Let disk request come to a disk driver for cylinders in the order 10, 22, 20, 2, 40, 6 and 38, at the time when the disk driver is reading from cylinder 20. If the seek time is 6 ms per cylinder then, the total seek time for the disk arm scheduling time algorithm FCFS (First Come First Serve) is:

Question

Accepted Answer

The correct option is (4):

This question requires us to calculate the total seek time for disk scheduling using the First Come First Serve (FCFS) algorithm. The FCFS algorithm processes disk requests strictly in the order they arrive in the queue, regardless of the current position of the disk head, leading to potentially long seek times. We begin at the current cylinder position of 20, and the requests are served sequentially: 10, 22, 20, 2, 40, 6, and 38. The total movement of the disk arm is the sum of the absolute differences between consecutive cylinder accesses: |10-20| + |22-10| + |20-22| + |2-20| + |40-2| + |6-40| + |38-6|. This calculates to 10 + 12 + 2 + 18 + 38 + 34 + 32, totaling 146 cylinders moved. Since the seek time is 6 ms per cylinder, the total seek time is 146 cylinders multiplied by 6 ms/cylinder, which results in 876 ms. FCFS is simple to implement but often the least efficient scheduling algorithm for disk access.

The incorrect option is (1):
The value 360 ms is the result of a significantly lower total cylinder movement than calculated for the FCFS sequence. For 360 ms to be the correct answer, the total cylinder movement would need to be 60 cylinders (360 ms / 6 ms/cylinder). This result would likely be associated with a more optimized algorithm, such as Shortest Seek Time First (SSTF) or SCAN, which prioritizes requests closer to the current head position to minimize head travel. Under FCFS, which does not optimize for distance, the head must travel back and forth across the disk to serve the requests in their arrival order, making a low travel value like 60 cylinders impossible for this sequence.

The incorrect option is (2):
The value 212 ms is far too small to represent the total seek time for this set of requests using FCFS. This result would imply a total travel of approximately 35.3 cylinders (212 ms / 6 ms/cylinder), which is an unreasonably short distance for 7 disk accesses. A result this low would only be achievable if most requests were clustered very close to the starting cylinder 20, or if the initial starting cylinder was misidentified, or if the calculation was based on an incorrect total number of requests. FCFS inherently results in high seek times because it lacks any optimization logic.

The incorrect option is (3):
The value 848 ms is close to the correct answer but is not mathematically precise based on the FCFS calculation. A seek time of 848 ms would correspond to a total cylinder movement of approximately 141.33 cylinders (848 ms / 6 ms/cylinder). This suggests a calculation error, perhaps by missing one of the smaller movements, such as the movement from 22 to 20 (|20-22|=2) or from 2 to 6 (|6-2|=4 in a different order). Remember that FCFS is an exact, non-optimizing sequence, and therefore, the exact total cylinder movement must be calculated for precision.