T₁ (8) T₂ (6) O T3 (7) T4 (4) T5 (9) T6 (3) T7 (2) T8 (5) O T9 (2) O T10 (7) 5. Using the priority list T4, T3, T9, T10, T8, T5, T6, T1, T7, T2 schedule the project with two processors.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Contemporary Mathematics 

*Clear Writing Please* 

The image displays a directed graph with tasks labeled as \( T_1 \) through \( T_{10} \). Each task \( T \) is associated with a number that indicates the task's duration in some unspecified unit of time. The tasks and their respective durations are as follows:

- \( T_1 (8) \)
- \( T_2 (6) \)
- \( T_3 (7) \)
- \( T_4 (4) \)
- \( T_5 (9) \)
- \( T_6 (3) \)
- \( T_7 (2) \)
- \( T_8 (5) \)
- \( T_9 (2) \)
- \( T_{10} (7) \)

The arrows between the tasks indicate dependencies, meaning a task with an arrow pointing to another task must be completed before the subsequent task can begin. 

Key directed edges in this graph are:
- \( T_1 \) leads to \( T_5 \) and \( T_6 \).
- \( T_2 \) leads to \( T_6 \).
- \( T_3 \) leads to \( T_6 \).
- \( T_4 \) leads to \( T_7 \).
- \( T_5 \) leads to \( T_9 \) and \( T_8 \).
- \( T_6 \) leads to \( T_8 \).
- \( T_7 \) leads to \( T_8 \).
- \( T_8 \) leads to \( T_{10} \).

The task at the bottom of the image is a scheduling prompt: 

5. Using the priority list \( T_4, T_3, T_9, T_{10}, T_8, T_5, T_6, T_1, T_7, T_2 \), schedule the project with two processors.

This indicates that an attempt should be made to allocate tasks to two processors while respecting the given priority list and task dependencies.
Transcribed Image Text:The image displays a directed graph with tasks labeled as \( T_1 \) through \( T_{10} \). Each task \( T \) is associated with a number that indicates the task's duration in some unspecified unit of time. The tasks and their respective durations are as follows: - \( T_1 (8) \) - \( T_2 (6) \) - \( T_3 (7) \) - \( T_4 (4) \) - \( T_5 (9) \) - \( T_6 (3) \) - \( T_7 (2) \) - \( T_8 (5) \) - \( T_9 (2) \) - \( T_{10} (7) \) The arrows between the tasks indicate dependencies, meaning a task with an arrow pointing to another task must be completed before the subsequent task can begin. Key directed edges in this graph are: - \( T_1 \) leads to \( T_5 \) and \( T_6 \). - \( T_2 \) leads to \( T_6 \). - \( T_3 \) leads to \( T_6 \). - \( T_4 \) leads to \( T_7 \). - \( T_5 \) leads to \( T_9 \) and \( T_8 \). - \( T_6 \) leads to \( T_8 \). - \( T_7 \) leads to \( T_8 \). - \( T_8 \) leads to \( T_{10} \). The task at the bottom of the image is a scheduling prompt: 5. Using the priority list \( T_4, T_3, T_9, T_{10}, T_8, T_5, T_6, T_1, T_7, T_2 \), schedule the project with two processors. This indicates that an attempt should be made to allocate tasks to two processors while respecting the given priority list and task dependencies.
Expert Solution
Step 1: Solution

Time 0: There are two processer say P1 and P2 and they are ready to take task, so according to priority list P1 took T4 and P2 took T3

Priority list: T4,T3,T9,T10,T8,T5,T6,T1,T7,T2

            0P1T44P2T37

Time 4:P1 completes T4 and ready to take task and according to availability and priority list P1 took T1

Priority list: T4,T3,T9,T10,T8,T5,T6,T1,T7,T2

            0                         4P1T44---T18P2T37----

Time 7: P2 completes T3 and ready to take available task and according to priority list and available task P2 is assigned with T7

Priority list: T4,T3,T9,T10,T8,T5,T6,T1,T7,T2

            0                         4                 7P1T44---T18---P2T37----          --T72

Time 9: P2 completes T7 and and ready to take available task and according to priority list and available task P2 is assigned with T2

Priority list: T4,T3,T9,T10,T8,T5,T6,T1,T7,T2

            0                         4                 7                9P1T44---T18---          --P2T37----          --T72-T26

Time 12: P1 completes T1 and there is no available task 

Priority list: T4,T3,T9,T10,T8,T5,T6,T1,T7,T2

            0                         4                 7                9                 12P1T44---T18---          --          --        P2T37----          --T72-T26---

Time 15: P2 completes T2  and the available task is T5,T6, and according to priority list P1 is assigned with T5 and P2 with T6

Priority list: T4,T3,T9,T10,T8,T5,T6,T1,T7,T2

            0                         4                 7                9                 12                15P1T44---T18---          --          --       --T59    P2T37----          --T72-T26---        --T63 

Time 18: P2 completes T6 and the available only task is T8 so P2 is assigned with T8

Priority list: T4,T3,T9,T10,T8,T5,T6,T1,T7,T2

            0                         4                 7                9                 12                15                  18P1T44---T18---          --          --       --T59---    P2T37----          --T72-T26---        --T63--T85

Time 23:P2 completes T8 and there is no available task 

Priority list: T4,T3,T9,T10,T8,T5,T6,T1,T7,T2

            0                         4                 7                9                 12                15                  18                     23P1T44---T18---          --          --       --T59---          -----P2T37----          --T72-T26---        --T63--T85----

Time 24:P1 completes T5 and both P1 and P2 is available to take task and according to priority list P1 is assigned with T9, P2  with T10

Priority list: T4,T3,T9,T10,T8,T5,T6,T1,T7,T2

            0                         4                 7                9                 12                15                  18                     23      24                                     P1T44---T18---          --          --       --T59---          -----     T92P2T37----          --T72-T26---        --T63--T85----   T107

Time 26:P1 completes its task T9 and there is no available task

            0                         4                 7                9                 12                15                  18                     23      24              26                                   P1T44---T18---          --          --       --T59---          -----     T92   -|P2T37----          --T72-T26---        --T63--T85----   T107  --

Time 31: P2 completes its task T10

            0                         4                 7                9                 12                15                  18                     23      24              26                 31        P1T44---T18---          --          --       --T59---          -----     T92   -|P2T37----          --T72-T26---        --T63--T85----   T107  --   -----|

 

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