A tricky task scheduling technique to optimize time cost and reliability in mobile computing environment
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The document presents a research paper focusing on a new task scheduling technique designed to optimize time cost and reliability within mobile computing environments (MCE). It highlights the significance of efficient task allocation to multiple processors and discusses strategies for minimizing processing time and cost while maximizing processing reliability. The proposed method seeks to ensure optimal resource utilization in MCE, particularly when the number of tasks exceeds the available processors.
![IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
_______________________________________________________________________________________
Volume: 03 Issue: 05 | May-2014, Available @ http://www.ijret.org 824
order to achieve minimum processing time, processing cost
and maximum processing reliability in MCE. Some of the
task allocation schemes have been reported in the literature,
such as Task modeling [1], Scheduling of tasks [2, 5, 7, 8,
11], Task allocation scheme [3, 15, 20], Resource allocation
[4, 13, 14, 16, 19], Load balancing [10], Static task
assignment [6], Resource scheduling [9], Job scheduling
algorithm [12], Resource management and scheduling [17],
Application scheduling in Mobile Cloud Computing [18].
This research paper propose a new task scheduling technique
to task allocation in MCE by using the proper utilization of
processors of the MCE so the problem of load balancing can
be avoid.
2. NOTATIONS
p Processor
t Task
n Number of Processors
m Number of Tasks
TCR Task Cost Reliability
MTCR Modified Task Cost Reliability
3. OBJECTIVE
The objective of this research paper is to solve task
scheduling problem in an efficient manner so that maximum
level of optimization is achieved in order to minimize
processing cost and time and maximize reliability by the
proper utilization of resource in Mobile Computing
Environment (MCE). The applied technique would also
ensure that processing of all the tasks and its sub tasks as task
modules are more than the numbers of processors in the
MCE. The type of assignment of tasks to the processor is
static. In this research paper performance is measured in term
of processing time, cost and reliability of the task that have to
be get processed on the processors of the environment and it
have to be optimally processed i.e., time, cost to be
minimized and reliability maximized.
4. TECHNIQUE
In order to obtain the overall optimal processing cost or
processing time or processing reliability of a Mobile
Computing Environment (MCE), this research paper consider
a problem of task scheduling where a set P = {p1, p2,
p3,………pn} of „n‟ processors with different processing
capabilities and a set T = {t1, t2, t3,………tm} of „m‟ tasks,
where m>n, every task has also contain some number of sub
tasks module. Processing time, cost and reliability are known
for each tasks module to the processor and arrange in TCTR.
Initially processing cost, processing time will be initializing
as zero (0) and processing reliability as one (1). Task
scheduling algorithm will find for the minimum value by row
(without repeating the column in the matrix) for processing
time, cost or maximum for processing reliability, in result
would get the tasks equal to number of processors available
in the MCE and those task will get assigned. The process will
repeat until number of tasks will remain lesser than the
processor available in the environment. Once that situation
will occur where the numbers of processors are greater than
the tasks waiting for the processing then will make slide
change in the technique. Instead of searching element row
wise, the search will be column wise that will make enable
the final allocation of remaining unscheduled task in MCE.
The function to calculate overall time [Etime], cost [Ecost]
and reliability [Ereilability] is given here:
Etime = ETij Xij
n
i=1
n
i=1
(i)
Ecost = ECij Xij
n
i=1
n
i=1
(ii)
Ereliablity = ERij
n
i=0
n
i=1
Xij (iii)
5. ALGORITHM
1. Start Algorithm
2. Read the number of task in m
3. Read the number of processor in n
4. Store task and Processing Cost, time and reliability into
Matrix PCTR (,) n x m of order
5. While (All task! = Assigned)
{
i. Check if the matrix containing numbers of tasks are
greater than or equal to numbers of processors (m>=n)
then go to step (ii) else step (iv)
ii. Search minimum value row wise in the matrix for
time, cost or maximum value for reliability.
iii. Check if the column is previously selected for
minimum/maximum value then GO TO step – (ii) to
find next minimum value for the row else Goto step
(vi) to assign eligible task.
iv. Search the minimum value for cost, time or maximum
value for reliability column wise in the matrix
v. Check if the row is previously selected for minimum
or maximum value then GO TO step – (iv) to find
next minimum or maximum value for the column else
Goto step (vi) to assign eligible task.
vi. Assign the eligible tasks to available processors
}
6. State the results
7. End of algorithm
6. IMPLEMENTATION
This research paper consider Mobile Computing
Environment (MCE) which consist a set P of 3 processors
{p1, p2, p3}, and a set T of 3 tasks {t1, t2, t3}. Each tasks
contained some number of modules and these modules
belongs to different tasks would be process on available
processors in MCE as mentioned in mentioned in Figure 1.](https://image.slidesharecdn.com/atrickytaskschedulingtechniquetooptimizetimecostandreliabilityinmobilecomputingenvironment-140813055040-phpapp02/85/A-tricky-task-scheduling-technique-to-optimize-time-cost-and-reliability-in-mobile-computing-environment-2-320.jpg)
![IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
_______________________________________________________________________________________
Volume: 03 Issue: 05 | May-2014, Available @ http://www.ijret.org 828
task needs to be processed with optimal time, cost and
reliability. This paper consider three tasks i.e. t1, t2 and t3 with
different tasks module and process t1 with minimum time, t2
process with minimum cost and t3 process with maximum
reliability in MCE. The optimal output of the given example
that is consider in research paper to test the task scheduling
technique is mentioned in the implementation section of the
paper is mentioned in Table 12:
Table 12: Consolidated results for Time, Cost and Reliability in MCE
Task p1 p2 p3 Optimal
ETime
Optimal
ECost
Optimal
Ereliablity
t1 m11 * m14 m12 m13 * m15 93 --- ---
t2 m22 * m25 * m27 m23 * m24 m21 * m26 --- 820 ---
t3 m34 * m31 * m36 m33 * m37 * m38 m32* m35 --- --- 0.993508
Fig 5: Final Task Scheduling in Mobile Computing
Environment (MCE)
The technique stated in pseudo code applied on several sets
of input data and that verified the objective of get maximum
processing reliability for given tasks for their execution. The
analysis of an algorithm mainly focuses on time complexity.
The time complexity of above mentioned algorithm is
O(m+n). By taking several input examples, the above
algorithm returns results as mentioned in Table 13.
Table 13 Time Complexity
Number of
Processors
(n)
Number
of tasks
(m)
Complexity of
algorithm [5]
O(mn2
)
Complexity
of present
algorithm
O(m+n)
3 5 45 8
3 6 54 9
3 7 63 10
3 8 72 11
3 9 81 12
4 5 80 9
4 6 96 10
4 7 112 11
4 8 128 12
4 9 144 13
5 6 125 11
5 7 150 12
5 8 175 13
5 9 200 14
5 10 225 15
Time complexity comparisons (as mentioned in Table 13) are
shown in Figure 6, 7 and 8.
Fig 6: Time complexity for No of Processors 3
Fig 7: Time complexity for No of Processors 4](https://image.slidesharecdn.com/atrickytaskschedulingtechniquetooptimizetimecostandreliabilityinmobilecomputingenvironment-140813055040-phpapp02/85/A-tricky-task-scheduling-technique-to-optimize-time-cost-and-reliability-in-mobile-computing-environment-6-320.jpg)
![IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
_______________________________________________________________________________________
Volume: 03 Issue: 05 | May-2014, Available @ http://www.ijret.org 829
Fig 8: Time complexity for No of Processors 5
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A tricky task scheduling technique to optimize time cost and reliability in mobile computing environment
- 1. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 03 Issue: 05 | May-2014, Available @ http://www.ijret.org 823 A TRICKY TASK SCHEDULING TECHNIQUE TO OPTIMIZE TIME COST AND RELIABILITY IN MOBILE COMPUTING ENVIRONMENT Faizul Navi Khan1 , Kapil Govil2 1 Department of Computer Application, Teerthanker Mahaveer University, Moradabad - 244 001, UP, INDIA 2 Department of Computer Application, Teerthanker Mahaveer University, Moradabad - 244 001, UP, INDIA Abstract Mobile Computing Environment (MCE) consisting portable computing devices interconnected by wireless medium, are increasingly being used in many area of science, business and education etc nowadays. It is the computation made over physical mobility. MCE facilitate the user to perform a task from a distant place from the device. This provides flexible communication between user and continuous access to networked services. Mobile computing shares many features with distributed computing as the application runs in MCE executes in distributed manner i.e. an application is combination of multiple tasks and these task schedule on the available resources to be execute. The performance of an application is depending on task scheduling technique in MCE. Task scheduling technique consist in finding an allocation of the tasks to the processors such that the total execution cost and time are minimized or processing reliability is maximized. So the ultimate objective of finding task scheduling technique is to improve the performance in terms to minimize cost and time and maximize reliability of MCE. In MCE an application can be seen as one or multiple task modules and each of the task modules allocate on available processor for its execution. Therefore, in this paper, the problem of scheduling the tasks in mobile computing environment is explore with objectives to minimize processing cost, processing time or maximize the processing reliability through a new task scheduling technique to optimize performance in MCE. The nature of the assignment will be static. Keywords – Cost, Mobile Computing Environment, Performance, Reliability, Task scheduling --------------------------------------------------------------------***------------------------------------------------------------------- 1. INTRODUCTION Advances in communication and computing technologies have introduced a new way of computing environment, called „Mobile Computing Environment (MCE)‟, which allows mobility of users thereby providing “anytime anywhere” computing environment. The mobility of user (or device) results in a highly dynamic environments with respect to the availability of resources/infrastructures for any application running on the mobile devices. Also, in a mobile computing environment, location has a profound effect. A Mobile Computing Environment (MCE) consists of a set of multiple processors interconnected by wireless communication links and equipped with software systems to produce an integrated and consistent processing environment. The task partitioning and scheduling strategies also play an important role for achieving high performance in MCE and an efficient task scheduling technique can utilize the resources in the MCE to complete the task execution at the earliest or in optimize manner. Task scheduling is a very common and challenging problem in MCE and it deals with finding an optimal scheduling of tasks to the processors so that the processing cost and processing time are be minimized and the processing reliability is maximized without violating any of the system constraints. Processing time is referred as the time taken by the task for its execution, expenses occurs during the task execution is describe as the processing cost and reliability can be consider as the reliability of its processors as well as the reliability of its communication links. Distribute data across processors unevenly so that each processor performs the volume of computation proportional to its speed is a common approach to solve task scheduling problem in MCE. This problem deals with finding an optimal task scheduling technique to the processors so that the processing time and cost can be minimized and processing reliability can be maximized for task scheduling in MCE. In MCE, the objective is to make processors busy executing tasks all the time by ensuring that it does not get idle and this serves the purpose. Task optimization is highly dependent on the tasks allocation method onto the available processor. In order to improve the performance of MCE, application workloads are divided into small independents units called tasks and these tasks need to be execute on available processor through a task scheduling technique. Task scheduling technique should be capable enough in terms of optimize processing capabilities in MCE i.e. minimize processing cost, minimize processing time and maximize processing reliability. This research paper explore task scheduling problem with n number of processors and m number of tasks where m>n in MCE and these tasks are need to schedule on the available processors in optimize manner with satisfying the processing constraints i.e. time, cost and reliability. In task scheduling problem once available processors are scheduled with a single task while the remaining tasks have to wait (if the numbers of task are greater than numbers of processor) until the present scheduled task will execute. To overcome such problem in a MCE, a task scheduling technique would be needed where more than one task to a single processor can be schedule in
- 2. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 03 Issue: 05 | May-2014, Available @ http://www.ijret.org 824 order to achieve minimum processing time, processing cost and maximum processing reliability in MCE. Some of the task allocation schemes have been reported in the literature, such as Task modeling [1], Scheduling of tasks [2, 5, 7, 8, 11], Task allocation scheme [3, 15, 20], Resource allocation [4, 13, 14, 16, 19], Load balancing [10], Static task assignment [6], Resource scheduling [9], Job scheduling algorithm [12], Resource management and scheduling [17], Application scheduling in Mobile Cloud Computing [18]. This research paper propose a new task scheduling technique to task allocation in MCE by using the proper utilization of processors of the MCE so the problem of load balancing can be avoid. 2. NOTATIONS p Processor t Task n Number of Processors m Number of Tasks TCR Task Cost Reliability MTCR Modified Task Cost Reliability 3. OBJECTIVE The objective of this research paper is to solve task scheduling problem in an efficient manner so that maximum level of optimization is achieved in order to minimize processing cost and time and maximize reliability by the proper utilization of resource in Mobile Computing Environment (MCE). The applied technique would also ensure that processing of all the tasks and its sub tasks as task modules are more than the numbers of processors in the MCE. The type of assignment of tasks to the processor is static. In this research paper performance is measured in term of processing time, cost and reliability of the task that have to be get processed on the processors of the environment and it have to be optimally processed i.e., time, cost to be minimized and reliability maximized. 4. TECHNIQUE In order to obtain the overall optimal processing cost or processing time or processing reliability of a Mobile Computing Environment (MCE), this research paper consider a problem of task scheduling where a set P = {p1, p2, p3,………pn} of „n‟ processors with different processing capabilities and a set T = {t1, t2, t3,………tm} of „m‟ tasks, where m>n, every task has also contain some number of sub tasks module. Processing time, cost and reliability are known for each tasks module to the processor and arrange in TCTR. Initially processing cost, processing time will be initializing as zero (0) and processing reliability as one (1). Task scheduling algorithm will find for the minimum value by row (without repeating the column in the matrix) for processing time, cost or maximum for processing reliability, in result would get the tasks equal to number of processors available in the MCE and those task will get assigned. The process will repeat until number of tasks will remain lesser than the processor available in the environment. Once that situation will occur where the numbers of processors are greater than the tasks waiting for the processing then will make slide change in the technique. Instead of searching element row wise, the search will be column wise that will make enable the final allocation of remaining unscheduled task in MCE. The function to calculate overall time [Etime], cost [Ecost] and reliability [Ereilability] is given here: Etime = ETij Xij n i=1 n i=1 (i) Ecost = ECij Xij n i=1 n i=1 (ii) Ereliablity = ERij n i=0 n i=1 Xij (iii) 5. ALGORITHM 1. Start Algorithm 2. Read the number of task in m 3. Read the number of processor in n 4. Store task and Processing Cost, time and reliability into Matrix PCTR (,) n x m of order 5. While (All task! = Assigned) { i. Check if the matrix containing numbers of tasks are greater than or equal to numbers of processors (m>=n) then go to step (ii) else step (iv) ii. Search minimum value row wise in the matrix for time, cost or maximum value for reliability. iii. Check if the column is previously selected for minimum/maximum value then GO TO step – (ii) to find next minimum value for the row else Goto step (vi) to assign eligible task. iv. Search the minimum value for cost, time or maximum value for reliability column wise in the matrix v. Check if the row is previously selected for minimum or maximum value then GO TO step – (iv) to find next minimum or maximum value for the column else Goto step (vi) to assign eligible task. vi. Assign the eligible tasks to available processors } 6. State the results 7. End of algorithm 6. IMPLEMENTATION This research paper consider Mobile Computing Environment (MCE) which consist a set P of 3 processors {p1, p2, p3}, and a set T of 3 tasks {t1, t2, t3}. Each tasks contained some number of modules and these modules belongs to different tasks would be process on available processors in MCE as mentioned in mentioned in Figure 1.
- 3. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 03 Issue: 05 | May-2014, Available @ http://www.ijret.org 825 Fig 1: Task modules originating from different mobile hosts are waiting in queue. Table 1: Tasks and their modules t1 {m11, m12, m13, m14,m15, m16} t2 {m21, m22, m23, m24, m25, m26, m27} t3 {m31, m32, m33, m34, m35, m36, m37, m38} Each task contained different individual task components which are known as modules. The processing time (t), processing cost (c) and processing reliability (r) of each task modules to each processor are known and mentioned in Processing Cost Time Reliability (PCTR) matrix as mentioned in Table 2 Table 2: Processing Time Cost Reliability Matrix Processors p1 p2 p3 Task Modules t-c-r t-c-r t-c-r t1 m11 15-100-0.999111 18-135-0.999125 17-110-0.999450 m12 16-110-0.999429 20-125-0.999159 18-115-0.999429 m13 21-115-0.999423 16-105-0.999328 15-120-0.999418 m14 18-120-0.999218 22-130-0.999419 23-100-0.999458 m15 19-105-0.999451 30-150-0.999480 26-125-0.999450 m16 33-125-0.999329 25-145-0.999219 28-155-0.998219 t2 m21 16-110-0.999112 18-125-0.941124 17-115-0.999418 m22 17-100-0.999149 20-135-0.982152 18-110-0.999429 m23 22-125-0.999533 16-130-0.979317 15-120-0.999418 m24 19-110-0.973218 22-105-0.999419 23-100-0.999413 m25 29-105-0.929431 30-150-0.989411 26-125-0.999414 m26 33-125-0.979328 25-145-0.969019 28-150-0.998226 m27 31-115-0.924322 22-140-0.924219 25-155-0.998214 t3 m31 15-125-0.999669 19-110-0. 997854 18-150-0. 998967 m32 18-100-0.999433 21-135-0. 998780 19-110-0. 999232 m33 26-130-0.998798 14-125-0. 998955 16-115-0. 987432 m34 21-110-0.999754 21-135-0. 987432 22-100-0. 999876 m35 29-105-0. 998766 32-155-0. 999578 24-185-0. 999866 m36 37-115-0. 998654 22-145-0. 998643 29-140-0. 998456 m37 35-125-0. 999478 25-160-0. 998903 24-105-0. 999754 m38 30-155-0. 999268 21-140-0. 998458 25-165-0. 996371 To proceed further with task scheduling problem in PCTR matrix, considering that t1 is based on processing time (t) (it may be processing cost or reliability), task t2 is based on processing cost (c) (it may be processing time and reliability) and task t3 is based on processing reliability (r) (it may be processing time and processing cost). Hence a new matrix named MPCTR can be derived by using PCTR, In MPCTR task t1 will represent processing time (t), t2 task processing cost (c) and t3 task processing reliability (r). New matrix MPCTR represent as Table 3: Table 3: Modified Processor Cost Time Reliability Matrix Processors p1 p2 p3 Task Modules t-c-r t-c-r t-c-r t1 m11 15-…-… 18-…-… 17-…-… m12 16-…-… 20-…-… 18-…-… m13 21-…-… 16-…-… 15-…-… m14 18-…-… 22-…-… 23-…-… m15 19-…-… 30-…-… 26-…-…
- 4. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 03 Issue: 05 | May-2014, Available @ http://www.ijret.org 826 m16 33-…-… 25-…-… 28-…-… t2 m21 ...-110-… ...-125-… ...-115-… m22 ...-100-… ...-135-… ...-110-… m23 ...-125-… ...-130-… ...-120-… m24 ...-110-… ...-105-… ...-100-… m25 ...-105-… ...-150-… ...-125-… m26 ...-125-… ...-145-… ...-150-… m27 ...-115-… ...-140-… ...-155--… t3 m31 …-…-0. 999669 …-…-0. 997854 …-…-0. 998967 m32 …-…-0. 999433 …-…-0. 998780 …-…-0. 999232 m33 …-…-0.998798 …-…-0. 998955 …-…-0. 987432 m34 …-…-0. 999754 …-…-0. 987432 …-…-0. 999876 m35 …-…-0. 998766 …-…-0. 999578 …-…-0. 999866 m36 …-…-0. 998654 …-…-0. 998643 …-…-0. 998456 m37 …-…-0. 999478 …-…-0. 998903 …-…-0. 999754 m38 …-…-0. 999268 …-…-0. 998458 …-…-0. 996371 MPCTR can be break into three different tables for each constraint i.e. Table 4 for processing time, Table 5 for processing cost and Table 6 for processing reliability in order to demonstrate all the three constraints of processing i.e. time cost and reliability in Mobile Computing Environment (MCE). Table 4: Processing Time m11 m12 m13 m14 m15 p1 15 16 21 18 19 p2 18 20 16 22 30 p3 17 18 15 23 26 Table 5: Processing Cost m21 m22 m23 m24 m25 m26 m27 p1 110 100 125 110 105 125 115 p2 125 135 130 105 150 145 140 p3 115 110 120 100 125 150 155 Table 6: Processing Reliability m31 m32 m33 m34 m35 m36 m37 m38 p1 0. 999669 0. 999433 0.998798 0. 999754 0. 998766 0. 998654 0. 999478 0. 999268 p2 0. 997854 0. 998780 0. 998955 0. 987432 0. 999578 0. 998643 0. 998903 0. 998458 p3 0. 998967 0. 999232 0. 987432 0. 999876 0. 999866 0. 998456 0. 999754 0. 996371 To demonstrate new scheduling technique, this research paper is initially considering Table 4 for task scheduling in MCE. Table 4 represent number of five modules which are originally belongs to task t1 need to get schedule on number of 3 processors. In Table 4 numbers of task modules are 5 and the numbers of processors are 3 (m>n), scheduling technique will determine minimum value for each row and will get the resulting output as mentioned in Table 7: Table 7: Matrix representing minimum value m11 m12 m13 m14 m15 p1 15 p2 16 p3 18 Hence there are only three processors in the environment, employed technique would schedule only three task module in MCE as mentioned in Table 8. Table 8: Scheduling Table Processor Task Processing Cost p1 m11 15 p2 m12 16 p3 m13 18 After the first task scheduling step execution, still two task in the queue and gets unscheduled, here numbers of processors are greater than number of task (two) (m<n), now the element will be searched by column wise and that approach will ensure that none of the task module will get remain
- 5. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 03 Issue: 05 | May-2014, Available @ http://www.ijret.org 827 unexecuted. And the final task scheduling is mentioned in Table 9. Table 9: Overall processing time Processor Task Processing time Etime p1 m11 * m14 33 93 p2 m12 16 p3 m13 * m15 44 Graphical representation of overall processing time is mentioned in Fig 2: Fig 2: Overall processing time taken by the processor in MCE By applying the same task scheduling technique, this research paper would also calculate processing cost and processing reliability for the given example in this research paper as mentioned in Table 10 and Table 11 respectively. Table 10: Overall processing cost Processor Task Processing Cost Ecost p1 m22 * m25 * m27 320 820 p2 m23 * m24 235 p3 m21* m26 265 Graphical representation of overall processing cost is mentioned in Fig 3: Fig 3: Overall processing cost occurred during the execution in MCE Table 11: Overall processing reliability Processor Task Processing Cost Ereliability p1 m31* m34 * m36 0.998077 0.993508 p2 m33 * m37 * m38 0.996320 p3 m32* m35 0.999098 Figure 4 showing graphical representation of overall processing reliability of given example: Fig 4: Overall processing reliability of the task in MCE 7. CONCLUSIONS This research paper provide the solution to the problem of task scheduling through a smart task scheduling technique, in which the number of the tasks is more than the number of processors in Mobile Computing Environment (MCE). Opted scheduling technique will ensure to satisfy various constraints i.e. time, cost and reliability in MCE. The task scheduling technique is presented in pseudo code and applied on the several sets of input data to test the performance and effectiveness of the pseudo code. Optimization of task is the common objective for any task scheduling problem that the
- 6. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 03 Issue: 05 | May-2014, Available @ http://www.ijret.org 828 task needs to be processed with optimal time, cost and reliability. This paper consider three tasks i.e. t1, t2 and t3 with different tasks module and process t1 with minimum time, t2 process with minimum cost and t3 process with maximum reliability in MCE. The optimal output of the given example that is consider in research paper to test the task scheduling technique is mentioned in the implementation section of the paper is mentioned in Table 12: Table 12: Consolidated results for Time, Cost and Reliability in MCE Task p1 p2 p3 Optimal ETime Optimal ECost Optimal Ereliablity t1 m11 * m14 m12 m13 * m15 93 --- --- t2 m22 * m25 * m27 m23 * m24 m21 * m26 --- 820 --- t3 m34 * m31 * m36 m33 * m37 * m38 m32* m35 --- --- 0.993508 Fig 5: Final Task Scheduling in Mobile Computing Environment (MCE) The technique stated in pseudo code applied on several sets of input data and that verified the objective of get maximum processing reliability for given tasks for their execution. The analysis of an algorithm mainly focuses on time complexity. The time complexity of above mentioned algorithm is O(m+n). By taking several input examples, the above algorithm returns results as mentioned in Table 13. Table 13 Time Complexity Number of Processors (n) Number of tasks (m) Complexity of algorithm [5] O(mn2 ) Complexity of present algorithm O(m+n) 3 5 45 8 3 6 54 9 3 7 63 10 3 8 72 11 3 9 81 12 4 5 80 9 4 6 96 10 4 7 112 11 4 8 128 12 4 9 144 13 5 6 125 11 5 7 150 12 5 8 175 13 5 9 200 14 5 10 225 15 Time complexity comparisons (as mentioned in Table 13) are shown in Figure 6, 7 and 8. Fig 6: Time complexity for No of Processors 3 Fig 7: Time complexity for No of Processors 4
- 7. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 _______________________________________________________________________________________ Volume: 03 Issue: 05 | May-2014, Available @ http://www.ijret.org 829 Fig 8: Time complexity for No of Processors 5 REFERENCES [1] Ana Isabel Molina, Miguel Ángel Redondo, Manuel Ortega, 2007, Applying Task Modeling and Pattern- based techniques in Reengineering Processes for Mobile Learning User Interfaces: A case study, JOURNAL OF COMPUTERS, VOL. 2, Issue 4, 23- 30 [2] Benazir Fateh, G. Manimaran, 2013, Joint Scheduling of Tasks and Messages for Energy Minimization in Interference-aware Real-time Sensor Networks, IEEE Transactions on Mobile Computing, 25 June 2013. IEEE computer Society Digital Library. IEEE Computer Society, <http://doi.ieeecomputersociety.org/10.1109/TMC.20 13.81>, ISSN: 1536-1233 [3] Faizul Navi Khan, Kapil Govil, 2013, Distributed Task Allocation Scheme for Performance Improvement in Mobile Computing Network, International Journal of Trends in Computer Science, vol: 2 issue: 3, pp: 809-817 [4] Hongbin Liang, Dijiang Huang, Lin X. Cai, Xuemin (Sherman) Shen, Daiyuan Peng, 2011, Resource Allocation for Security Services in Mobile Cloud Computing, IEEE INFOCOM 2011 Workshop on M2MCN-2011, ISBN: 978-1-4244-9920-5, 191-195 [5] Ilavarasan E, Manoharan R, 2010, High Performance and Energy Efficient Task Scheduling Algorithm for Heterogeneous Mobile Computing System, International Journal of Computer Science & Information Technology, Vol. 2, Issue 2, 10-27 [6] Kapil Govil and Dr. Avanish Kumar. 2011. A modified and efficient algorithm for Static task assignment in Distributed Processing Environment. International Journal of Computer Applications, Vol. 23, Number 8, Article 1, 1–5, ISBN: 978-93-80752- 82-3, ISSN: 0975 – 8887 [7] L. Yu, G. Zhou, Y. Pu, 2011, An Improved Task Scheduling Algorithm in Grid Computing Environment, Int'l J. of Communications, Network and System Sciences, Vol. 4 No. 4, 227-231. doi: 10.4236/ijcns.2011.44027. [8] Marjan Kuchaki Rafsanjani, Amid Khatibi Bardsiri, 2012, A New Heuristic Approach for Scheduling Independent Tasks on Heterogeneous Computing Systems, International Journal of Machine Learning and Computing, Vol: 2, No 4, 371-376 [9] S. Nagendram, J. Vijaya Lakshmi, D. Venkata Narasimha Rao, 2011, Efficient resource scheduling in data centers using MRIS, Indian Journal of Computer Science and Engineering, vol. 2, no. 5, pp. 764–769. [10] S. Suryadevera, J. Chourasia, S. Rathore, A. Jhummarwala, 2012, Load balancing in computational grids using ant colony optimization algorithm,” International Journal of Computer & Communication Technology, vol. 3, Issue 3, 20-23 [11] S. Thenmozhi , A. Tamilarasi, K. Thangavel, 2012, Fuzzy Based Task Scheduling for Hierarchical Resource Allocation in Mobile Grid Environment, International Journal of Soft Computing, Vol: 7, Issue: 3, 97-103 [12] Sandeep Kaur, Sukhpreet Kaur, 2013, Survey of Resource and Grouping Based Job Scheduling Algorithm in Grid Computing, International Journal of Computer Science and Mobile Computing, Vol: 2, Issue. 5, 214-218 [13] Sayed Chhattan Shah, Myong-Soon Park, 2010, Resource Allocation Scheme to Minimize Communication Cost in Mobile Ad Hoc Computational Grids, International Conference on Intelligent Networking and Collaborative Systems, ISBN: 978-0-7695-4278-2, 169-176 [14] Sayed Chhattan Shah, Qurat-Ul-Ain Nizamanib, Sajjad Hussain Chauhdaryc, Myong-Soon Park, 2012, An effective and robust two-phase resource allocation scheme for interdependent tasks in mobile ad hoc computational Grids, Journal of Parallel and Distributed Computing, Vol: 72, Issue 12, 1664–1679 [15] T. Xie and X. Qin, 2008, An Energy-Delay Tunable Task Allocation Strategy for Collaborative Applications in Networked Embedded Systems, IEEE Trans. Computers, Vol: 57, Issue 3, 329-343. [16] Thenmozhi S., A. Tamilarasi and P.T. Vanathi, 2012, A Fault Tolerant Resource Allocation Architecture for Mobile Grid, Journal of Computer Science, Vol: 8, Issue 6, 978-982 [17] Vignesh V, Sendhil Kumar KS, Jaisankar N, 2013, Resource Management and Scheduling in Cloud Environment, International Journal of Scientific and Research Publications, Volume 3, Issue 6, 1-6 [18] Xianglin Wei,Jianhua Fan, Ziyi Lu,Ke Ding, 2013, Application Scheduling in Mobile Cloud Computing with Load Balancing, Journal of Applied Mathematics, Vol: 2013, 1-13 [19] Yashpal Rohilla, Preeti Gulia, 2012, Resource Allocation in cellular Network : A cross layer approach, International Journal of Engineering Research and Applications, Vol. 2, Issue 4, 912-915 [20] Yichao Jin, Jiong Jin, Alexander Gluhak, Klaus Moessner and Marimuthu Palaniswami, 2012, An Intelligent Task Allocation Scheme for Multihop Wireless Networks, IEEE Transactions on Parallel and Distributed Systems, Vol: 23, Issue 3, 444-451