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…

  1. A.

    {2, 3, 5, 6, 8, 9}

  2. B.

    {2, 3, 4, 5, 6}

  3. C.

    {2, 3, 6, 7, 9}

  4. D.

    {2, 3, 6, 9}

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Show answer & explanation

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

  1. The penultimate reference is the 25th value, 2; the final value 7 is outside the requested instant.

  2. The five-reference window ending at the 25th value is 3, 3, 9, 6, 2.

  3. 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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