To find the average waiting time for the SJF (Shortest Job First) scheduling algorithm with preemption, we can use the following steps:
- Sort the processes based on their arrival times.
- Initialize a priority queue (min-heap) to keep track of the processes based on their remaining burst times.
- Iterate through the processes in the order of their arrival.
- At each step, check if there is any process with a shorter remaining burst time in the priority queue. If so, preempt the current process and execute the one with the shorter burst time.
- Calculate the waiting time for each process.
- Find the average waiting time.
Let's calculate:
Process |
Arrival Time |
CPU Time |
P1 |
0 |
10 |
P2 |
0 |
5 |
P3 |
2 |
3 |
P4 |
5 |
20 |
P5 |
10 |
2 |
Sorted processes based on arrival time:
- P1 (Arrival Time: 0, CPU Time: 10)
- P2 (Arrival Time: 0, CPU Time: 5)
- P3 (Arrival Time: 2, CPU Time: 3)
- P4 (Arrival Time: 5, CPU Time: 20)
- P5 (Arrival Time: 10, CPU Time: 2)
Now, let's simulate the execution:
- At time t=0, both P1 and P2 are available. P2 has a shorter burst time, so execute P2.
- At time t=5, P3 arrives. Preempt P2 and execute P3.
- At time t=8, P1 arrives. Preempt P3 and execute P1.
- At time t=18, P4 arrives. Preempt P1 and execute P4.
- At time t=38, P5 arrives. Preempt P4 and execute P5.
Calculate waiting time for each process:
- P1: (t=8) - (arrival time=0) = 8
- P2: (t=0) - (arrival time=0) = 0
- P3: (t=5) - (arrival time=2) = 3
- P4: (t=18) - (arrival time=5) = 13
- P5: (t=38) - (arrival time=10) = 28
-
Average waiting time = (8 + 0 + 3 + 13 + 28) / 5 = 52 / 5 = 10.4 ms
Therefore, the correct answer is not provided among the options (a), (b), (c), and (d). The calculated average waiting time is 10.4 ms.