GATE CS 2014 Set 2 Q55 — Memory Management and Virtual Memory

To find the maximum number of stores (write requests) that can be initiated in $1\text{ ms}$, we need to analyze the constraints imposed by both the system bus and the memory modules.

1. System Bus Constraint

• Each write request occupies the system bus for $100\text{ ns}$.
• Since only one request can be on the bus at any time, the maximum rate at which requests can be sent over the bus is: $$\text{Rate}_{\text{bus}} = \frac{1\text{ request}}{100\text{ ns}}$$

2. Memory Module Constraint

• Each memory module takes $100\text{ ns}$ (during bus occupation) plus $500\text{ ns}$ thereafter to complete a write cycle. $$\text{Total cycle time per module} = 100\text{ ns} + 500\text{ ns} = 600\text{ ns}$$
• There are $8$ memory modules whose operations can overlap in time.
• Therefore, the maximum rate at which the $8$ modules collectively can process requests is: $$\text{Rate}_{\text{modules}} = \frac{8\text{ requests}}{600\text{ ns}} = \frac{1\text{ request}}{75\text{ ns}}$$

3. Determining the Bottleneck

The overall maximum rate of initiating write requests is limited by the slower of the two components (the bottleneck):

Since $8 \times 100\text{ ns} = 800\text{ ns} \ge 600\text{ ns}$, we can continuously cycle through the $8$ modules without any module being busy when its turn arrives again. Thus, the system bus is the sole bottleneck.

4. Calculation for 1 Millisecond

Convert $1\text{ millisecond}$ to nanoseconds:

The maximum number of stores that can be initiated in $1\text{ ms}$ is: