Consider the following set of processes with the arrival time and length of…

We use the non-preemptive Highest Response Ratio Next (HRN) scheduling algorithm.

For HRN, the response ratio (also called weighted turnaround ratio) for each ready process is:

Response ratio = (Waiting time + Burst time) / Burst time

1. At time 0, only P1 has arrived, so schedule P1 from 0 to 5.

2. At time 5, P2, P3, and P4 are ready. Compute response ratios:

   • P2: waiting = 5 − 2 = 3, ratio = (3 + 3) / 3 = 2.0

   • P3: waiting = 5 − 2 = 3, ratio = (3 + 2) / 2 = 2.5

   • P4: waiting = 5 − 5 = 0, ratio = (0 + 3) / 3 = 1.0

   P3 has the highest ratio, so schedule P3 from 5 to 7.

3. At time 7, P2, P4, and P5 (arrived at time 6) are ready. Compute response ratios:

   • P2: waiting = 7 − 2 = 5, ratio = (5 + 3) / 3 ≈ 2.67

   • P4: waiting = 7 − 5 = 2, ratio = (2 + 3) / 3 ≈ 1.67

   • P5: waiting = 7 − 6 = 1, ratio = (1 + 1) / 1 = 2.0

   P2 has the highest ratio, so schedule P2 from 7 to 10.

4. At time 10, P4 and P5 are ready. Compute response ratios:

   • P4: waiting = 10 − 5 = 5, ratio = (5 + 3) / 3 ≈ 2.67

   • P5: waiting = 10 − 6 = 4, ratio = (4 + 1) / 1 = 5.0

   P5 has the highest ratio, so schedule P5 from 10 to 11, then schedule P4 from 11 to 14.

Final schedule (start → finish): P1: 0 → 5, P3: 5 → 7, P2: 7 → 10, P5: 10 → 11, P4: 11 → 14.

• P1: arrival = 0, burst = 5, completion = 5 → waiting = 0, turnaround = 5, weighted turnaround = 5 / 5 = 1.0

• P3: arrival = 2, burst = 2, completion = 7 → waiting = 5, turnaround = 5, weighted turnaround = 5 / 2 = 2.5

• P2: arrival = 2, burst = 3, completion = 10 → waiting = 5, turnaround = 8, weighted turnaround = 8 / 3 ≈ 2.67

• P5: arrival = 6, burst = 1, completion = 11 → waiting = 4, turnaround = 5, weighted turnaround = 5 / 1 = 5.0

• P4: arrival = 5, burst = 3, completion = 14 → waiting = 6, turnaround = 9, weighted turnaround = 9 / 3 = 3.0

The average weighted turnaround time is the mean of these values:

(1.0 + 2.5 + 2.67 + 5.0 + 3.0) / 5 ≈ 14.17 / 5 ≈ 2.834 ms.

So, the average weighted turnaround time for these processes using HRN is approximately 2.834 ms.