# Given only TLB Lookup time, and memory access time, can the TLB hit rate be negative?

I'm given the following problem:

TLB lookup time is given as 8ns and memory access time for a computer system is given as 40ns. What should be the TLB miss rate to achieve effective memory access time 60ns ?

I use the following formula where x is the TLB Hit Rate, and (1-x) is the TLB miss rate:

TLB Hit Rate * TLB Lookup Time + TLB Miss Rate * (TLB Lookup Time + Memoery Access Time) = effective memory access time


8x + (1 – x)(8 + 40) = 60

And solving for x I get:

8x + (1 – x)(8 + 40) = 60
8x + (1 – x)(48) = 60
8x + 48 – 48x = 60
-40x = 12
X = -0.3

TLB Hit Rate = -30%
TLB Miss Rate = (1 – TLB Hit rate)
TLB Miss rate = (1 – (-.3))
TLB Miss Rate = 1.3
TLB Miss Rate = 130%


Is it possible in this case for the hit rate to be negative, and miss rate to be over 100%? Or am I messing up on either the formula or the calculations?

• Just consider what assumed memory access time (40) < target effective time (60) means. – greybeard Nov 26 '19 at 16:56
• (On the plus side, you did notice something's counter-intuitive.) – greybeard Nov 26 '19 at 16:57
• After the TLB miss and loading data from memory to fix the TLB miss, you still need to access the actual memory you want. 8x + 48 (1-x) + 40 = 60. – gnasher729 Nov 26 '19 at 17:31