Question $1$

TRANSLATION: A page replacement algorithm should minimize the number of page faults.

We can achieve this minimization by distributing heavily$-$used pages equally memory, rather than having them compete for a small number of page frames. a small number of page frames. We can associate with each page frame a counter for the number of pages associated with that frame. Then, to replace a page, we can search for the page frame with the smallest counter.

a$)$Define a page replacement algorithm using this basic idea. In

in particular: i$.$What is the initial value of the

counters? ii$.$ When are the countersincreased? iii. When are meters

decreased? iv$.$ How is the page to be replaced selected?

b$)$ How many page faults does your algorithm generate for the following reference string? for four page frames?

$1,2,3,4,5,3,4,1,6,7,8,7,8,9,7,8,9,5,4,5,4,2.$

c$)$ What is the minimum number of page faults for an optimal strategy of replacing the reference string in part b with four page frames?

replacement of the reference string in part b with four page frames?