Math Problem Statement
Calculate the total time to read a file consisting of 10 blocks, where each block takes 5ms to read, using a disk that rotates at 7200 RPM and has an average seek time of 10ms
Solution
To calculate the total time to read a file consisting of 10 blocks, we need to account for three factors:
- Seek Time: The time taken to move the disk head to the desired track.
- Rotational Latency: The time the disk waits for the desired sector to rotate under the read/write head.
- Transfer Time: The time taken to transfer the data (here, time to read each block).
Let's break these down:
Given Information:
- Number of blocks:
- Time to read each block:
- Disk rotation speed:
- Average seek time:
Step 1: Seek Time
The average seek time is given as .
Step 2: Rotational Latency
Rotational latency is half of the time it takes for the disk to complete one full rotation.
The disk rotates at , which is 7200 revolutions per minute. To convert this to revolutions per millisecond: The average rotational latency is half of this time:
Step 3: Transfer Time
Each block takes to read, and there are 10 blocks. So the total transfer time is:
Step 4: Total Time
The total time includes one seek time, one rotational latency, and the time to transfer all 10 blocks. So:
Thus, the total time to read the file is approximately 64.17 ms.
Would you like more details or have any questions?
Here are 5 related questions:
- How would the time change if the disk rotated at 5400 RPM?
- What is the impact of increasing the seek time on overall read performance?
- How does rotational latency affect file reading performance?
- What would happen if the file consisted of 100 blocks instead of 10?
- Can caching techniques help reduce the read time?
Tip: Seek time and rotational latency are the two most significant contributors to disk read delays, so minimizing these can greatly improve performance.
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Math Problem Analysis
Mathematical Concepts
Disk Performance Analysis
Rotational Latency
Seek Time
Transfer Time
Formulas
Rotational latency = 1 / (2 * Rotations per second)
Total transfer time = Number of blocks * Time to read each block
Total time = Seek time + Rotational latency + Transfer time
Theorems
-
Suitable Grade Level
Undergraduate (Computer Science, Disk Management, Performance Analysis)
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