Q11

In the three-level memory hierarchy shown in the following table, $p_i$ denotes the probability that an access request will refer to $M_i$.

$$\begin{array}{|c|c|c|c|} \hline \textbf {Hierarchy Level } & \textbf{Access Time}& \textbf{Probability of Access} & \textbf{Page Transfer Time} \\ (M_i) &(t_i)&(p_i) &(T_i)\\ \hline M _1 & 10^{-6} & 0.99000 & \text{0.001 sec} \\ M _2 & 10^{-5} & 0.00998 & \text{0.1 sec} \\ M _3 & 10^{-4} & 0.00002 & \text{---} \\\hline \end{array}$$

If a miss occurs at level $M_i$, a page transfer occurs from $M_{i+1}$ to $M_i$ and the average time required for such a page swap is $T_i$. Calculate the average time $t_A$ required for a processor to read one word from this memory system.