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Suppose that the virtual page reference stream contains repetitions of long sequences of page references followed occasionally by a random page reference. For example, the sequence$: 0, 1, \dots, 511, 431, 0, 1, \dots , 511, 332, 0, 1, \dots$ consists of repetitions of the sequence $0, 1, \dots , 511$ followed by a random reference to pages $431$ and $332.$

  1. Why will the standard replacement algorithms $(\text{LRU, FIFO, clock})$ not be effective in handling this workload for a page allocation that is less than the sequence length?
  2. If this program were allocated $500$ page frames, describe a page replacement approach that would perform much better than the $\text{LRU, FIFO, or clock} $ algorithms.
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