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:

  1. Seek Time: The time taken to move the disk head to the desired track.
  2. Rotational Latency: The time the disk waits for the desired sector to rotate under the read/write head.
  3. 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: 1010
  • Time to read each block: 5ms5 \, \text{ms}
  • Disk rotation speed: 7200RPM7200 \, \text{RPM}
  • Average seek time: 10ms10 \, \text{ms}

Step 1: Seek Time

The average seek time is given as 10ms10 \, \text{ms}.

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 7200RPM7200 \, \text{RPM}, which is 7200 revolutions per minute. To convert this to revolutions per millisecond: 7200RPM=720060=120RPS(revolutions per second)7200 \, \text{RPM} = \frac{7200}{60} = 120 \, \text{RPS} \, (\text{revolutions per second}) Time per revolution=1120seconds=1000120ms8.33ms\text{Time per revolution} = \frac{1}{120} \, \text{seconds} = \frac{1000}{120} \, \text{ms} \approx 8.33 \, \text{ms} The average rotational latency is half of this time: Average rotational latency=8.332ms4.17ms\text{Average rotational latency} = \frac{8.33}{2} \, \text{ms} \approx 4.17 \, \text{ms}

Step 3: Transfer Time

Each block takes 5ms5 \, \text{ms} to read, and there are 10 blocks. So the total transfer time is: Total transfer time=10×5ms=50ms\text{Total transfer time} = 10 \times 5 \, \text{ms} = 50 \, \text{ms}

Step 4: Total Time

The total time includes one seek time, one rotational latency, and the time to transfer all 10 blocks. So: Total time=Seek time+Rotational latency+Transfer time\text{Total time} = \text{Seek time} + \text{Rotational latency} + \text{Transfer time} Total time=10ms+4.17ms+50ms64.17ms\text{Total time} = 10 \, \text{ms} + 4.17 \, \text{ms} + 50 \, \text{ms} \approx 64.17 \, \text{ms}

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:

  1. How would the time change if the disk rotated at 5400 RPM?
  2. What is the impact of increasing the seek time on overall read performance?
  3. How does rotational latency affect file reading performance?
  4. What would happen if the file consisted of 100 blocks instead of 10?
  5. 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

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Suitable Grade Level

Undergraduate (Computer Science, Disk Management, Performance Analysis)