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Consider a system has hit ratio as h%. Average access time to service a page fault is s milliseconds and average effective memory access time is e in milliseconds. What is the memory access time in microseconds (m is considered with service time)?
- a)100 × (10 × (s - e) + s × h)
- b)1000 × e - 1000 × s + 100 × s × h
- c)10 × (100 × (e - s) + s × h)
- d)100 × (10 × (e - s) + s × h)
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Consider a system has hit ratio as h%. Average access time to service ...
Service time = s milliseconds = 1000s microseconds
Hit ratio = h % = h ÷ 100
∴ miss ratio = p = (1 - h ÷ 100) (page fault rate)
EMAT = e millisecond = 1000e microseconds
If m is considered
EMAT = p × (s + m) + (1 - p) × m
EMAT = p × s + m
Substitute the values:
1000e = (1 – (h ÷ 100)) 1000s + m
∴ m = 1000 × e - 1000 × s + 10 × s × h
∴ m = 10 × (100 × (e - s) + s × h)
Important Points:
EMAT → effective memory access time
EMAT → effective memory access time
p → page fault rate
s → service time
m → memory access time
Confusion point:
m is very large, in this case m is ignored and not take with service time
EMAT = p × s + (1 - p) × m
If m is considered
EMAT = p × (s + m) + (1 - p) × m
EMAT = p × s + m
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Consider a system has hit ratio as h%. Average access time to service ...
Understanding Memory Access Time
To find the memory access time (m) that includes the service time, we need to consider the hit ratio (h), average access time for a page fault (s), and effective memory access time (e).
Key Concepts
- Hit Ratio (h%): The percentage of time that a requested page is found in memory.
- Page Fault Service Time (s): The time taken to service a page fault when it occurs.
- Effective Memory Access Time (e): The average time taken to access memory, considering both hits and misses.
Effective Memory Access Time Calculation
The effective memory access time can be calculated as:
e = h * (time for hit) + (1 - h) * (s + time for hit)
Where:
- Time for hit = time taken to access memory without a page fault.
This can be rearranged to derive the relationship between e, s, and h.
Memory Access Time (m)
To compute the memory access time (m) incorporating service time, we can manipulate the equation involving e:
m = 10 * (100 * (e - s) + s * h)
This reflects the impact of both hit and miss scenarios on overall memory access time, factoring in service times.
Conclusion
Thus, the correct formula for memory access time, considering the service time, is:
Option C: 10 * (100 * (e - s) + s * h)
This equation effectively captures the relationship between effective memory access time, page fault servicing time, and hit ratio.
To find the memory access time (m) that includes the service time, we need to consider the hit ratio (h), average access time for a page fault (s), and effective memory access time (e).
Key Concepts
- Hit Ratio (h%): The percentage of time that a requested page is found in memory.
- Page Fault Service Time (s): The time taken to service a page fault when it occurs.
- Effective Memory Access Time (e): The average time taken to access memory, considering both hits and misses.
Effective Memory Access Time Calculation
The effective memory access time can be calculated as:
e = h * (time for hit) + (1 - h) * (s + time for hit)
Where:
- Time for hit = time taken to access memory without a page fault.
This can be rearranged to derive the relationship between e, s, and h.
Memory Access Time (m)
To compute the memory access time (m) incorporating service time, we can manipulate the equation involving e:
m = 10 * (100 * (e - s) + s * h)
This reflects the impact of both hit and miss scenarios on overall memory access time, factoring in service times.
Conclusion
Thus, the correct formula for memory access time, considering the service time, is:
Option C: 10 * (100 * (e - s) + s * h)
This equation effectively captures the relationship between effective memory access time, page fault servicing time, and hit ratio.
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