Question 29

Initial head position: cylinder 100.
Pending request queue: $\{30, 85, 90, 100, 105, 110, 135, 145\}$.

1. At cylinder 100, distance to request 100 is $|100 - 100| = 0$.

   • Service cylinder 100 (1st request serviced).
   • Remaining queue: $\{30, 85, 90, 105, 110, 135, 145\}$.
   • Current head position: 100.

2. Distances from 100:

   • $|100 - 105| = 5$
   • $|100 - 90| = 10$
   • Minimum seek distance is 5 (to cylinder 105).
   • Service cylinder 105 (2nd request serviced).
   • Remaining queue: $\{30, 85, 90, 110, 135, 145\}$.
   • Current head position: 105.

3. Distances from 105:

   • $|105 - 110| = 5$
   • $|105 - 90| = 15$
   • Minimum seek distance is 5 (to cylinder 110).
   • Service cylinder 110 (3rd request serviced).
   • Remaining queue: $\{30, 85, 90, 135, 145\}$.
   • Current head position: 110.

4. Distances from 110:

   • $|110 - 90| = 20$
   • $|110 - 135| = 25$
   • Minimum seek distance is 20 (to cylinder 90).
   • Cylinder 90 is the 4th request serviced.

Therefore, cylinder 90 is serviced after servicing 3 requests (100, 105, and 110).