Presenting an Algorithm for Tasks Scheduling in Grid Environment along with Increasing Efficiency by using Fuzzy Models

International Journal of Computer Applications Technology and Research
Volume 5– Issue 5, 312 - 319, 2016, ISSN:- 2319–8656
www.ijcat.com 312
Presenting an Algorithm for Tasks Scheduling in Grid
Environment along with Increasing Efficiency by using
Fuzzy Models
Abolfazl Jafari
Department Of Computer
Engineering, Islamic Azad
University. Sari, Iran
Homayoun Motameni
Alireza Ghonoodi
Abstract: Nowadays, human faces with huge data. With regard to expansion of computer technology and detectors, some terabytes are
produced. In order to response to this demand, grid computing is considered as one of the most important research fields. Grid technology
and concepts were used to provide resource subscription between scientific units. The purpose was using resources of grid environment
to solve complex problems.
In this paper, a new algorithm based on Mamdani fuzzy system has been proposed for tasks scheduling in computing grid. Mamdani
fuzzy algorithm is a new technique measuring criteria by using membership functions. In this paper, our considered criterion is response
time. The results of proposed algorithm implemented on grid systems indicate priority of the proposed method in terms of validation
criteria of scheduling algorithms like ending time of the task and etc. Also, efficiency increases considerably.
Keywords: Grid scheduling, Mamdani fuzzy system, execution time, membership functions
1. INTRODUCTION
The computing grid is a software and hardware ultra structure
and it provides stable, universal, cheap, compatible and reliable
accessing to computing resources of the network. In grid
environment, tasks are not individually executed in a system.
These tasks are divided into subtasks, and each of them is
transferred to resources that are the member of grid for
execution, Resources of the network are connected to each
other by using connection links. A link provides
communication and information exchange between two related
computers. RMS communicates with all network computers in
star topology. The task of RMS is to distribute subtasks
between computers and to receive their results. Suppose that
we have m machines Mj=(j=1,…,), and these machines process
n tasks in the form of Ji=(j=1,…,n). In this way, a scheduler for
j task is dedication of one or more machines in various times to
execute that task.
There are two sets in grid environment scheduling. as follows:
1) Tasks set, 2) computing elements. The purpose of scheduling
algorithm is to schedule applications on computing resources
transferred by various users to grid systems.
Tasks scheduling in grid involves three basic stages:
The first stage: resources detection that is accessible resource
detection. In this step, resources used to solve the problems are
detected and identified.
The second stage: Information collection. In this step,
information like speed of resource computing, its failure rate,
communication like band width of resource, resources
management system and etc are collected by schedules. Then,
the best set involving resources and tasks; are selected
according to tasks characteristics and related information.
The third stage: Task execution. This stage involves execution
of task, collecting the results and finally cleaning up the
memory and being prepared for next scheduling. The policies
of tasks scheduling are divided into two main groups. The first
group is system-oriented group, while purpose is to increase
throughout of the system to decrease response time of whole
system and to create a load balance or combining them. These
kinds of scheduling algorithms have high performance
Unpredictable, insecure and dynamic environment shares
different services between various users. Due to heterogeneous
and dynamic nature of grid, methods used in old systems cannot
be used for grid scheduling, so new methods must be taken into
account. The research and studies show that revelation
optimization methods inspired from the nature have better

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effect and efficiency than other methods. Bat algorithm is a
evolutionary model based on algorithms inspired from the
nature. This algorithm is used to solve optimization problems.
The proposed methods dynamically provide an optimized
schedule to complete transferred tasks with minimum time of
flowtime and makes pan.
2. LITERATURE REVIEW
kang presented grid scheduling algorithm on the basis of self-
adjustable tabu search in 2010. The proposed algorithm is
suitable to reduce makespan of transferred tasks. In the
proposed method, during scheduling time, the panel signs and
keeps the list of local optimized solutions in future search
process to obtain a simple search method for these solutions. In
the proposed algorithms resources utilization is not considered
the most important function in tabu search algorithm is
neighboring function. In 2012, Egrawal proposed scheduling
algorithm to minimize makes pan. The presented algorithm is
based on standard genetic algorithm. This method requires a
coding design, and should show all possible solutions for
scheduling problem. Each special solution can be shown by a
chromosome (scheduler) chromosomes are manipulated by two
genetic operators and different methods until it stops. In order
to manipulate it appropriately, a fitness function is required. In
the proposed method it is supplied that tasks are independent.
In 2009, Chang proposed scheduling algorithm to minimize
MAKESPAN and loud balance. The proposed algorithm has all
characteristics of ants optimization algorithm, and it is
considered to decrease ending time of tasks by considering the
load of each resource in ionic grid environment, and it is used
in Taiwan University. This algorithm changes pheromone
intensity according to resources conditions by applying the
function of updating local and global pheromone, and it tries to
minimize ending time, while the system loud balance is kept.
Izakian suggested optimization algorithm of discrete particles
swarm to solve the problem of tasks scheduling in 2010. In the
proposed algorithm, minimization of Flowtime and Makespan
is simultaneously taken into account. In this method,
optimization algorithm of binary particles swarm has been
used. The matrix element, are considered as zero and one. Each
particle can be converted from Zero to one and vise versa.
In 2009, Chen presented PSO-SA involving combination of
optimization algorithm of particles swarm and gradual
simulation to reduce MAKESPAN time in grid tasks
scheduling. One of the main problems of optimization
algorithm of particles swarm is to be deceived by local
optimization. In order to solve this problems, gradual
simulation that is considered as local search algorithms.
Krouz presented GA-SA algorithm that is a combination of
gradual simulation and genetic algorithm in 2010 to decrease
MAKESPAN time in grid tasks scheduling. Since genetic
algorithm searches whole problem space, and it performs in
weak local search, it has been tried to solve this problem by
combining it with thermal simulation that is considered as local
algorithms
3. PROPOSED ALGORITHM
By using the presented algorithm, Tasks of grid network can be
appropriately scheduled. The difference between the presented
method and previous methods is that both response time and
cost can be considered in this method. In other words, by
providing a balance between response time and cost of task,
scheduling can be performed in the best way. The results show
that, in this proposed algorithm, criteria for measuring the
quality of scheduling algorithm (completion time, waiting time
and etc) can be improved in comparison to other precisions
methods.
3.1 Proposed algorithm description
Since some parameters may be described indefinitely to
schedule tasks, they should be designed in mechanism may so
that these variables can be analyzed in tasks scheduling. One of
variables can be analyzed in tasks scheduling. One of the
methods to create this mechanism, Mamdani fuzzy system has
been used and considered in this research. In our proposed
algorithm, Mamdani system uses membership functions to
convert input values to Fuzzy equivalents. Membership
function is a function by which input data are converted to
fuzzy data; that is, each input in fuzzy system is converted to
the number from one to Zero. Membership function is defined
for both input and output data. There are various types of
membership functions such as trapezoidal, triangular, sigmoid
and Gaussian membership functions. In this research,
trapezoidal membership function is used to convert indefinite
input parameters. Since input variables of the system should be
converted to fuzzy values, system input variables should be
firstly explained as follows:

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3.2 Input variables
1- In order to obtain the response time in a system, criteria of
processes priority, computing power of processes and input and
output operation speed are used. Now we explain these criteria.
Processing priority: This criterion identifies priority of each
processing for execution. In order to measure processing
priority two criteria involving burst time and real priority of
processing are used. After inserting above values, these values
are converted to Fuzzy equivalents by using membership
functions.
𝝁 𝒃 = 𝟏 −
𝒂𝒄𝒕𝒖𝒂𝒍 𝒃𝒖𝒔𝒓𝒕 𝒕𝒊𝒎𝒆
𝐦𝐚𝐱𝐢𝐦𝐮𝐦 𝒃𝒖𝒓𝒔𝒕 𝒕𝒊𝒎𝒆+𝟏
𝝁 𝒑 =
𝒂𝒄𝒕𝒖𝒂𝒍 𝒑𝒆𝒓𝒊𝒐𝒓𝒊𝒕𝒚
𝐦𝐚𝐱𝐢𝐦𝐮𝐦 𝒑𝒆𝒓𝒊𝒐𝒓𝒊𝒕𝒚+𝟏
After measuring above mentioned values, new priority is
introduced as follows. In other words, the process whose
processing time requires less execution time and the process
that has higher real priority are executed soon.
𝝁 𝒏𝒆𝒘 =
𝐦𝐚𝐱(𝝁 𝒃, 𝝁 𝒑)
After detecting and identifying the new priority for each
process, by using “linguistic Variables” of low, intermediate
and high: this criterion is converted to equivalent linguistic
variable. Diagram of membership function of priority
parameter is as follows.
Figure. 1 Diagram of membership function of
priority parameter
2- Next input criterion of Mamdani inference system of
response time is processors’ power. It’s clear that if computing
power of processors is high, they will be executed quicker, and
finally the response time is low, In order to state this parameter
by using linguistic variables, variables of ‘weak, normal and
strong’ are used. Diagram of membership function of
processors'’ power is as follows.
Figure. 2. Diagram of membership function of processors; power
3) Next input criterion is execution speed of input and output
operations. They involve operations of entering a process to the
system (loading in the memory, and time between service
completion and exiting it from the system. If these operations
are performed with higher speed, response time is less. In order
to state this parameter, linguistic variables including “low,
normal and quick” are used. Following feature shows
membership function of input and output operations speed
parameter.
Figure. 3. Diagram of membership function of execution speed in
input and output operations
4) After identifying input membership functions, output
membership function must be determined as well. In this way,
the result of each rule is stated. Output of this algorithm belongs
to five intervals between Zero and one, and they include “low,
relatively low, intermediate, relatively high, high”. The
following feature shows output fuzzy membership function.
Figure. 4 . Diagram of membership function Response
Time

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In the second stage, rules database is created. Generally, it can
be said that, in fuzzy inference stage, linguistic variables are
executed on the basis of input linguistic variables, system rules
and membership function, (fuzzy values). In Mamdani method,
the methods of “multiplication-maximum” and “minimum-
maximum” are used. In our proposed method, “maximum-
minimum” method is used for fuzzy inference. The formula
used for this purpose is as follows.
𝑶𝑹 = 𝝁 𝑶𝑹 𝑨𝑩(𝒙)
= 𝐦𝐚𝐱[𝝁𝑨(𝒙), 𝝁𝑩(𝒙)]
𝑨𝑵𝑫 = 𝝁 𝑨𝑵𝑫 𝑨𝑩(𝒙)
= 𝐦𝐢𝐧[𝝁𝑨(𝒙), 𝝁𝑩(𝒙)]
After identifying formula, we follow fuzzy rules of knowledge
base. According to input criteria and linguistic variables, rules
of knowledge base are defined as follows.
Table 1. The rules of knowledge base of Mamdani fuzzy system
Response
Time
C
on
dition
R
ule
H
igh
t
hen
(priority is
low AND
power of
processor is
weak AND
speed of
input/output
is slow)
R
1 if
H
igh
(prio
rity is low
AND power
of processor
is weak AND
speed of
input/output
is average)
R
2
S
lightly
high
(priority is
low AND
power of
processor is
weak AND
speed of
input/output is
high)
R
3
S
lightly
high
(priority is
low AND
power of
processor is
normal AND
speed of
R
4
input/output is
slow )
S
lightly
high
(priority is
low AND
power of
processor is
normal AND
speed of
input/output is
average )
R
5
A
verage
(priority is
low AND
power of
processor is
normal AND
speed of
input/output is
quick )
R
6
A
verage
(priority is
low AND
power of
processor is
strong AND
speed of
input/output is
slow)
R
7
A
verage
(priority is
low AND
power of
processor is
strong AND
speed of
input/output is
average)
R
8
A
verage
(priority
is low AND
power of
processor is
strong AND
speed of
input/output is
quick)
R
9
A
verage
(priority
is average
AND power of
processor is
weak AND
speed of
input/output is
slow)
R
10
A
verage
(priority
is average
AND power of
processor is
weak AND
speed of
R
11

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input/output is
average)
S
lightly
low
(priority
is average
AND power of
processor is
weak AND
speed of
input/output is
high)
R
12
A
verage
(priority
is average
AND power of
processor is
normal AND
speed of
input/output is
slow )
R
13
S
lightly
low
(priority
is average
AND power of
processor is
normal AND
speed of
input/output is
average )
R
14
S
lightly
low
(priority
is average
AND power of
processor is
normal AND
speed of
input/output is
quick )
R
15
S
lightly
low
(priority
is average
AND power of
processor is
strong AND
speed of
input/output is
slow)
R
16
S
low
(priority
is average
AND power of
processor is
strong AND
speed of
input/output is
average)
R
17
S
low
(priority
is average
AND power of
processor is
strong AND
speed of
R
18
input/output is
quick)
A
verage
(priority
is high AND
power of
processor is
weak AND
speed of
input/output is
slow)
R
19
A
verage
(priority
is high AND
power of
processor is
weak AND
speed of
input/output is
average)
R
20
S
lightly
low
(priority
is high AND
power of
processor is
weak AND
speed of
input/output is
high)
R
21
A
verage
(priority
is high AND
power of
processor is
normal AND
speed of
input/output is
slow)
R
22
A
verage
(priority
is high AND
power of
processor is
normal AND
speed of
input/output is
average )
R
23
S
lightly
low
(priority
is high AND
power of
processor is
normal AND
speed of
input/output is
quick )
R
24
S
lightly
low
(priority
is high AND
power of
processor is
strong AND
speed of
R
25

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input/output is
slow)
L
ow
(priority
is high AND
power of
processor is
strong AND
speed of
input/output is
average)
R
26
L
ow
(priority
is high AND
power of
processor is
strong AND
speed of
input/output is
quick)
R
27
Now, we want to reduce some rules of this knowledge base by
using an algorithm; as a result, complexity of proposed
Mamdani fuzzy system decreases. Numbers 1-3 are
respectively assigned to each of linguistic variables showing
criteria. By considering input criteria and linguistic variables of
these criteria, matrix is as follows:
Table 2. Converting the rules of knowledge base to numerical
equivalent
1 1 1 1
1 1 2 1
1 1 3 2
1 2 1 2
1 2 2 2
1 2 3 3
1 3 1 3
1 3 2 3
1 3 3 3
2 1 1 3
2 1 2 3
2 1 3 4
2 2 1 3
2 2 2 4
2 2 3 4
2 3 1 4
2 3 2 5
2 3 3 5
3 1 1 3
3 1 2 3
3 1 3 4
3 2 1 3
3 2 2 3
3 2 3 4
3 3 1 4
3 3 2 5
3 3 3 5
As it is observer in this table, the first-third column of the left
side shows criteria values of Mamdani fuzzy system. The last
column shows output criterion values of Mamdani fuzzy
system. Now, we want to simplify these rules by using
karnaugh map. The following karnaugh map demonstrates
knowledge base rules of Mamdani fuzzy systems.
karnaugh map of the proposed Mamdani fuzzy system
1 1 2 2 2 3 3 3 3
3 3 4 3 4 4 4 5 5
3 3 4 3 3 4 4 5 5
In this table, the rows show the first criteria, table the columns
indicate the second and third criterion, Also are want to
simplify the above mentioned table on the basis of karnaugh
map. As an example, if we are going to simplify some cells of
the table involving the value of 2, we consider the following
mode:

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Table 3. Classification of karnaugh map with numerical
values of 2
1 1 2 2 2 3 3 3 3
3 3 4 3 4 4 4 5 5
3 3 4 3 3 4 4 5 5
=1)OR3=2)] AND [(x2=1) OR(x2=1) AND [(x1If((x
=2final=3)]) THEN X3(x=2)OR3(x
In this rule, X1-X3 shows input criteria, and Xfinal
demonstrated output parameter.
Table 4. The rules of knowledge base after simplification
Rule Condition Response Time Rule
R1 If((x1=1)AND
(x2=1)AND(x3=1
OR 2))
HIGH R1
R2 If((x1=1) AND
[(x2=1) OR(x2=2)]
AND [(x3=1)OR
(x3=2)OR (x3=3)])
THEN
SLOWLY
HIGH
R2
According to the rules obtained from above table, it is observed
that the rules reduce from 27 to 11 rules, and in this case,
complexity of Mamdani system decreases. For example, we
consider the action of and as 8 units, then we have:
For 27 rules: Execution time 27*2*2=108
For 11 rules: Execution time=22*2+21*1=65
3.3 Case Study
Now, we want to implement our proposed algorithm on a
system, and measure reliability and response time in the
mentioned methods. In case studies, we try to find small and
comprehensive examples. In this case, there isn't any
complexity, and it is a small sample of other big and real
examples. The example of bank ATM lacks much complexity,
and it involves architecture products. In this example,
appropriate architecture frame of CαISR has been taken into
account. We compute reliability and response time by using the
proposed method and executable model simulation.
3.4 Implementation
The following table shows the values of input criteria in the
proposed system for processes.
Table 5. The values of each input parameters ATM system
S.I/OP.O.PA.PET
43118
9732
2221
5964
3653
781112
81713
ET is execution time of the process, A.P is real priority of the
process, P.O.P refers to the processor's power and S.I/O points
to execution speed of input and output operations. Also, it is
supposed that all processes enter the system in zero time.
After entering required parameters of proposed Mamdani
system, we should determine the priority of processes for
execution by using the mentioned membership function of the
algorithm. The following table shows this procedure as well as
possible.
Table 6. converting each value of input parameters to fuzzy
equivalents
Linguistic variable
for new priority
μnewμpμb
Low0.0830.08330.0528
High0.8950.250.8948
High0.950.1660.9474
High0.790.50.7895
High0.840.41660.8422
High0.9170.91660.3685
Average0.580.58330.3158
After obtaining a new priority for processes, execution
procedure of these processes is as follows:
P3,P6,P2,P5,P4,P7,P1
After identifying execution procedure of processes, the
response time is as follows.
Waiting time= 14.86
Response time= 33
After determining input parameters positions, we follow the
heart of Mamdani system called inference system of knowledge
base. After implementing Mamdani system in CPN, we use
MATLAB to obtain output results and to display output
membership functions by using input membership functions.
X1
X2X3

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Figure 5. Obtained diagram for response time by
implementing the system on MATLAB
As it can be observed in the figure, we can measure response
time of ATM system by using simple Mamdani fuzzy system.
4. CONCLUSION
Computing grids provide inexpensive and reliable accessing to
others, computing resources. These recourses are
heterogeneous, and they are distributed. Also, they are
commonly used. On the other side, resources in grid belong to
different organizations having managerial policies, models and
costs for various users in different time. In this way, owners
and users of resources have different objectives, strategies and
different supply and demands. In order to manage such a
complex environment, common methods trying to optimize
efficiency in system level cannot be used to manage the
resources.
In this thesis, a new method has been presented to schedule
tasks in computing grid environment. In this method applied on
the basis of Mamdani fuzzy system, execution time parameter
is considered to improve efficiency and performance. In this
algorithm, parameters required to evaluate the response time
are firstly calculated by using membership functions in
Mamdani fuzzy system. Then, the criterion of response time is
measured for Mamdani fuzzy system by using output
MATLAB software. The results indicate priority of the
proposed algorithm in comparison with other previous
algorithms.
5. SUGGESTIONS
One of the ideas stated about heuristic algorithm is to study and
present new scheduling methods combining other parameters
like reliability, load balance and etc and obtaining interesting
results. In terms of using Mamdani fuzzy system algorithm, it
can be proposed that this algorithm is used in combination with
other algorithms. Another suggestion is using some
mechanisms for applications classification and dividing the
problems to subtasks. If we can do this task by a mechanism
with high precision and speed and by considering tasks duration
as a determinant of load balance in distributed systems
especially grid system, then scheduling precision and speed
will be high. In this case, resources are appropriately dedicated,
and efficiency and performance increases in grid system.
Future suggestions a terms of scheduling in grid environment
are as follows:
1) Studying the methods of error tolerance in proposed
algorithms
2) Presenting scheduling in hierarchical order
3) Measuring several parameters in Mamdani fuzzy system
6. REFERENCES
[1] Afzal, A., McGough, A.S., Darlington, J., "Capacity
planning and scheduling in Grid computing environment",
Journal of Future Generation Computer Systems 24 , pp
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[2] BenDaly Hlaoui Y., Jemni BenAyed L.; "Toward
anUML-based Composition of Grid Services
Workflows",Research Unit of Technologies of
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ACM,AUPC’08, July 2008.
[3] . Dai, Y.S., Levitin, G., "Optimal Resource Allocation for
Maximizing Performance and Reliability in Tree-
Structured Grid Services", IEEE Transaction on
Reliability, Vol. 56, No.3, September 2007.
[4] Dai, Y.S., Xie, M., Poh, K.l., "Reliability of grid service
systems", Computers & Industrial Engineering 50,
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[5] Foster, I., Kesselman, C., The Grid 2: Blueprint for a New
Computing Infrastructure, Los Alios, Morgan-
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[6] G. Murugesan1, An Economic-based Resource
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Applications, IJCSI International Journal of Computer
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[7] Kordic V., Petri Net Theory and Applications,
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Author:Boucheneb H., Hadjidj R., I-Tech Education and
Publishing, Vienna, Austria, First Edition, February 2008.
[8] Levitin, G., Dai, Y.S., "Service reliability and
performance in grid system with star topology",
Reliability Engineering and System Safety 92, pp. 40-46,
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[9] Li, M., Baker, M., The Grid Core Technologies, John
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[10] Yagoubi, B., Slinani, Y., "Task Load Balancing Strategy
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[11] Saeed Parsa. Fereshteh- Azadi Parand. 2012.Estimation of
service reliability and performance in gr id environment:
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Presenting an Algorithm for Tasks Scheduling in Grid Environment along with Increasing Efficiency by using Fuzzy Models

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Presenting an Algorithm for Tasks Scheduling in Grid Environment along with Increasing Efficiency by using Fuzzy Models