enhanced ant colony algorithm for grid scheduling - CiteSeerX

D.Maruthanayagam, Dr.R.Umarani.,Int.J.Comp.Tech.Appl, Vol 1 (1) 43-53

ENHANCED ANT COLONY ALGORITHM FOR GRID SCHEDULING D.Maruthanayagam Head, Department of computer Applications, Vivekanandha College of Arts Sciences for Women, Tiruchengode, Tamilnadu, India ([email protected])

Dr.R.UmaRani Associate Professor, Department of Computer Science, Sri Sarada College for Women, Salem, Tamilnadu, India ([email protected])

Abstract Grid computing is to make multiple machines

depending upon the performance of the grid

that may be in different physical locations,

systems.

behave like they are one large virtual machine.

Key words: Grid Computing, Job Scheduling,

Grid scheduling environment is a arranging the

Heuristic

machines in the course of find it fast called the

scheduling

Ant algorithm. The find for resource in the

algorithm.

collection

1. INTRODUCTION

of

geographically

distributed

Algorithm, algorithm

Load

Balancing,

simulation,

ant

heterogeneous computing systems and making

In large scale computing systems such as grid

scheduling decisions, taking into consideration

computing systems, there are often large

eminence of service. Allocation of resources to a

amounts of resources available to be used for

large number of jobs in a grid computing

computing jobs. Since these resources can cost

environment presents more difficulty than in

up to millions of dollars maximizing their

network computational environments. Resource

utilization is an important problem. Scheduling

and job will have been allocating by resource

in a grid computing system is not as simple as

discovery

and

of the

scheduling on a many machine because of

selection

of

specific

several factors. These factors include the fact

scheduling and job submission. This algorithm is

that grid resources are sometimes used by paying

evaluated using the simulated execution times for

customers who have interest in how their jobs

a grid environment. Before starting the grid

are being scheduled. Also, grid computing

scheduling, the expected execution time for each

systems usually operate in remote locations so

task on each machine must be estimated and

scheduling tasks for the clusters may be

represented by an Expected Time calculation.

occurring over a network. It is because of these

The proposed scheduler allocates adopt the

reasons that looking at scheduling in grid

system environment freely at runtime. This

computing is an interesting and important

resource optimally and adaptively in the

problem to examine [1].

filtering, resources

composed and

idea

scalable, dynamic and distribute controlled environment.

Conclude

of

this

Grid

propose

environment

is

a

distributed

environment including different processors with various capabilities. One of the most important

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D.Maruthanayagam, Dr.R.Umarani.,Int.J.Comp.Tech.Appl, Vol 1 (1) 43-53

issues in resources is the problem of job

different problems are to be satisfied by the

scheduling. In most of the works accomplished

scheduling chosen. Specific knowledge of the

in this field the purpose is finding an appropriate

underlying grid infrastructure is put to use by the

scheduling which minimizes the total tardiness

existing approaches for grid scheduling by

time. To select schedulers that minimizes the

queuing systems and ad hoc schedulers in order

mean waiting time of processes in queues and

to achieve an efficient allocation of resources.

also the mean length of queues [2]. The efficient

These approaches fail in dealing with the

scheduling of jobs on Grid systems is clearly

complexity of the problem as the nature of the

critical because long wait time or queue's long

grid is dynamic. Scheduling of jobs in grid

length leads to grate waste of computational

computing is multi objective and hence we need

resources and also leads to finalization of

approaches to optimization that can solve

deadline of some processes [3].

objectives that are conflicting.

This technology makes it possible to share, select

and

aggregate

resources

that

2. LITERATURE REVIEW

are

Many algorithms were designed for the

geographically distributed like super computers,

scheduling of Meta tasks in computational grids

databases, data sources and specialized devices

is reviewed in this section. One of the easiest

belonging to different organizations. However,

techniques in grid scheduling is Opportunistic

there are certain issues in the area of grid

Load Balancing (OLB).It workflow tasks in Grid

computing that need to be addressed. Allocation

environments are difficult because resource

of resources to a large number of jobs in a grid

availability often changes during workflow

computing environment presents more difficulty

execution.

than in LAN computational environments [4].

attempts to improve the response time of user’s

Another significant factor is the load balancing

of

available

resources

Opportunistic

Load

Balancing

submitted applications by ensuring maximal

in

utilization of available resources. A typical

computational grids. Applications differ in their

distributed system will have a number of

characteristics and their demand for resources.

interconnected

Hence the most significant technical challenges

independently or in cooperation with each other.

in the Grid are efficient and application adaptive

Each resource has owner workload, which

management of resources and scheduling. A lot

represents an amount of work to be performed

of applications that are beyond the scopes of

and every one may have a different processing

distribution and resource sharing now use grid

capability. To minimize the time needed to

computing. Scheduling of grid resources alone

perform all tasks, the workload has to be evenly

renders the distributed resources useful. To

distributed over all resources based on their

achieve high performance grid computing, we

processing speed.

need to make use of optimal schedulers as

resources

who

can

work

Heuristic Task Scheduling Algorithm in Grid

opposed to poor schedulers that gives contrasting

computing

performance. A variety of constraints on

predictive execution time of tasks. It obtains a

environment

based

upon

the

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D.Maruthanayagam, Dr.R.Umarani.,Int.J.Comp.Tech.Appl, Vol 1 (1) 43-53

scheduling strategy by employing mean load as

computer

heuristic information and then selects both the

compared to problems arising in natural work

maximum-load and the minimum-load machines.

distribution processes like that of scheduling all

We reassign tasks between two machines to raise

activities (tasks) needed to construct a large

the load of the machine with lower-load and

building [5]. The essential objective of a load

reduce that of the machine with higher-load

balancing consists primarily in optimizing the

under the mean load heuristic.

average response time of applications, which often

Ant Colony was used to solve many problems

systems.

means

This

problem

maintaining

the

can

be

workload

such as traveling salesman problem, vehicle

proportionally equivalent on the whole resources

routing problem, graph coloring problem, etc.

of

using ACO in Grid processor scheduling

observational approach and exploits the idea of

problem leads to finding an optimal or near

scheduling a job to a site that will probably run it

optimal solution after reasonable amount of time.

faster. The opportunistic algorithm takes into

A new heuristic function is introduced to lead

account the dynamic characteristics of Grid

ants to select best processor for executing each

environments without the need to probe the

process. Also a new fitness function is presented

remote sites. We compared the performance of

to evaluate the fitness of solutions founded by

the

each iteration's ants. The pheromone updating

scheduling algorithms in a context of a workflow

rule is defined so that prompt new iterations' ants

execution running in a real Grid environment.

to follow the best solutions found in previous

The Opportunistic algorithm benefits from the

iterations.

dynamic aspects of the Grid environment. If a

a

system.

opportunistic

The

algorithm

algorithm

adopts

with

an

different

A hybrid heuristic to solve parallel machines’

site happens to perform poorly, then the number

job-shop scheduling problem. In this work,

of jobs assigned to this site decreases. Similarly,

genetic

if a site process jobs quickly, then more jobs are

algorithms

(GA)

and

ant

colony

optimization (ACO) share data structures and co-

scheduled to that site [6].

evolve in parallel in order to improve the

2.2 Heuristic Task Scheduling

performance of the algorithm. In ant algorithm

Efficient task scheduling is critical to

for balanced job scheduling in Grids is

achieving high performance on grid computing

introduced in which the Grid is considered a

environment.

heterogeneous multi processor and the purpose is

A

heuristic

task

scheduling

algorithm satisfied resources load balancing on

to produce a good job scheduling algorithm to

grid environment is presented in this paper. The

assign jobs to resources in both computing Grid

algorithm schedules tasks by employing mean

and data Grid [2].

load based on task predictive execution time as

2.1 Opportunistic Load Balancing (OLB)

heuristic

information

to

obtain

an

initial

Load balancing for a huge no of system is

scheduling strategy. Then an optimal scheduling

important problems which have to be solved in

strategy is achieved by selecting two machines

order to enable the efficient use of parallel

satisfied condition to change their loads via

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D.Maruthanayagam, Dr.R.Umarani.,Int.J.Comp.Tech.Appl, Vol 1 (1) 43-53

reassigning their tasks under the heuristic of their

repeated with the remaining unmapped tasks.

mean load. Methods of selecting machines and

Compared to MCT, Min-min considers all

tasks are given in this paper to increase the

unmapped tasks at a time.

throughput of the system and reduce the total

2.6. Max-min

waiting time [7]. The proposed heuristic

Max-min begins with a set of all unmapped

scheduling algorithm Min-mean works has the

tasks. The completion time for each job on each

job allocation is done based on the Min-min

machine is calculated. The machine that has the

algorithm &

the mean of all machines

minimum completion time for each job is

completion time is taken. The machine whose

selected. From the set, the algorithm maps the

completion time is greater than the mean value is

job with the overall maximum completion time

selected. The tasks allocated to the selected

to the machine. Again the above process is

machines are reallocated to the machines whose

repeated with the remaining unmapped tasks.

completion time is less than the mean value.

Similar to Min-min, Max min also considers all

2.3. Minimum Execution Time (MET)

unmapped tasks at a time [8, 9].

The minimum execution time or MET assigns

2.7 Ant Colony Algorithm

each job to the machine that has the minimum

Ant colony optimization (ACO) was first

expected execution time. It does not consider the

introduced by Marco Dorigo as his Ph.D. thesis

availability of the machine and the current load

and was used to solve the TSP problem [10].

of the machine.

ACO was inspired by ants’ behavior in finding

2.4. Minimum Completion Time (MCT)

the shortest path between their nests to food source. Many varieties of ants deposit a chemical

The algorithm calculates the completion time

pheromone trail as they move about their

for a job on all machines by adding the

environment, and they are also able to detect and

machine’s availability time and the expected

follow pheromone trails that they may encounter.

execution time of the job on the machine. The

With time, as the amount of pheromone in the

machine with the minimum completion time for

shortest path between the nest and food source

the job is selected. The MCT considers only one

increases, the number of ants attracted to the

job at a time. This causes that particular machine

shortest path also increases. This cycle continues

may have the best expected execution time for

until most of the ants choose the shortest path.

any other job.

As this work is a cooperative one and none of the

2.5. Min-min

ants could find the shortest path separately, ACO

Min-min algorithm starts with a set of all

algorithm can be categorized as a swarm

unmapped tasks. The completion time for each

intelligent algorithm. Various types of ACO

job on each machine is calculated. The machine

algorithm are presented. Each of them has some

that has the minimum completion time for each

special properties, i.e., Ant Colony System

job is selected. Then the job with the overall

(ACS), Max-Min Ant System (MMAS).

minimum completion time is selected and

Fast

Ant System (FANT), Max-Min Ant System is

mapped to the machine. Again, this process is

based on the basic ACO algorithm but considers

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D.Maruthanayagam, Dr.R.Umarani.,Int.J.Comp.Tech.Appl, Vol 1 (1) 43-53

low and upper bound values and limits the

solved in this area. The grid scheduler must

pheromone range to be between these values.

allocate the jobs to the resources efficiently. The

Defining those values, lets MMAS avoid ants to

efficiency depends upon two criteria; one is

converge too soon in some ranges. In Fast Ant

makespan and the other is flow time.

System version of ACO just one ant participate

These two criteria are very much important in

in each iteration search and also there is no

the grid system. The makespan measures the

pheromone evaporation rule in this version.

throughput of the system and flow time measures

Hence the ant algorithm is suited for usage in

its QoS. The following assumptions are made

Grid computing task scheduling. In the grid

before discussing the algorithm. The collection

environment, the algorithm can carry out a new

of independent tasks with no data dependencies

task scheduling by experience, depending on the

is called as a meta-task. Each machine executes a

result in the previous task scheduling. In the grid

single task at a time.

computing environment, this type of scheduling

The meta-task size is one and the numbers of

is very much helpful. Hence this paper proposes

machines are ‘m’. The ant based algorithm is

the ant algorithm for task scheduling in Grid

evaluated using the simulated execution times

Computing.

for a grid environment. Before starting the grid

3. PROBLEM DESCRIPTION

scheduling, the expected execution time for each

In this section, the grid is composed of

task on each machine must be estimated and

number of systems. Each host has several

represented by an ET matrix. Each row of ET

computational resources. The resources may be

matrix consists of the estimated execution time

homogeneous

grid

for a job on each resource and every column of

scheduler finds out the better resource of a

the ET matrix is the estimated execution time for

particular job and submits that job to the selected

a particular resource of list of all jobs in the job

systems. The grid scheduler does not have

pool. ETij is the expected execution time of task

control over the resources and also on the

ti and the machine mj . The time to move the

submitted jobs. Any machine in grid can execute

executables and data associates with the task ti

any job, but the execution time differs. The

includes the expected execution matrix ETij . For

resources are dynamic in nature. As compared

this algorithm, it is assumed that there are no

with the expected execution time, the actual time

inter-task communications, each task can execute

may be varied at the time of running the jobs to

on each machine, and the estimated expected

the allocated resource.

execution times of each task on each machine is

or

heterogeneous.

The

known [11].

The grid scheduler’s aim is to allocate the

The ET matrix will have N x M entries,

jobs to the available nodes. The best match must be found from the list of available jobs to the list

where N is the number of independent jobs to be

of available resources. The selection is based on

scheduled and M is the number of resources

the prediction of the computing power of the

which

resource. So, lots of problems are needed to be

workload is measured by million of instructions

is

currently

available.

Each

job’s

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D.Maruthanayagam, Dr.R.Umarani.,Int.J.Comp.Tech.Appl, Vol 1 (1) 43-53

T1

T2

T3 Ready Time

0.00

0.5

188.90

239.6

178.8

236.88

238.20 188.8

236.4 290.6

178.5

R1

R2

280.6

Expected Time

T2 and R1 ready time :188.90 T2 and R1 expected time :238.20

Figure 1. Timing Allottment for Tasks. and the capacity of each resource is measured by

T2 and R2 ready time :178.86 T2 and R2 expected time :236.48

MIPS. The Ready time (Readym) indicates the time resource ‘m’ would have finished the

T3 and R1 ready time :239.60 T3 and R1 expected time :280.62

previously assigned jobs. The completion time of ith job on the jth machine is CTij = Readyi + ETij

66

T3 and R2 ready time :236.88 T3 and R2 expected time :290.66

(1)

Here the involve of two machines and three

Using the ETC matrix model, the scheduling

working process than the workload and timing allotment results are shown in figure. 1

problems are number of independent jobs to be

No of job & resources: 3 2 Jobs :T1 Jobs :T2 Jobs :T3 Resourse:R1 Resourse:R2 -----------------------------------------------workload and timing allotments -----------------------------------------------T1 and R1 ready time :0.0 T1 and R1 expected time :188.88

allocated to the available grid resources. Because

T1 and R2 ready time :0.5 T1 and R2 expected time :178.56

completing the previously assigned jobs. ETC

of No preemptive scheduling, each job has to be processed completely in a single machine. Number of machines is available to participate in the allocation of tasks. The workload of each job(in millions of instructions). The Computing capacity of each resources (in MIPS). Ready mrepresents the ready time of the machine after

matrix of size t * m, where t-represents the

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D.Maruthanayagam, Dr.R.Umarani.,Int.J.Comp.Tech.Appl, Vol 1 (1) 43-53

T1

T2

189.38

Completion timing

417.06

T3

415.34

179.06

527.54

517.50

R2

R1 Figure 2.Completion time of task and resource number of jobs and m-represents the number of

CT time [0][0] CT time [0][1] CT time [1][0] CT time [1][1] CT time [2][0] CT time [2][1]

machines. Job scheduling system is the most important part of grid resource management system. The scheduler receives the job request, and chooses

189.38. MIPS 179.06 .MIPS 417.06 .MIPS 415.34 .MIPS 517.50. MIPS 527.54 .MIPS

Maxs (CTij ) is the makespan of the complete

appropriate resource to run that job. In this

schedule. Makespan is used to measure the

paper, the formulation of job scheduling is based

throughput of the grid system. In general the

on the expected time to compute (ETC) matrix.

existing heuristic mapping can be divided into

meta-task is defined as a collection of

two categories. One is on line mode and the

independent task (i.e. task doesn’t require any

other one is batch mode. In the on line mode, the

communication with other tasks). Tasks derive

scheduler is always in ready mode. Whenever a

mapping statically. For static mapping, the

new job arrives to the scheduler, it is

number of tasks, t and the number of machines,

immediately allocated to one of the existing

m is known a priori. ETC (i,j) represents the

resources required by that job. Each job is

estimated execution time for task ti on machine

considered

mj. The expected completion time of the task ti

only

once

for

matching

and

scheduling. In the batch mode, the jobs and

on machine mj is ct (ti, mj) = ready (i) + ETC(ti,

resources

mj) ready (i) is the machine availability time,

are

collected

and

mapped

at

prescheduled time. In this mode, it takes better

i.e. the time at which machine mj completes any

decision because the scheduler knows details of

previously assigned tasks [12].The last working

the available jobs and resources. The proposed

of 2x3 (resource and task) processing completion

algorithm is also a heuristic algorithm for batch

time are shown in figure 2.

mode. The result of the algorithm will have four

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D.Maruthanayagam, Dr.R.Umarani.,Int.J.Comp.Tech.Appl, Vol 1 (1) 43-53

values (task, machine, starting time, expected

where

completion time).

² ´ij is the attractiveness of the move as computed

Then the new value of free(j) is the starting

by

some

heuristic

information

time plus ETij . A heuristic function is used to

indicating a prior desirability of that move

find out the best resource

² Tij is the pheromone trail level of the move,

ij =1 / free(j)

indicating how profitable it has been in the past

(2)

Using the formula 3 the highest priority

to make that particular move(it represents

machine is found which is free earlier. Here four

therefore a posterior indication of the desirability

ants are used. Each ant starts from random

of that move)

resource and task (they select ETij randomly jth

² Pk i;j is the probability to move from a state i to

resource and ith job). All the ants maintain a

a state j is depending on the combination of

separate list. Whenever they select next task and

above two values.

resource, they are added into the list. At each

4. COMPUTATIONAL RESULTS

iteration, the ants calculate the new pheromone

To overcome this disadvantage a new

level of the elements of the solutions is changed

algorithm is proposed. In this method four ants

by applying following updating rule

are used. The number of ants used is less than or equal to the number of tasks. From all the

Tij = 1 / Etij

(3)

possible scheduling lists find the one having

In this algorithm two set of tasks are

minimum makespan and uses the corresponding

maintained. One is set of scheduled tasks and the

scheduling list. Here two kinds of ET matrices

other is set of arrived. and unscheduled tasks.

are formed, first one consists of currently

The algorithm starts automatically, whenever the

scheduled jobs and the next consists of jobs

set of scheduled jobs become empty. The first

which have arrived but not scheduled. The

task to be performed and the machine in which it

scheduling algorithm is executed periodically. At

is performed is chosen randomly. Next, the task

the time of execution, it finds out the list of

to be run and the machine in which it is to be run

available resources (processors) in the grid

is computed by the following formula and also

environment, form the ET matrix and start

probality makespan are shown in table 1.

scheduling. When all the scheduled jobs are dispatched to the corresponding resources, the

Pij = Tij ij / Tij ij (4) Table 1. Probality makespan of running tasks. ----------------------------------------------Probability Makespan -----------------------------------------------[0][0] 1.00 [0][1] 0.51 [1][0] 0.28 [1][1] 0.22 [2][0] 0.16 [2][1] 0.13 ------------------------------------------------

scheduler starts scheduling over the unscheduled task matrix ET. This is guaranteed that the machines will be fully loaded at maximum time. The Pij ’s value has been modified to include th ETij is modified to the following equation and also probality makespan are shown in table 2. Pij = Tij

ij(1/ETij) / Tij

ij(1/ ETij)

(5)

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D.Maruthanayagam, Dr.R.Umarani.,Int.J.Comp.Tech.Appl, Vol 1 (1) 43-53

(6)

Table 2. Probality makespan of running tasks include ETij -----------------------------------------------Probability Makespan time with ETij -----------------------------------------------[0][0] 100.00 [0][1] 52.46 [1][0] 23.01 [1][1] 18.72 [2][0] 11.88 [2][1] 9.84 ------------------------------------------------

formula still produces better results are

shown in Table 4 . Pij = Tij

ij /

Tij

ij

(6)

Table 4. Probality makespan of running tasks include Tij = 1/ CT ij -----------------------------------------------Probability Makespan time with Tij = 1/ CT ij -----------------------------------------------[0][0] 100.00 [0][1] 40.56 [1][0] 23.43 [1][1] 14.57 [2][0] 11.33 [2][1] 7.41 ------------------------------------------------

The inclusion of ETij execution time of the ith job by the jth machine (predicted) in the calculation of probability, that the jth machine

will be free, has shown a positive result in performance improvement. This improvement is

The ant algorithm can be improved using

in terms of the decrease in makespan time.

some form of local search algorithm. Apply the

Further more, instead of adding ETij, execution

local optimum techniques to the output of the ant

time of the ith job by the jth machine (predicted),

algorithm. In this method first find the problem

in the calculation of probability, the (6) formula

resource-those with total execution times equal

still produces better results.

to the makespan of the solution, and attempt to

The inclusion of ETij execution time of the

move or swap set of jobs from the problem

ith job by the jth machine (predicted) in the

processor to another resource that has the

calculation of probability, that the jth machine

minimum makespan as compared with all other

will be free, has shown a positive result in

resources.This is shown in figure 3.

performance improvement. This improvement is in terms of the decrease in makespan time.It

shows table 3. Table 3. Performance Improvement

Etij

Tij = 1/Ctij 100

100

52.46

40.56

23.01

23.43

18.72

14.57

11.88

11.33

9.84

7.41

Further more, instead of adding ETij,

Figure-3.Graphical

execution time of the ith job by the jth machine

representation

for

comparision of makespan values

(predicted), in the calculation of probability, the

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D.Maruthanayagam, Dr.R.Umarani.,Int.J.Comp.Tech.Appl, Vol 1 (1) 43-53

After

applying

the

above

local

optimum

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