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Critical Path Analysis & List Processing Algorithm. Scheduling Tasks. A processor is a person, machine, computer, or robot etc., which works on a task. To solve a scheduling problem typically the tasks are scheduled to minimize completion times.

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scheduling tasks
Scheduling Tasks
  • A processor is a person, machine, computer, or robot etc., which works on a task.
  • To solve a scheduling problem typically the tasks are scheduled to minimize completion times.
  • Make sure to consider importance of a task, does one task need to be completed before another task.
assumptions and rules
ASSUMPTIONS AND RULES
  • If a processor starts working on a task, the work will continue until that task is complete.
  • No processor stays idle if there is a task to be done.
  • The CPA has an associated order-requirement digraph.
  • The tasks are arranged in a priority list that is independent of the digraph.
goals of cpa
Goals of CPA
  • Minimize the completion time for a given number of processors
  • Minimize processor idle time
  • Minimize the number of processors needed to complete the job in a specified time.

A task is considered ready if all its predecessors (prerequisite tasks) in the digraph have been completed.

list processing algorithm
LIST PROCESSING ALGORITHM
  • Assignment of Processors: The lowest numbered idle processor is assigned to the highest priority ready task until either all processors are assigned or all ready tasks are being worked on
  • Status Check: When a processor completes a task, that processor becomes idle. Check for ready tasks and tasks not yet completed and determine which of the following applies
    • If there is a ready task repeat step 1.
    • If there are no ready tasks bunt not every task has been completed, the idle processor remains idle until more tasks are completed.
    • If all tasks are completed, the job is done.
example
EXAMPLE:
  • What is the completion time for the job shown in the digraph below using the priority list using one processor
slide7

T1-10

T4-22

T3-7

T2-18

T5-29

P1

example1
EXAMPLE:
  • What is the completion time for the job shown in the digraph below using the priority list using two processors?
slide9

T2-15

T3-7

T5-22

P1

P2

IDLE-7

T1-3

T4-11

IDLE-15

IDLE-22

making fajitas
Making Fajitas
  • Tortillas
  • Chicken
  • 1 onion
  • Seasoning
  • Tomatoes
  • Cilantro

T1: slice chicken & onions – 5 min

T2: Cook chicken – 10 min

T3: Cook onions – 5 min

T4: Add seasoning – 1 min

T5: Chop tomato – 4 min

T6: Mix tomato and cilantro – 2 min

T7: Warm tortillas – 1 min

T8: Serve – 1 min

Priority list: ,,

slide11
, ,

T7-28

T2-21

T3-26

T5-4

T6-6

T1-11

P1

T4-27

T8-29

slide12
, ,

T8-22

T4-21

T7-7

IDLE

P1

T3-20

T5-4

T6-6

P2

IDLE

T2-15

T1-5

IDLE

slide14

IDLE

T3-14

T10-18

T8-10

T1-1

T5-5

P1

T4-15

IDLE

T6-9

P2

IDLE

T9-17

T7-7

IDLE

T2-12

slide15

T8-10

T4-13

T10-16

T3-12

P1

T6-9

T1-1

T5-5

P2

T7-7

IDLE

IDLE

T9-15

P3

T2-10

IDLE

IDLE

critical path schedules
Critical Path Schedules
  • Find a task that heads a critical (longest) path in the order-requirement digraph
  • Place the task found in step 1 next in the priority list
  • Remove the task found in step 1 from the digraph
  • If all tasks have been removed, the list is completed. If tasks remain return to step one.
critical path
Critical path

T5-12

T6-10

T3-7

P1

T8-16

P2

T4-10

T1-5

T2-8

T7-11

slide19

T9-15

T10-16

T1-1

T5-5

P1

T3-12

T2-10

P2

IDLE

T6-9

T7-11

IDLE

T4-13

T8-12

slide20

Critical path algorithm on 3 processors

T10-16

P1

T1-1

T3-12

T9-15

T5-5

T2-10

P2

T4-13

T6-9

IDLE

T8-10

P3

T7-7

IDLE

IDLE

slide21

List process algorithm on 3 processors

T8-10

T4-13

T10-16

T3-12

P1

T6-9

T1-1

T5-5

P2

T7-7

IDLE

IDLE

T9-15

P3

T2-10

IDLE

IDLE

slide22

Critical path algorithm on 2 processors

T9-15

T10-16

T1-1

T5-5

P1

T3-12

T2-10

P2

IDLE

T6-9

T7-11

IDLE

T4-13

T8-12

slide23

Critical path algorithm on 3 processors

T10-16

P1

T1-1

T3-12

T9-15

T5-5

T2-10

P2

T4-13

T6-9

IDLE

T8-10

P3

T7-7

IDLE

IDLE