Galvin Edition 9 Exercise 9 Question 19 (Page No. 453)

Question

Assume that we have a demand-paged memory. The page table is held in registers. It takes $8$ milliseconds to service a page fault if an empty frame is available or if the replaced page is not modified and $20$ milliseconds if the replaced page is modified. Memory-access time is $100$ nanoseconds. Assume that the page to be replaced is modified $70$ percent of the time. What is the maximum acceptable page-fault rate for an effective access time of no more than $200$ nanoseconds ?

Answer 1

$0.2 μsec = (1 - P) × 0.1 μsec + (0.3P) × 8 millisec + (0.7P) × 20 millisec$
$0.1 = -0.1P + 2400 P + 14000 P$
$0.1 ≃ 16,400 P$
$P ≃ 0.000006$