, we add to the smaller set dummy vectors

and set their edge weight to inﬁnite. Because of

the strict selection in the MAC step, based on the

intersection of the tasks, there should be not many

dummy vectors in our matrix. After building the

matrix, the Kuhn-Munkers algorithm successively

improves the mapping between both sets. To deter-

mine the similarity between two sets of vectors, after

Kuhn-Munkers has ﬁnished, we build the sum of

the edges between the sets is build. Since this is a

distance function, the similarity function for Kuhn-

Munkers is sim

(tcv1, tcv2) = 1 −

1+d

m(tcv1,tcv2)

(Agrawal et al., 1993) is mentioned, that the run time

of Kuhn-Munkers is O(n

) where n is the number

of task cloud vectors, but that the run time can be

improved to O(n

). This is very compute intensive, in

particular this has to be computed for each candidate,

selected during the MAC step, therefor the selection

of the MAC step should be very strict.

4 EVALUATION

In this section, we discuss the evaluation of our simi-

larity function. The experimental setup is as follows:

A case base with real, measured cases is extended by

artiﬁcial cases. Two human experts are employed in a

leave-one-out study to create a golden standard of re-

trieval results. An ablation study compares the results

of both, the FAC step only and the full MAC/FAC

retrieval, with the case ranking from the golden stan-

dard. To achieve the experimental data, we have im-

plemented seven workﬂows from the music master-

ing domain in jBPM citejBPM. Figure 5 depicts one

of the implemented workﬂows. The ﬁrst three tasks

’init parameters’, ’generate random set’, and ’choose

ﬁle’ are automated tasks, which don’t need web ser-

vices for their functionality, followed by a sequence

of automated tasks that are executed by web services,

and a ﬁnal task that writes the resulting music data

automatically to a ﬁle.

The further six workﬂows have at least one task

that requires a web service. The Channels Only

workﬂow, for example, uses the channels web ser-

vice, the Limiter Only workﬂow uses the limiter web

service. To create a set of cases for our case base we

executed each workﬂow with real music data in a real

cloud environment and recorded the workﬂow at an

arbitrary state of execution where no SLA violation

was observed. These snapshots serve as the solution

Figure 5: Workﬂow from the music mastering domain.

part of a case each. We extended our case base with

artiﬁcial cases. Some of them are just variations of

the measured cases with different resource utilization

values or slight changes of the execution environment.

Further cases have been created manually, to include

artiﬁcial cases that do not have any similar solutions.

Each case includes one to three active tasks that re-

quire a web service. In the artiﬁcial cases, every task

was randomly assigned to either a container or a VM.

For the real measured cases, we used the cloud plat-

form OpenShift (OpenShift, 2019) as an execution en-

vironment. In those cases, the tasks were assigned

to containers only. The overall case base comprises

of 30 cases. The problem part of the cases was ar-

tiﬁcially produced from the solution part with some

rules. In a ﬁrst step we infused some problems to

the cases, such as CPU / Memory over-provisioning

/ under-provisioning, Storage under-provisioning or a

Missing web service. After the problem parts were

conﬁgured, the solution placement was copied and

manually adapted to create the problem part. If the

problem was a missing web service, the cloud node

for the according task was deleted. If the problem

was a provisioning problem, the node was either al-

tered to a different cloud node (container or vm) with

a different set of hardware resources (either higher or

lower as before depending whether the problem was

an over- or under-provisioning problem), or the hard-

ware set was just altered for the cloud node. For our

experiments, two human experts selected randomly

14 of the 30 cases as queries (the problem case), and

ranked the other 29 cases (solution cases) into three

categories for each query.The categories were:

Very Helpful. The solution of the solution case can

be applied to the problem case without any

changes.

Partial Helpful. The solution of the solution case

can be applied to the problem case with some ad-

justments (for example: starting a different web

A CBR MAC/FAC Approach for Cloud Management

125

service, or increasing / decreasing resources with

a different amount).

Not Helpful. The solution of the solution case can

not be applied to the problem case at all (because

of different problems).

We investigated how our MAC/FAC approach per-

formed in comparison to the human experts. In addi-

tion, we investigated the results for only applying the

MAC step, or the FAC step alternatively. The aim was

to get insights whether the MAC or the FAC step can

run on its own to achieve similar results or whether

the combination of MAC/FAC is a more feasible so-

lution. For this experiment, we consider all cases with

a similarity value of 90% or higher as very useful.

For partial helpful cases we have chosen the two high-

est similarity values (rounded) lower than 90%. This

can include several cases if some cases have achieved

the same similarity values(after rounding). All other

cases are considered as not helpful. Table 1 shows the

results for very helpful cases.

Table 1: Results for very helpful cases for the MAC/FAC

approach in comparison to the human experts.

Case

Num-

ber

Human MAC/

FAC

MAC

only

FAC

only

case1 3 3 3 3

case2 none none none none

case4 26 26 19, 24,

case5 10, 16 10, 16 10, 16 10, 16

case6 15 15 15, 17,

22, 25

case10 5, 16 5, 16 5, 16,

5, 16

case16 5, 10 5, 10 5, 10,

5, 10

case18 none none none none

case20 none none none none

case22 none none none none

case25 none none none none

case27 none none none none

case28 none none none none

case30 none none none none

As one can see, if there was a perfectly ﬁtting so-

lution for the human experts, the algorithm always

suggests the same cases. However, the MAC step

only approach found some false positive very help-

ful cases. The MAC step only considers the tasks and

the problems of the case. However, for case 4, 6, 10

and 16, the assigned nodes were different, i.e. the so-

lutions from the solution cases 4, 6, 10 and 16 are

not applicable without any changes and therefore not

very helpful, only partial helpful. For the partial help-

ful cases the picture is quite different, as depicted in

Table 2.

Table 2: Results for partial helpful cases for the MAC/FAC

approach in comparison to the human experts.

Case Num-

ber

Human MAC/FAC MAC only FAC only

case1 4 5 9 10 11

16 17 18 21

8 12 8 12 4 5 6 9 10

11 14 15 16

17 18 19 21

22 23 25 26

28 29

case2 11 5 8 9 10 11 12

16 21 23 29

2 13 5 9 10 16

21 29

case4 1 3 5 6 9 10

11 14 15 16

17 18 21

11 19 7 11 27 30 1 3 5 6 9 10

15 16 18 19

case5 1 3 4 6 9 11

14 15 17 18

21 23 26

12 23 2 10 12 13

1 3 4 6 9 15

18 21 23 26

case6 1 2 3 4 5 9

10 11 14 16

17 18 21 25

26 27 30

8 14 8 14 27 30 1 3 4 5 9 10

14 16 17 18

21 22 26

case10 1 3 4 9 11

14 15 17 18

20 21 26

2 12 13 20 23 2 12 13 20 1 3 4 6 9 15

18 21 23 26

case16 1 3 4 6 9

11 14 15

171821 23

12 23 2 12 13 20 1 3 4 6 9 15

18 21 23 26

case18 1 3 4 5 6 9

10 11 14 15

16 17 21 28

11 12 29 7 11 12 14

20 29

14 29

case20 7 14 5 7 10 11 13

14 16 18 23

28 29

2 5 10 12

16 18 23 28

18 28

case22 6 8 12 19

23 28 30

817 8 14 27 30 6 15 17

case25 27 6 8 14 15 17

8 14 27 30 1 3 4 5 6 9

10 14 15 16

17 18 19 21

22 26 28

case27 25 4 6 7 8 11 14

15 19 22 24

25 26

4 6 15 17

19 22 24 25

26 30

6 8 13 15

25 30

case28 12 14 18 19

23 30

11 12 14 18

20 29

7 11 12 14

20 29

1 3 4 5 6 9

10 14 15 16

18 19 20 21

25 26 29

case30 19 23 28 78 11 14 19 4 6 7 14 15

17 19 22 24

25 26

1 2 3 4 5 6 7

9 10 14 15

16 17 18 19

20 21 22 24

25 26 28 29

If the case does not provide a perfect solution, the

results of the human experts and the algorithms are

different. Table 3 shows the cases, that have the hu-

man experts and the algorithms in common. In all

cases, the human experts have a different set of par-

tial helpful cases than the algorithms. The MAC/FAC

algorithm has in many cases fewer suggestions for

partial helpful cases then the other algorithms. The

most suggestions has the FAC step. As Table 4

shows, the ratio of correct suggestions to the overall

number of suggestions is for the FAC only step the

best. The worst is achieved by the MAC only step.

The MAC/FAC approach performs slightly better than

MAC only. It seems that the MAC step is the weak

spot in this similarity function. The goal of the MAC

step is to collect a set of promising candidates for the

KMIS 2019 - 11th International Conference on Knowledge Management and Information Systems

126

FAC step, but in its current form it ﬁlters too many

feasible cases.

Table 3: The partial helpful cases of the algorithms in ac-

cordance with the human experts.

Case Number MAC/FAC MAC only FAC only

case1 none none 4, 5, 9, 10, 11,

16, 17, 18, 21,

case2 11 none none

case4 11 11 1, 3, 5, 6, 9,

10, 15, 16, 18,

case5 23 none 1, 3, 4, 6, 9,

15, 18, 21, 23,

case6 14 14 1, 3, 4, 5, 9,

10, 14, 16, 17,

18, 21, 26

case10 20 20 1, 3, 4, 6, 9,

15, 18, 21, 23

case16 23 none 1, 3, 4, 6, 9,

15, 18, 21, 26

case18 11, 29 11, 14, 29 14, 29

case20 7 none none

case22 8 8 6

case25 14 14 14

case27 25 25 25

case28 12, 14, 18 12, 14 14, 18, 19

case30 19 19 19, 28

Table 4: Percentages of correct suggestions of cases for the

algorithm.

MAC/FAC MAC only FAC only

Cases in com-

mon

16 12 60

False positive

suggestions

70 73 149

Percentage

of correct

suggestions

22,9% 16,4% 40,3%

To get an impression of the execution time of the

particular algorithms, we created in addition to our

initial case base (with 1-3 instances per case) some

new case bases with 30 cases each. Each case con-

sists of 10, 50 or 100 active tasks. Table 5 depicts

the average execution time (in ms) that was taken to

compute the similarity for two cases.

Table 5: Average execution time (in ms) to compute the

similarity for two cases.

Number

of tasks

in case

MAC/FAC MAC

only

FAC only

1-3 tasks 0,04 less then

0.01

0,04

10 tasks 0,14 0,04 0,3

50 tasks 4,2 2,2 7,78

100 tasks 22,8 0,46 44,96

The results show clearly that the MAC step is very

fast, even for a larger set of tasks. The FAC step seems

with only 45ms for 100 tasks also relatively fast. But

this is only the time to compare two cases. If the case-

base contains 1000 cases, and for each case the FAC

similarity has to be computed sequentially, the entire

computation time sums up to around 45sec. Obvi-

ously, it depends on the number of instances per case

and the number of cases in the case base. Splitting

the similarity determination seems a good idea. How-

ever, to do so the MAC step should deliver a more

promising set of candidates than it currently does.

5 CONCLUSION

In this paper we presented the evaluation of our

MAC/FAC approach for the task placement problem

in cloud computing. The results of the experiments

show that the approach performs well if there is a

very similar case to be retrieved. However, if there

does not exist an obvious candidate in the case base

the results differ from the suggestions of the human

experts

. The MAC step in particular needs some ad-

justments to perform better. It seems that the focus

on tasks and problems is not sufﬁcient to ﬁnd feasi-

ble candidates, the structure of complex cases is more

important than expected. The FAC step on the other

hand performs much better, but the execution time

is as high as expected. Since the similarity for each

case is independent from the other cases, this prob-

lem can be parallelised very well to improve the ex-

ecution time. Still, the performance of the FAC step

should be improved too. In future, we will adjust the

weights of the similarity function. In particular, the

part of the resource utilization should be valued less

in comparison to the other parts. The next step will be

to investigate if we can improve the results by chang-

ing the structure of the cases in such a way that not the

entire placement but only the Task Cloud Vector with

the problem is included. This would reduce the com-

plexity and therefore improve the execution time and

probably the result. On the other hand, if a case only

contains a part of the placement, migration actions

would be much more complicated. One idea to solve

this problem is a dynamic case structure that depends

on the degree of complexity of the problem descrip-

tion. Short representations of the Task

Cloud Vector

model only would be sufﬁcient for simple problem

cases while a long representation covering the entire

task placement is required for rather complex cases.

The results of this work highlight the feasibility of

CBR for cloud management and contributes a novel

use case scenario for MAC/FAC approaches.

Special thanks to our human experts Bahram Salimi

and Jan H

ocher.

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127

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