Answer to Question #324655 in Computer Networks for Kojo

Question

A processor accesses main memory with an average access time of T2. A smaller cache memory is interposed between the processor and main memory. The cache has a significantly

faster access time of T1<T2. The cache holds, at any time, copies of some main memory words

and is designed so that the words more likely to be accessed in the near future are in the cache. Assume that the probability that the next word accessed by the processor is in the cache is H, known as the hit ratio.

a. For any single memory access, what is the theoretical speedup of accessing the word in the cache rather than in main memory?

b. Let T be the average access time. Express T as a function of T1 , T2, and H. What is the

overall speedup as a function of H?

Answer 1

Solution

a)$Speedup=\frac{time to access in main memory}{time to access in cache}$

$=\frac{T1}{T2}$

b) $T=H\times T1+(1-H)\times(T1+T2)$

$=T1+(1-H)\times T2$