GATE CS 2024 Set 2 Q43 — I/O Scheduling

To find the total time required to read the entire file, we need to calculate the time taken to access and read a single sector, and then multiply it by the total number of randomly located sectors ($3000$).

Step 1: Calculate Rotation Time and Average Rotational Latency

• Rotation speed: $6000\text{ RPM}$ (Rotations Per Minute)
• Time for one full rotation: $$\text{Rotation Time} = \frac{60\text{ seconds}}{6000} = 0.01\text{ seconds} = 10\text{ ms}$$
• Average rotational latency ($T_{\text{rot}}$): $$T_{\text{rot}} = \frac{1}{2} \times \text{Rotation Time} = \frac{10\text{ ms}}{2} = 5\text{ ms}$$

Step 2: Calculate Sector Transfer Time

• There are $500$ sectors per track. Reading one full track takes one full rotation ($10\text{ ms}$).
• Transfer time for one sector ($T_{\text{trans}}$): $$T_{\text{trans}} = \frac{\text{Rotation Time}}{\text{Sectors per track}} = \frac{10\text{ ms}}{500} = 0.02\text{ ms}$$

Step 3: Calculate Time to Access and Read One Random Sector

Since the sectors are located randomly on the disk, each sector access requires a seek operation, rotational delay, and transfer time:

Step 4: Calculate Total Time for 3000 Sectors

Thus, the total time to read the entire file is $30.06$ seconds.