Storage Management

Here’s a step-by-step explanation of the solution using Shortest Seek Time First (SSTF) for the given problem. Given:

• Cylinder queue (requests): P, Q, R, S, T with positions:
  • P at 155
  • Q at 85
  • R at 110
  • S at 30
  • T at 115
• Disk head starts at position: 100 Goal:
• Serve requests in the order that minimizes the seek time from the current head position (SSTF). If there’s a tie, break it with a predefined rule (usually lower cylinder first or by the given problem’s tie rule). How SSTF is applied here:

1. Start at head = 100.
2. Compute seek distance to each pending request:
   • P (155): |155 - 100| = 55
   • Q (85): |85 - 100| = 15
   • R (110): |110 - 100| = 10
   • S (30): |30 - 100| = 70
   • T (115): |115 - 100| = 15
3. Pick the minimum distance: R at 110 (distance 10). Serve R first.
   • Head moves from 100 to 110.
   • Remaining requests: P(155), Q(85), S(30), T(115).
4. Update distances from new head position (110):
   • P (155): |155 - 110| = 45
   • Q (85): |85 - 110| = 25
   • S (30): |30 - 110| = 80
   • T (115): |115 - 110| = 5
5. Choose the smallest distance: T at 115 (distance 5). Serve T next.
   • Head moves from 110 to 115.
   • Remaining: P(155), Q(85), S(30).
6. Update distances from head = 115:
   • P (155): |155 - 115| = 40
   • Q (85): |85 - 115| = 30
   • S (30): |30 - 115| = 85
7. Smallest distance: Q at 85 (distance 30). Serve Q next.
   • Head moves from 115 to 85.
   • Remaining: P(155), S(30).
8. Update distances from head = 85:
   • P (155): |155 - 85| = 70
   • S (30): |30 - 85| = 55
9. Smallest distance: S at 30 (distance 55) vs P at 155 (70). So S is next.
   • Head moves from 85 to 30.
   • Remaining: P(155).
10. Finally, serve P at 155.
    • Head moves from 30 to 155. Resulting order (one plausible SSTF sequence given the starting position and the problem’s data):

• R (110) → T (115) → Q (85) → S (30) → P (155) Directional notes cited in the solution:
• When the head moved from 100 toward higher cylinders, R and T were serviced early (they’re relatively close on the high side).
• After reaching around 115, the head moved toward the lower region to service Q and S, then finally moved up to P.
• The problem’s explanation mentions “R and T are serviced before P,” and that “Q is serviced when head is moving towards lower cylinders, P when moving towards higher cylinders,” which aligns with SSTF’s behavior of picking the nearest request at each step and may involve a direction change at S. Conclusion:
• The solution states that option B is correct, based on the SSTF sequence above. The exact order can vary if the tie-breaking rule differs, but the key idea is always selecting the nearest pending request from the current head position and updating distances after each service.