Consider the following timeline of page references: 9 6 2 3 4 4 4 4 3 4 4 2 5…
2013
Consider the following timeline of page references: 9 6 2 3 4 4 4 4 3 4 4 2 5 8 6 8 5 5 3 2 3 3 9 6 2 7. What is the working set at the penultimate page reference when Δ = 5?
Answer: D. {2, 3, 6, 9} — ConceptAt reference time t, the working set W(t, Δ) is the set of distinct pages appearing in the most recent Δ page references ending at t. Repeated…
- A.
{2, 3, 5, 6, 8, 9}
- B.
{2, 3, 4, 5, 6}
- C.
{2, 3, 6, 7, 9}
- D.
{2, 3, 6, 9}
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Correct answer: D
Concept
At reference time t, the working set W(t, Δ) is the set of distinct pages appearing in the most recent Δ page references ending at t.
Repeated references to the same page count once because a working set records membership, not frequency.
Application
The penultimate reference is the 25th value, 2; the final value 7 is outside the requested instant.
The five-reference window ending at the 25th value is 3, 3, 9, 6, 2.
Removing the repeated 3 leaves the distinct-page set {2, 3, 6, 9}.
Cross-check
Moving the window one reference forward to the final value would produce 3, 9, 6, 2, 7 and would include page 7. Its absence at the penultimate instant confirms the boundary used above. Therefore, the working set is {2, 3, 6, 9}.
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