The document discusses task scheduling algorithms in grid computing. It introduces the Min-Min and Max-Min algorithms. Min-Min schedules tasks based on minimum completion time, selecting the task-resource pair with the lowest expected completion first. Max-Min selects the task with the maximum minimum expected completion time across all resources first. The document hypothesizes that Min-Min performs better with heavier tasks while Max-Min is better with lighter tasks. It outlines a simulation to test this, modeling tasks, resources, and scheduling algorithms to calculate makespan and evaluate the hypothesis.

1. Task Scheduling in Grid
Computing
Team Coda

2. Hardik Navin Nagda
hnn8556@rit.edu
Divin Jagdish Visariya
djv9999@rit.edu
Team Members

3. Agenda
• Task Scheduling in Grid Computing
• Min-Min Algorithm and Max-Min Algorithm
• Hypothesis
• Our Simulation Idea
• Design of our code
• Code structure explanation
• Demo

4. Task Scheduling in Grid Computing
• Grid is globally distributed and consists of
heterogeneous, loosely coupled data and resources
• Grid changes the resources quite frequently and the
systems are heterogeneous in nature
• Task scheduling challenge is to find the best or
optimal resources in order to minimize the tasks
computation time

5. Min-Min Algorithm
• Static Task Scheduling Algorithm
• Tasks are scheduled based on minimum completion time
• Example : Expected Completion Time
M1 M2 M3
Task 1 3 6 7
Task 2 4 12 8
Task 3 6 20 18

6. Min-Min Algorithm
M1 M2 M3
Task 1 3 6 7
Task 2 4 12 8
Task 3 6 20 18
Step 1 :

7. Step 2 :
Min-Min Algorithm
M1 M2 M3
Task 2 4 + 3 12 8
Task 3 6 + 3 20 18

8. Min-Min Algorithm
M1 M2 M3
Task 3 9 + 4 20 18
Step 3 :

9. Min-Min algorithm
Image Taken from Paper : An Improved Scheduling Algorithm for Grid Tasks
Image Taken from Paper : An Improved Scheduling Algorithm for Grid Tasks

10. Max-Min Algorithm
• Static Task Scheduling Algorithm
• Two Phases
• First Phase : Set of all minimum expected completion time are
found for every task and resource
• Second phase : Task with the maximum value within the above
set is selected for execution
• Example : Expected Completion Time
M1 M2 M3
Task 1 3 6 7
Task 2 4 12 8
Task 3 6 20 18

11. Max-Min Algorithm
M1 M2 M3
Task 1 3 6 7
Task 2 4 12 8
Task 3 6 20 18
Step 1 :

12. Max-Min Algorithm
M1 M2 M3
Task 1 3 + 6 6 7
Task 2 4 + 6 12 8
Step 2 :

13. Max-Min Algorithm
M1 M2 M3
Task 1 9 6 7
Task 2 10 12 8
Step 3 :

14. Max-Min Algorithm
M1 M2 M3
Task 1 9 6 7 + 8
Step 4 :

15. Max-Min Algorithm
Image Taken from Paper : An Improved Scheduling Algorithm for Grid Tasks

16. Min-Min v/s Max-Min Algorithm
• If there are many lighter tasks, Max-Min
algorithm is better than Min-Min in terms of
makespan and resource utilization
• If there are many heavier tasks, Min-Min
algorithm is better than Max-Min

17. Hypothesis
• Grid scheduling using Min-Min algorithm gives lower
makespan as compared to the Max-Min algorithm if
there are more heavy computational jobs
• Likewise, Max-Min Algorithm gives lower makespan
as compared to Min-Min Algorithm if there are
more lighter jobs
• Makespan means the entire completion time for
the fix number of jobs

18. Simulation Idea

19. Design of Min-Min Algorithm
• T = {T1, T2 … Tm} : The Set of Tasks
• R = {R1, R2 … Rn} : The Set of Resources
• Expected Execution Time Table
• The m x n matrix which contains the time taken by the
task to complete execution for given resource
• Expected Completion Time Table
• The m x n matrix which contains the time taken by the
task to complete execution for given resource + waiting
time of the task for obtaining the desired resource
• Running Time for Resources
• The total time taken by resource to execute all task
assigned

20. Design of Min-Min Algorithm
• Simulate Task
• Task id is generated randomly and its added to the set
• Arrival time of the task is recorded
• Scheduler Algorithm is invoked accordingly
• Removes the task from the set after it is served
• Min-Min Scheduler
• Computes the Expected Execution Time :
• Expected Execution Time = Size of task (MI) / CPU processing
power (MIPS)
• Computes the Expected Completion Time :
• Expected Completion Time = Expected Execution Time
+ Resource Running Time - Task Arrival Time

21. Design of Min-Min Algorithm (Cont..)
• Min-Min Scheduler Continued
• Contacts Resource Monitor to check if any resource is idle
• If yes, then finds the task with the minimum Expected
Completion Time and also the resource for that task
• Assigns the task to the resource and change the resource
status to “Running”
• Adds the Execution Time of the resource to the resource
Waiting Time and updates resource Running Time
• Also updates Expected Completion Time based on the
resource Waiting Time
• After serving the task the resource again follows the same
procedure until all task are served

22. Design of Min-Min Algorithm (Cont..)
• Resource Monitor
• Maintains the status of all the resources after every
task is being served or resource being idle

23. T1
Set of Tasks
Resources

24. T1
Set of Tasks
Resources

25. T2
T1
Set of Tasks
Resources

26. T1
T2
Set of Tasks
Resources

27. T1
T2
T3
Set of Tasks
Resources

28. T1
T2
T3T4
Set of Tasks
Resources

29. T1
T2
T3T4T5
Set of Tasks
Resources

30. T4
T2
T5 T3
Set of Tasks
Resources

31. Task

32. Resource

33. Simulate

34. Demo

35. MakeSpan Calculation

36. Progress made so far
• Prepared the design of the system for simulation
• Written the code to simulate the Min-Min algorithm
• To be Done:
• Implement Max-Min algorithm
• Perform experiments for different cases
• Evaluate the makespan calculation and check the
results
• Prove or Disprove our hypothesis

37. Questions ?
THANK YOU