Understanding the SSTF Disc Scheduling Technique

The Shortest Seek Time First (SSTF) algorithm is a disk scheduling method designed to minimize the total seek time. It selects the request that is closest to the current head position first.

Calculating Total Head Movement with SSTF

We need to calculate the total movement of the disk head based on the given requests and the starting position using the SSTF algorithm.

Initial Setup:

• Initial head position: 58
• Requests: {45, 81, 185, 33, 175, 99, 150, 77}

Step-by-Step Execution of SSTF:

Step 1: Initial Move

• Current Head Position: 58
• Distances to pending requests:
  • $|58 - 45| = 13$
  • $|58 - 81| = 23$
  • $|58 - 185| = 127$
  • $|58 - 33| = 25$
  • $|58 - 175| = 117$
  • $|58 - 99| = 41$
  • $|58 - 150| = 92$
  • $|58 - 77| = 19$
• The closest request is 45 (distance 13).
• Move head from 58 to 45.
• Movement: 13 cylinders.
• Total Movement so far: 13.
• Remaining Requests: {81, 185, 33, 175, 99, 150, 77}

Step 2: Second Move

• Current Head Position: 45
• Distances to pending requests:
  • $|45 - 81| = 36$
  • $|45 - 185| = 140$
  • $|45 - 33| = 12$
  • $|45 - 175| = 130$
  • $|45 - 99| = 54$
  • $|45 - 150| = 105$
  • $|45 - 77| = 32$
• The closest request is 33 (distance 12).
• Move head from 45 to 33.
• Movement: 12 cylinders.
• Total Movement so far: $13 + 12 = 25$.
• Remaining Requests: {81, 185, 175, 99, 150, 77}

Step 3: Third Move

• Current Head Position: 33
• Distances to pending requests:
  • $|33 - 81| = 48$
  • $|33 - 185| = 152$
  • $|33 - 175| = 142$
  • $|33 - 99| = 66$
  • $|33 - 150| = 117$
  • $|33 - 77| = 44$
• The closest request is 77 (distance 44).
• Move head from 33 to 77.
• Movement: 44 cylinders.
• Total Movement so far: $25 + 44 = 69$.
• Remaining Requests: {81, 185, 175, 99, 150}

Step 4: Fourth Move

• Current Head Position: 77
• Distances to pending requests:
  • $|77 - 81| = 4$
  • $|77 - 185| = 108$
  • $|77 - 175| = 98$
  • $|77 - 99| = 22$
  • $|77 - 150| = 73$
• The closest request is 81 (distance 4).
• Move head from 77 to 81.
• Movement: 4 cylinders.
• Total Movement so far: $69 + 4 = 73$.
• Remaining Requests: {185, 175, 99, 150}

Step 5: Fifth Move

• Current Head Position: 81
• Distances to pending requests:
  • $|81 - 185| = 104$
  • $|81 - 175| = 94$
  • $|81 - 99| = 18$
  • $|81 - 150| = 69$
• The closest request is 99 (distance 18).
• Move head from 81 to 99.
• Movement: 18 cylinders.
• Total Movement so far: $73 + 18 = 91$.
• Remaining Requests: {185, 175, 150}

Step 6: Sixth Move

• Current Head Position: 99
• Distances to pending requests:
  • $|99 - 185| = 86$
  • $|99 - 175| = 76$
  • $|99 - 150| = 51$
• The closest request is 150 (distance 51).
• Move head from 99 to 150.
• Movement: 51 cylinders.
• Total Movement so far: $91 + 51 = 142$.
• Remaining Requests: {185, 175}

Step 7: Seventh Move

• Current Head Position: 150
• Distances to pending requests:
  • $|150 - 185| = 35$
  • $|150 - 175| = 25$
• The closest request is 175 (distance 25).
• Move head from 150 to 175.
• Movement: 25 cylinders.
• Total Movement so far: $142 + 25 = 167$.
• Remaining Requests: {185}

Step 8: Final Move

• Current Head Position: 175
• Distance to pending request:
  • $|175 - 185| = 10$
• The closest request is 185 (distance 10).
• Move head from 175 to 185.
• Movement: 10 cylinders.
• Total Movement so far: $167 + 10 = 177$.
• Remaining Requests: {}

Summary Table: SSTF Head Movement

Conclusion

The total head movement for the SSTF disc scheduling technique, starting from cylinder 58 and servicing the requests {45, 81, 185, 33, 175, 99, 150, 77}, is 177 cylinders.