Management Notes

# Management Notes

Reference Notes for Management

# Three non-preemptive jobs J1, J2, J3 are waiting to be run. Their expected processor times are 6, 3 and 5 time units respectively. In which order should they be run to minimize the average response time?

## Three non-preemptive jobs J1, J2, J3 are waiting to be run. Their expected processor times are 6, 3 and 5 time units respectively. In which order should they be run to minimize the average response time?

Options:

(a) J1, J2, J3
(b) J1, J3, J2
(c) J2, J3, J1
(d) J2, J1, J3
(e) J3, J2, J1

### The Correct Answer Is:

(c) J2, J3, J1

To minimize the average response time for non-preemptive jobs J1, J2, and J3 with expected processor times of 6, 3, and 5 time units respectively, let’s delve into the rationale behind the correct order, and then I’ll discuss why the other options are not optimal.

Correct Answer Explanation: (c) J2, J3, J1

To understand this, consider the concept of minimizing average response time in non-preemptive scheduling. With non-preemptive scheduling, once a job starts, it runs to completion without interruption.

• Start with J2: It has the shortest expected processor time (3 units). By running the shortest job first, we reduce the waiting time for other jobs in the queue.
• Follow with J3: After J2, the next shortest job is J3 (5 units). Running J3 second ensures that a relatively short job follows immediately after the completion of J2, further minimizing the average response time.
• Finish with J1: Finally, J1 (6 units) is scheduled last. By placing the longest job at the end, we aim to minimize its impact on the average response time. This job being last allows shorter jobs to run beforehand, reducing their wait times.

Now, let’s analyze why the other options are not the most optimal choices:

(a) J1, J2, J3:

Initiating with J1, the longest job, creates increased waiting times for the shorter jobs (J2 and J3). When the longest job is processed first, it prolongs the start time of subsequent shorter jobs, resulting in higher average response times.

This sequence prioritizes the longest task, which is counterintuitive in non-preemptive scheduling as it doesn’t minimize waiting times.

(b) J1, J3, J2:

Similar to (a), starting with the longest job (J1) leads to increased waiting times for shorter jobs (J3 and J2). While J3 is shorter than J1, scheduling it after the longest job still increases overall response time. Then scheduling J2 last among the three jobs prolongs its wait time, affecting the average response time unfavorably.

(d) J2, J1, J3:

This sequence begins with the shortest job (J2), which is a step in the right direction. However, placing the longest job (J1) as the second task results in increased waiting times for the subsequent shorter job (J3).

J1 being processed before J3 elongates the wait time for J3, affecting the average response time.

(e) J3, J2, J1:

Starting with the longest job (J3) significantly extends the waiting times for both J2 and J1. While J3 is shorter than J1, initiating with the longest job still impacts the overall response time negatively. Additionally, processing the longest job last (J1) doesn’t effectively reduce the waiting time for shorter jobs (J2 and J3).

In essence, in non-preemptive scheduling, initiating with the shortest job among the available tasks is beneficial as it reduces the waiting time for subsequent jobs. Optimal scheduling aims to minimize waiting times for all tasks collectively, and starting with the longest job does not align with this goal.

Therefore, arranging the jobs in the order of shortest to longest expected processor times (J2, J3, J1) ensures the most optimal average response time by prioritizing shorter tasks and minimizing overall wait times.

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