Prerequisite – Belady’s Anomaly
Belady’s Anomaly is when the number of page faults increases even after increasing the number of frames.
In this article, we demonstrate Belady’s Anomaly using FIFO page replacement algorithm.
Examples:
Reference array is: 1, 2, 3, 4, 1, 2, 5, 1, 2, 3, 4, 5 Output : When number of frames is 3, page fault : 9 When number of frames is 4, page fault : 10 Reference array is: 0, 1, 5, 3, 0, 1, 4, 0, 1, 5, 3, 4 Output : When number of frames is 3, page fault : 9 When number of frames is 4, page fault : 10
Implementation :
FIFO page replacement algorithm is used to showcase the Belady’s Anomaly. Firstly, an array of size equal to the number of frames is used, this array simulates the page frames, the operations on this array are performed in a circular array type fashion. A count variable is used to calculate the page fault, this variable is incremented whenever an element is inserted / rewritten in the page frame array.
In this code:
Two frame sizes 3 and 4 are tested respectively, with increase in number of frames the page faults should have decreased, but an anomaly is witnessed as 3 frames result in 9 page faults whereas 4 frames result in 10 page faults. This is Belady’s Anomaly, it is observed in special cases of reference array and frame size.
#include <bits/stdc++.h> using namespace std;
void pageFault( int frame_size, int * ref, int len)
{ // To dynamically allocate an array,
// it represents the page frames.
int * arr = new int [frame_size];
// To initialize the array
for ( int i = 0; i < frame_size; i++) {
arr[i] = -1;
}
// To count page faults
int cnt = 0;
int start = 0;
int flag;
int elm;
for ( int i = 0; i < len; i++) {
elm = ref[i];
// Linear search to find if the page exists
flag = 0;
for ( int j = 0; j < frame_size; j++) {
if (elm == arr[j]) {
flag = 1;
break ;
}
}
// If the page doesn't exist it is inserted,
// count is incremented
if (flag == 0) {
if (start < frame_size) {
arr[start] = elm;
start++;
}
else if (start == frame_size) {
arr[0] = elm;
start = 1;
}
cnt++;
}
}
cout << "When the number of frames are: " << frame_size << ", " ;
cout << "the number of page faults is : " << cnt << endl;
} int main()
{ // Reference array
int ref[] = { 1, 2, 3, 4, 1, 2, 5, 1, 2, 3, 4, 5 };
int len = sizeof (ref) / sizeof (ref[0]);
// The frame size
int frame_size = 3;
pageFault(frame_size, ref, len);
// Increase value of frame size
frame_size = 4;
// The page fault increases
// even after increasing the
// the number of frames.
// This is Belady's Anomaly
pageFault(frame_size, ref, len);
} |
// Java Implementation of the above approach class GFG
{ static void pageFault( int frame_size,
int []ref, int len)
{ // To dynamically allocate an array,
// it represents the page frames.
int []arr = new int [frame_size];
// To initialize the array
for ( int i = 0 ; i < frame_size; i++)
{
arr[i] = - 1 ;
}
// To count page faults
int cnt = 0 ;
int start = 0 ;
int flag;
int elm;
for ( int i = 0 ; i < len; i++)
{
elm = ref[i];
// Linear search to find
// if the page exists
flag = 0 ;
for ( int j = 0 ; j < frame_size; j++)
{
if (elm == arr[j])
{
flag = 1 ;
break ;
}
}
// If the page doesn't exist it is inserted,
// count is incremented
if (flag == 0 )
{
if (start < frame_size)
{
arr[start] = elm;
start++;
}
else if (start == frame_size)
{
arr[ 0 ] = elm;
start = 1 ;
}
cnt++;
}
}
System.out.print( "When the number of frames are: " +
frame_size + ", " );
System.out.println( "the number of page faults is : " + cnt);
} // Driver Code public static void main (String[] args)
{ // Reference array
int ref[] = { 1 , 2 , 3 , 4 , 1 , 2 ,
5 , 1 , 2 , 3 , 4 , 5 };
int len = ref.length;
// The frame size
int frame_size = 3 ;
pageFault(frame_size, ref, len);
// Increase value of frame size
frame_size = 4 ;
// The page fault increases
// even after increasing the
// the number of frames.
// This is Belady's Anomaly
pageFault(frame_size, ref, len);
} } // This code is contributed by AnkitRai01 |
# Python3 Implementation of the above approach def pageFault(frame_size, ref, len ):
# To dynamically allocate an array,
# it represents the page frames.
arr = [ 0 ] * frame_size;
# To initialize the array
for i in range (frame_size):
arr[i] = - 1 ;
# To count page faults
cnt = 0 ;
start = 0 ;
for i in range ( len ):
elm = ref[i];
# Linear search to find if the page exists
flag = 0 ;
for j in range (frame_size):
if (elm = = arr[j]):
flag = 1 ;
break ;
# If the page doesn't exist it is inserted,
# count is incremented
if (flag = = 0 ):
if (start < frame_size):
arr[start] = elm;
start + = 1 ;
elif (start = = frame_size):
arr[ 0 ] = elm;
start = 1 ;
cnt + = 1 ;
print ( "When the number of frames are: " ,
frame_size, end = ", " );
print ( "the number of page faults is : " , cnt);
# Driver Code # Reference array ref = [ 1 , 2 , 3 , 4 , 1 , 2 ,
5 , 1 , 2 , 3 , 4 , 5 ];
len = len (ref);
# The frame size frame_size = 3 ;
pageFault(frame_size, ref, len );
# Increase value of frame size frame_size = 4 ;
# The page fault increases # even after increasing the # the number of frames. # This is Belady's Anomaly pageFault(frame_size, ref, len );
# This code is contributed by 29AjayKumar |
// C# Implementation of the above approach using System;
class GFG
{ static void pageFault( int frame_size,
int []refer, int len)
{ // To dynamically allocate an array,
// it represents the page frames.
int []arr = new int [frame_size];
// To initialize the array
for ( int i = 0; i < frame_size; i++)
{
arr[i] = -1;
}
// To count page faults
int cnt = 0;
int start = 0;
int flag;
int elm;
for ( int i = 0; i < len; i++)
{
elm = refer[i];
// Linear search to find
// if the page exists
flag = 0;
for ( int j = 0; j < frame_size; j++)
{
if (elm == arr[j])
{
flag = 1;
break ;
}
}
// If the page doesn't exist it is inserted,
// count is incremented
if (flag == 0)
{
if (start < frame_size)
{
arr[start] = elm;
start++;
}
else if (start == frame_size)
{
arr[0] = elm;
start = 1;
}
cnt++;
}
}
Console.Write( "When the number of frames are: " +
frame_size + ", " );
Console.WriteLine( "the number of page " +
"faults is : " + cnt);
} // Driver Code public static void Main()
{ // Reference array
int []refer = { 1, 2, 3, 4, 1, 2,
5, 1, 2, 3, 4, 5 };
int len = refer.Length;
// The frame size
int frame_size = 3;
pageFault(frame_size, refer, len);
// Increase value of frame size
frame_size = 4;
// The page fault increases
// even after increasing the
// the number of frames.
// This is Belady's Anomaly
pageFault(frame_size, refer, len);
} } // This code is contributed by kanugargng |
<script> // JavaScript Implementation of the above approach
function pageFault(frame_size, refer, len)
{
// To dynamically allocate an array,
// it represents the page frames.
let arr = new Array(frame_size);
// To initialize the array
for (let i = 0; i < frame_size; i++)
{
arr[i] = -1;
}
// To count page faults
let cnt = 0;
let start = 0;
let flag;
let elm;
for (let i = 0; i < len; i++)
{
elm = refer[i];
// Linear search to find
// if the page exists
flag = 0;
for (let j = 0; j < frame_size; j++)
{
if (elm == arr[j])
{
flag = 1;
break ;
}
}
// If the page doesn't exist it is inserted,
// count is incremented
if (flag == 0)
{
if (start < frame_size)
{
arr[start] = elm;
start++;
}
else if (start == frame_size)
{
arr[0] = elm;
start = 1;
}
cnt++;
}
}
document.write( "When the number of frames are: " +
frame_size + ", " );
document.write( "the number of page " +
"faults is : " + cnt + "</br>" );
}
// Reference array
let refer = [ 1, 2, 3, 4, 1, 2, 5, 1, 2, 3, 4, 5 ];
let len = refer.length;
// The frame size
let frame_size = 3;
pageFault(frame_size, refer, len);
// Increase value of frame size
frame_size = 4;
// The page fault increases
// even after increasing the
// the number of frames.
// This is Belady's Anomaly
pageFault(frame_size, refer, len);
</script> |
When the number of frames are: 3, the number of page faults is : 9 When the number of frames are: 4, the number of page faults is : 10