onsider a memory hierarchy with a $3$ level system cache and main memory. The cache levels L$1,$ L$2,$ L$3$ are arranged from the fastest to the slowest memory, and main memory $($RAM$)$ is over $1$ order of magnitude slower than the slowest L$3$ cache level. Memory and the cache levels have the following properties:

Access Time Hit Ratio

L$1$ T$1=1$ micro s H$1=0\mathrm{.}93$

L$2$ T$2=10$ micro s H$2=0\mathrm{.}90$

L$3$ T$3=50$ micro s

H$3=0\mathrm{.}95$

Main Memory $($RAM$)$ Tm $=1000$ micro s

N$/$A