Understanding the SCAN (LEFT) Disk Scheduling Algorithm

The SCAN (Scan) disk scheduling algorithm, also known as the elevator algorithm, works by moving the disk head in one continuous direction (e.g., towards cylinder 0 or the highest cylinder number) servicing all the requests in its path. Once it reaches the end of the disk, it reverses direction and scans back towards the other end, servicing the remaining requests.

In this specific problem, we are using the SCAN (LEFT) variant. This means the disk head starts moving from its current position towards cylinder 0.

Analyzing the Disk Request Queue and Head Position

The given disk requests are for cylinders: $45$, $81$, $185$, $33$, $175$, $99$, $150$, $77$.

The disk head initially starts at cylinder $58$.

The direction is LEFT, meaning the head will move towards cylinder $0$.

Step-by-Step Processing with SCAN (LEFT)

1. Initial Position: The head is at cylinder $58$.
2. Direction: The head moves LEFT (towards $0$).
3. Requests to the Left: Requests located at cylinders less than $58$ are $45$ and $33$.
4. Servicing the First Request: Moving from $58$ towards $0$, the head will first encounter cylinder $45$. So, the 1st request processed is $45$.
5. Servicing the Second Request: After servicing $45$, the head continues towards $0$. The next available request in this direction is cylinder $33$. Therefore, the 2nd request processed is $33$.
6. Reaching the End: The head continues to cylinder $0$.
7. Reversing Direction: After reaching $0$, the head reverses direction and moves towards the highest cylinder.
8. Servicing Remaining Requests: The remaining requests are $77$, $81$, $99$, $150$, $175$, $185$. The head will now service these in ascending order while moving right: $77$, $81$, $99$, $150$, $175$, $185$.

Conclusion

Following the SCAN (LEFT) disk scheduling algorithm, starting from cylinder $58$:

• The first request serviced is $45$.
• The second request serviced is $33$.

Thus, the 2nd request processed is $33$.