Question

If the page fault rate is given by F, and the TLB hit rate is given by H. Both F & H are in the range [0,1]. Give a formula for the effective memory access time of a paging system if the normal memory access time is N, and the time it takes to serve the page fault (i.e. to read the page from disk and update the page able) is T, and the time it takes to read the TLB is negligible, i.e. zero. A/

If the page fault rate is given by F, and the TLB hit rate is given by H. Both F & H are in the range [0,1]. Give a formula for the effective memory access time of a paging system if the normal memory access time is N, and the time it takes to serve the page fault (i.e. to read the page from disk and update the page able) is T, and the time it takes to read the TLB is negligible, i.e. zero.

Answer 1

We apply the formula for Average Memory Access Time (AMAT) for multiple levels of memory access.

The sequencing is as follows :

• First TLB is tried. If we get the page <=> frame mapping, we are done.
• If TLB is a miss, we try in main memory. If we get page <=> frame mapping, we are done.
• If main memory is also a miss, it means the page-fault has occurred, and thus the mapping is obtained after servicing the page-fault.

Thus, the AMAT is given by

= (TLB hit time) + (TLB miss rate) [ (Main memory hit time) + (Main memory miss rate) {Page fault service time} ]

= (TLB hit time) + (TLB miss rate) [ (Main memory hit time) + (Page fault rate) {Page fault service time} ]

= (0) + (1 - H) [ (N) + (F) {T} ]

= (1 - H) [ (N) + (F) {T} ]

Thus, the answer to be filled in is

(1 - H) (N + FT)