Formulation of the FIFO algorithm for N$-$level memory hierarchy:

$$ Set memory levels to N $($ML $=$ N$).$

$$ Set current memory level pointer to the highest $($L $=1).$

$1.$ Insertion of a new page:

$1\mathrm{.}1.$ If the current memory level pointer is higher than the lowest memory level

$($L $>$ ML$)$ :

$1\mathrm{.}1\mathrm{.}1.$ Return False. $/*$ Recursion Termination $*/$

$1\mathrm{.}2.$ Call to the page.

$1\mathrm{.}3.$ If the page exists in the memory $/$ storage:

$1\mathrm{.}3\mathrm{.}1.$ Check if placing in the L$-$level of memory is possible.

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$1\mathrm{.}3\mathrm{.}2.$ If placement possible:

$1\mathrm{.}3\mathrm{.}2\mathrm{.}1.$ Place the page at the L$-$level of memory.

$1\mathrm{.}3\mathrm{.}2\mathrm{.}2.$ Return True. $/*$ Recursion Termination $*/$

$1\mathrm{.}3\mathrm{.}3.$ Else If placement impossible:

$1\mathrm{.}3\mathrm{.}3\mathrm{.}1.$ I f the reference bit of at least one of the pages is set to $0$

$($R $=0)$:

$1\mathrm{.}3\mathrm{.}3\mathrm{.}1\mathrm{.}1.$ Remove a page with reference bit set to $0.$

$1\mathrm{.}3\mathrm{.}3\mathrm{.}1\mathrm{.}2.$ Place the page instead of the removed page.

$1\mathrm{.}3\mathrm{.}3\mathrm{.}1\mathrm{.}3.$ Do Insertion of the page with reference bit set to

$0$ to a lower level $($L $=$ L$+1)./*$ Recursion Invocation $*/$

$1\mathrm{.}3\mathrm{.}3\mathrm{.}2.$ Else If the reference bit of all of the pages is set to $1($R $=$

$1)$:

$1\mathrm{.}3\mathrm{.}3\mathrm{.}2\mathrm{.}1.$ Do Insertion of the page to a lower level $($L $=$

L$+1)./*$ Recursion Invocation $*/$

$1\mathrm{.}4.$ Else If page does not exist in the memory $/$ storage:

$1\mathrm{.}4\mathrm{.}1.$ Return False. $/*$ Recursion Termination $*/$

$2.$ Call to a page:

$2\mathrm{.}1.$ Calculate the addressing of the page in the memory $/$ storage.

$2\mathrm{.}2.$ If page found:

$2\mathrm{.}2\mathrm{.}1.$ Return Real Addressing.

$2\mathrm{.}3.$ Else If page was not found:

$2\mathrm{.}3\mathrm{.}1.$ Return False.

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$3.$ Remove of a specifc page:

$3\mathrm{.}1.$ Store the page in a temporary storage.

$3\mathrm{.}2.$ Free the addressing of the page.

$3\mathrm{.}3.$ Return the page from the temporary storage.

$4.$ Update of an existing page $($by the OS$)$:

$4\mathrm{.}1.$ If Read $/$ Write action performed on the page:

$4\mathrm{.}1\mathrm{.}1.$ Set R bit to $1($R $=1).$

$4\mathrm{.}2.$ If the page reached to the head of the FIFO queue and the page reference

bit is on $($R $=1)$:

$4\mathrm{.}2\mathrm{.}1.$ Turn of the reference bit $($R $=0)$ and moves the page to the tail of

the FIFO queue.