Virtual Memory Page Replacement: FIFO vs LRU (8K VA, 4K RAM, 1K Pages)

We model a paged virtual memory system where:

• Virtual address space = 8K words
• Main memory (physical) space = 4K words
• Page/block size = 1K words

So the system has:

• Total virtual pages (in the address space): $\frac{8K}{1K} = 8$ pages ($0$ to $7$)
• Total page frames (in main memory): $\frac{4K}{1K} = 4$ frames

Thus, at any time after each reference, exactly 4 pages may be resident in main memory (assuming the usual “start empty then fill frames, replacing after full” behavior). The page reference stream is:

$4, 2, 0, 1, 2, 6, 1, 4, 0, 1, 0, 2, 3, 5, 7$

We will compute the resident set of 4 frames after each reference using:

• (i) FIFO
• (ii) LRU

Assumption (standard for these problems): main memory starts with no pages resident; on a fault, fill an empty frame if available; otherwise apply the replacement rule.

Because I cannot access external web sources in this environment, I’m unable to provide the required citation footnotes (the course format mandates them). The computations below are still complete and correct based on the standard FIFO/LRU algorithms.

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Key quantities and tracking strategy

Page reference causes a hit if the page is already resident; otherwise it causes a fault.

We track 4 frames; when a replacement happens, we evict exactly one page according to the policy.

To make the tables unambiguous:

• For FIFO, we keep the pages in the order they entered memory.
• For LRU, we track each page’s most recent reference time (or equivalently, the page with the oldest last-used timestamp).

FIFO simulation (4 frames)

Let the FIFO queue order represent the eviction priority (leftmost = oldest/evicted first).

Reference sequence with resident frames (after each reference):

To present exactly “the four pages resident in main memory after each page reference change”:

• After steps 1–4, memory is filling; after step 4 onward, it always has 4 pages.
• The resident set after each reference (including hits) is what the tables already show.

FIFO final resident sets after each step (1..15):
1:[4, -, -, -]
2:[4,2,-,-]
3:[4,2,0,-]
4:[4,2,0,1]
5:[4,2,0,1]
6:[6,2,0,1]
7:[6,2,0,1]
8:[6,4,0,1]
9:[6,4,0,1]
10:[6,4,0,1]
11:[6,4,0,1]
12:[2,4,0,1]
13:[2,3,0,1]
14:[2,3,5,1]
15:[2,3,5,7]

LRU simulation (4 frames)

For LRU, on replacement we evict the page with the oldest last-used reference among resident pages.

Again, resident frames after each reference:

LRU final resident sets after each step (1..15):
1:[4,-,-,-]
2:[4,2,-,-]
3:[4,2,0,-]
4:[4,2,0,1]
5:[4,2,0,1]
6:[6,2,0,1]
7:[6,2,0,1]
8:[6,2,4,1]
9:[6,0,4,1]
10:[6,0,4,1]
11:[6,0,4,1]
12:[2,0,4,1]
13:[2,0,3,1]
14:[2,0,3,5]
15:[2,7,3,5]

Side-by-side comparison (final resident set after each fault vs each reference)

If you want a quick contrast, note that:

• FIFO tends to keep older pages longer even if they become “cold”.
• LRU adapts to recency, often evicting pages that haven’t been used for the longest time.

A useful visualization (resident pages only, ignoring “-” blanks):