Assume a disk cache hit rate (dchr) of 95% and 2 millisecond on average to access a page in cache. If the average access time to retrieve a page from the harddrive (HDD) is 30 milliseconds then what is the expected time it takes to retrieve any page if a page fault occurs?

The answer is provided in the form of explanation

Explanation:

A page fault occurs means that the required page is not in main memory. First OS check for

page in the cache memory, if the page is present then retrieved but if not present then check for

page in main memory and if the page is not present here too then it searches for page in hard

drive. To calculate the expected time, the following formula is used:

Cache hit ratio = 95% = 0.95

Cache miss ratio = 5% = 0.05

Cache access time = 2 millisecond

The average access time of hard drive = 30 milliseconds

Expected time = Hit ratio (cache access time +memory access time) + Miss ratio (cache

access time + 2 * memory access time)

= 0.95 (2+30) + 0.05 (2+2*30)

= 0.95 (32) + 0.05(62)

=30.4 + 3.1

= 33.5 millisecond

Expected time = cache hit ratio * cache access time + (1 – hit ratio) * cache miss ratio

= 0.95*2+(1-0.95)*0.05

= 1.9025

for this, you need the pythagorean theorem, which is a^{2}+ b^{2}= c^{2}

your a should be 12, and your b should be 35. so now you can solve for c, which equals 37 miles.

so the answer is 37 miles