GATE - 2007 | OS | A demand paging system takes 100 time units to service a page fault

GATE - 2007 [Operating System]

Question:

A demand paging system takes 100 time units to service a page fault and 300 time units to replace a dirty page. Memory access time is 1 time unit. The probability of a page fault is p. In case of a page fault, the probability of page being dirty is also p. It is observed that the average access time is 3 time units. Then the value of p is

A	0.194
B	0.233
C	0.514
D	0.981
E	0.0194

    

Solution:

Option (E) is Correct.

Given page fault service time = 100
(if the page is not dirty)
Page fault service time = 300
(if there is dirty page)
Probability of page fault = P
Probability pf page being dirty = P
So, total page fault service time
= P(300) + (1 - P)100
= 300P + 100 - 100P
= 300P + 100
Now given,
Effective average memory access time = 3
So,
3 = m + P × total page fault service time
= 1 + P(200P + 100)
= 1+ 200P² + 100P
⇒ 200P² + 100P - 2 = 0
⇒ P = 0.0194

Thank You