An input enhancement technique to maximize the performance of page replacement algorithms

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 04 Issue: 06 | June-2015, Available @ http://www.ijret.org 302
AN INPUT ENHANCEMENT TECHNIQUE TO MAXIMIZE THE
PERFORMANCE OF PAGE REPLACEMENT ALGORITHMS
Mahesh Kumar M R1
, Renuka Rajendra B2
1
Department of CSE, JSSATE, Bengaluru, India
2
Department of CSE, JSSATE, Bengaluru, India
Abstract
One of the main goals of the memory management is to allow multiprogramming. Several strategies are used to allocate a
memory to the process needed. These strategies require the entire process should be in the memory before execution and some of
these strategies suffer from fragmentation. Virtual memory does not require entire process to be in memory before execution. It
loads only those pages of the process in to the memory that are needed for execution. This can be achieved using paging scheme
having number of frames in the memory to accommodate for each pages. Whenever one of the page in the memory need to be
replaced, one of the page replacement algorithms are used. The performance of these page replacement algorithms depends on
the total number of page faults achieved. In this paper, a new algorithm called Comparison Counting FIFO (CC-FIFO) and
Distribution Counting FIFO (DC-FIFO) has been proposed using input enhancement technique. Our results and calculations
show that the proposed algorithm minimizes the page fault rate compared to FIFO, LRU and Optimal page replacement
algorithms.
Keywords-Page replacement; Page fault; FIFO; OPT; LRU; Comparison Counting; Distribution Counting;
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1. INTRODUCTION
Memory management allows multiprogramming so that
operating systems keeps several processes in the memory.
We need to allocate memory in the most efficient way
possible. Memory can be allocated using multiple partition
schemes, variable partition scheme (first fit, best fit, and
worst fit) [4]. But some of these strategies suffer from
fragmentation problem. We can avoid this problem using
paging and segmentation memory management scheme. All
these schemes require that entire process to be in the
physical memory before we can execute the process.
Virtual memory does not require the entire process to be in
the memory before we can execute because sometimes a
user does not require the entire process in the memory. User
may be interested in a few pages of the process rather than
the entire process at any point of time. In such a case, bring
only those pages from the disk into the memory that is
demanded during the execution. If the pages of the process
are not demanded, then these pages are never loaded in to
the memory. This technique is called demand paging [4].
If the process tries to access a page in the memory that was
not brought from the disk, then such page is called page
fault. In order to identify the page fault, we will use valid /
invalid bit scheme. If the bit is set as valid to one of the
page, then that page is in the memory. Otherwise, the page is
not valid and is currently on the disk not in the memory [4].
The page fault may occur when the desired page is not in the
memory or the desired page is currently on the disk and is
ready to bring it into the memory but the memory is full. At
this point to allow the execution of the desired page, either
bring the page from the disk into the memory or replace
some of the pages that are already in the memory using one
of the page replacement algorithms. Among all the page
replacement algorithms, optimal page replacement is the
most efficient algorithm which has less page fault rate.
In an attempt towards reducing the page fault compared to
the existing algorithms, we have proposed a new algorithm
CC-FIFO and DC-FIFO using input enhancement
techniques. Our algorithm takes less number of page fault
rate compared to FIFO, OPT and LRU replacement
algorithms.
The reminder of the paper is organised as follows. Section II
describes the different page replacement algorithms. Section
III describes the related work done in the area of page
replacement algorithm. Section IV input enhancement
techniques for comparison counting and distribution
counting. Section V describes the proposed algorithm.
Section VI describes results and observations for few test
cases. Section VII concludes with the summary.
2. PAGE REPLACEMENT ALGORITHMS
There are several page replacement algorithms that
determine which page to replace to accommodate a desired
page in to the memory.
2.1 First In First Out (FIFO)
This algorithm replaces the page that has been in the
memory for the longest period of time. In order to do this
the system must keeps track of the order in which pages
enter memory [5]. This algorithm will result in more page

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faults even the number of frames are increased called
belady’s anomaly.
2.2 Optimal or OPT
This algorithm replaces the page that will not be referenced
again for the longest period of time in the future. This
algorithm never suffers from belady’s anomaly.
2.3 Least Recently Used (LRU)
This algorithm replaces the page by considering the past
behaviour of the pages in the memory. This will replace the
page that has spent longest period of time in the memory
being unused.
2.4 Second Chance Algorithm
This algorithm is a variation of FIFO. It checks the bit of the
old page. If the bit is off, the algorithm immediately selects
the page for replacement. Otherwise the algorithm turns off
the bit and moves the page to the end of the FIFO queue [5].
2.5 Least Frequently Used (LFU)
This algorithm replaces the page that is least frequently
used. To do this, we will count the number of references
being made to each page. So finally replace the page that
having smallest count.
2.6 Most Frequently Used (MFU)
This algorithm replaces the page that is most frequently used
that results in largest count.
3. RELATED WORK DONE
In the recent years many researchers have came forward
with their work and ideas in the area of page replacement
algorithms.
 Wang hong, compared and analysed the page fault
and page fault frequency of different algorithm [1].
 Pooja khulbe, shruti pant, suggested a advanced
version of least recently used algorithm by reducing
the overall page fault rate [8].
 Yogesh Niranjan, Shailendra Tiwari, proposed a new
page replacement algorithm for proxy server [6].
 Anupam Battacharjee, Bideb Kumar Debnath,
proposed a new randomized algorithm approximating
random replament and least recently used scheme for
page replacement in web caches [3].
 Ali Khasrozadeh, Sanaz Pashmforoush, proposed a
page replacement algorithm based on LRu by
considering certain parameter that can offer better
improvement [7].
 Guangxia Xu, Lingling Ren, Yanbing Liu, proposed
an efficient page replacement algorithm called
FAPRA for NAND flas memory based storage
devices [2].
4. INPUT ENHANCEMENT TECHNIQUES
The idea is to pre-process the problem’s input and store the
additional information obtained to accelerate solving the
problem afterward [9]. The following two input
enhancement methods are used for our proposed algorithm.
4.1 Comparison Counting
In this sorting, for each element in a list to be sorted, count
the total number of element that are smaller than this
element and store the results in a table. These numbers
indicate the position of the elements in the sorted list [9].
 Consider the page reference string { 7, 0, 1, 2, 0, 3, 0,
4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1}. The number of
occurrence of each element is {7-21, 0-62, 1-43, 2-44,
3-35, 4-16}. Subscript number is for future references.
 The number of occurrence obtained in the above step
{21, 62, 43, 44, 35, 16} is an input to the comparison
counting algorithm.
 Once we apply the algorithm, the number of
occurrence gets sorted {16, 21, 35, 44, 43, 62} in
increasing order.
 For each element in the sorted list, replace with
corresponding number of occurrences of element
from the first step as shown below. The new page
reference string is {4, 7, 7, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1,
1, 0, 0, 0, 0, 0, 0}. This is considered as a new page
reference string in our proposed algorithm.
4.2 Distribution Counting
This algorithm sorts the n elements in the array. This
algorithm is recommended when the input array elements
consist of duplicate, random elements and also the elements
in the array are known to come from a set. Consider the
array A elements: {1, 2, 3, 4, 2, 1, 5, 6, 2, 1, 2, 3, 7, 6, 3, 2,
1, 2, 3, 6}
 The elements in the array elements are known to
come from the set S {1, 2, 3, 4, 5, 6, 7} where lower
bound is 1 and upper bound is 7. Suppose if one of
the elements in the set say 5 is not in the input array
elements, then the input array elements are not
derived from the set and hence this algorithm cannot
be applied.
 After analyzing the input, we have to calculate the
frequency of each element in the set from the input
array and distribution values for the element in the
set. For the above example the calculations are
shown below.
Table 1
Array
values Set S 1 2 3 4 5 6 7
Frequency 4 6 4 1 1 3 1
Distribution
Values D
4 10 14 15 16 19 20
 Now process the input array elements right to left.
Consider the last element in the array. In the above

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example A[19] = 6. Subtract it from the lower bound
that is 6 – 1 = 5. This value is used to access the
element stored in D[5] = 19 and subtract it by 1 that
is 19 – 1 = 18. So insert the element A[19] in the
position of new array B[18]. This new position
indicates the position in the sorted array B. This will
be repeated for each element in the given array from
right to left.
 Now the entire elements in the new array B are in
sorted array. For the above array elements, the final
sorted order after applying this algorithm is {1, 1, 1,
1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 6, 6, 6, 7}. This is
considered as a new page reference string in our
proposed algorithm.
 Since the array value is fixed, the time efficiency of
this algorithm is linear.
5. PROPOSED ALGORITHM
The main goal of our proposed algorithm is to minimize the
total number of page faults by obtaining a new page
reference string from the above algorithm compared to
FIFO, OPT and LRU page replacement algorithms.
5.1 Comparison Counting FIFO (CC-FIFO)
Algorithm
If the reference string contains random, duplicate elements
and the elements are not derived from the set, then we will
apply the below algorithm.
1) Read an array of page reference string and the
number of frames in the memory from the user.
2) Analyse the input carefully.
3) Apply comparison counting algorithm to sort the list
(shown in section IV).
4) The elements are now in the sorted order.
5) Apply FIFO page replacement algorithm to the new
page reference string obtained in the above step.
6) The number of page faults obtained using our
algorithm is less than to that of other page
replacement algorithm.
5.2 Distribution Counting FIFO (DC-FIFO)
Algorithm
If the page reference string contains random, duplicate
elements and the elements in the array are known to come
from the set, then we apply the below algorithm.
1) Read array of page reference string and the number
of frames in the memory from the user.
2) Analyse the input carefully.
3) Apply distribution counting algorithm to sort the
entire array (shown in section IV).
4) The elements are now in the sorted order.
5) Apply FIFO page replacement algorithm to the new
page reference string obtained in the above step.
6) The number of page faults obtained using our
algorithm is less than to that of other page
replacement algorithm.
6. RESULTS AND OBSERVATIONS
Before we implement the steps performed in the proposed
method, we have taken two different cases for both
comparison and distribution counting FIFO algorithm. For
each case we will implement the traditional algorithm and
also the proposed algorithm and calculate the page faults for
each algorithm. In the next section we will implement the
proposed algorithm and compare the results obtained in
these two cases with our new algorithm to show the
improved performance.
Case 1: Consider the page reference string
{7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1} Assume
three frames in the memory. Fig. 1 to Fig. 3 show the
representation of FIFO, OPT and LRU page replacement
algorithm.
Fig 1: FIFO Page Replacement algorithm
Total number of page faults in FIFO = 15
Fig 2: Optimal Page Replacement algorithm
Total number of page faults in Optimal = 9

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Fig 3: LRU Page Replacement algorithm
Total number of page faults in LRU = 12
{1, 2, 3, 4, 2, 1, 5, 6, 2, 1, 2, 3, 7, 6, 3, 2, 1, 2, 3, 6} Assume
three frames in the memory. Fig. 4 to Fig. 6 show the
representation of FIFO, OPT and LRU page replacement
algorithm.
Fig 4: FIFO Page Replacement algorithm
Total number of page faults in FIFO = 16
Fig 5: Optimal Page Replacement algorithm
Total number of page faults in Optimal = 11
Fig 6: LRU Page Replacement algorithm
Total number of page faults in LRU = 15
6.1 Proposed Method
In this section, we will apply the proposed algorithm for the
two cases to show how the pages can be accessed faster.
{7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1} Assume
three frames in the memory.
Since the page reference string are in random order and
contain duplicate elements. These elements are not known
from the set. Then apply the CC-FIFO algorithm shown in
section IV to obtain the new page reference string. The new
page reference string after sorting is {4, 7, 7, 3, 3, 3, 2, 2, 2,
2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0}. Now apply the remaining steps
in the algorithm to complete the task. Fig. 7 shows the
representation of CC-FIFO algorithm for the new page
reference string. Table II show the comparison of all the
algorithms with our proposed algorithm for case 1.
Fig 7: CC-FIFO algorithm
Total number of page faults in CC-FIFO = 6

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Table 2
Algorithms Total number of Page Faults
FIFO 15
Optimal 09
LRU 12
CC-FIFO 06
{1, 2, 3, 4, 2, 1, 5, 6, 2, 1, 2, 3, 7, 6, 3, 2, 1, 2, 3, 6} Assume
three frames in the memory.
Since the page reference string are in random order and
contain duplicate elements. The elements are said to be
come from the set {1, 2, 3, 4, 5, 6, 7}. Then apply the DC-
FIFO algorithm shown in section IV to obtain the new page
reference string. The new page reference string after
applying algorithm is {1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4,
5, 6, 6, 6, 7}. Now apply the remaining steps in the
algorithm to complete the task. Fig. 8 shows the
representation of DC-FIFO algorithm for the new page
reference string. Table III show the comparison of all the
algorithms with our proposed algorithm for case 2.
Fig 8: DC-FIFO algorithm
Total number of page faults in DC-FIFO = 7
Table 3
Algorithms Total number of Page Faults
FIFO 16
Optimal 11
LRU 15
DC-FIFO 07
6.2 Comparison
Fig. 9 shows the comparison of total number of page faults
in FIFO, Optimal and LRU with our algorithm called CC-
FIFO replacement algorithm for case 1. Thus from this
figure we showed that our new algorithm CC-FIFO results
in reduced page faults compared to other replacement
algorithms.
Fig 9: Comparison of page faults for case1
Fig. 10 shows the comparison of total number of page faults
in FIFO, Optimal and LRU with our algorithm called DC-
FIFO replacement algorithm for case 2. Thus from this
figure we showed that our new algorithm DC-FIFO results
in reduced page faults compared to other replacement
algorithms.
Fig 10: Comparison of page faults for case2
7. CONCLUSION
The performance page replacement algorithms like FIFO,
OPT, LRU, Second Chance, LFU and MFU is measured in
terms of number of page faults rate. We select one of the
algorithm that result in low page fault rate. Among all these
algorithms, optimal page replacement algorithm is efficient
since it results in lowest page fault rate of all the algorithms.
In an attempt towards this, we have proposed a new
algorithm called Comparison Counting FIFO (CC-FIFO)
and Distribution Counting FIFO (DC-FIFO) using input
enhancement technique and implemented the same for two
different reference strings. Our results and calculations show
that proposed algorithm reduces the total number of page
fault rate compared to the general approach of page
replacement algorithms.

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REFERENCES
[1] Wang Hong, “Study of Page Replacement Algorithm
based on Experiment”, International conference on
mechanical Engineering and Automation, Advances
in Biomedical Engineering, volume 10, 2012.
[2] Guangxia Xu, Lingling Ren and Yanbing Liu, “Flash
Aware Page Replacement Algorithm”, Mathematical
Problems in Engineering, Hindawi Publishing
Corporation, volume 2014.
[3] Anupam Bhattacharjee, Biolab Kumar Debnath, “A
New Web Cache Replacement Algorithm”, IEEE
Conference on Communications, Computers and
Signal Processing, August, 2005.
[4] Silberchatz, Galvin and Gagne, “Operating Systems
Concepts”, 8th edition, John Wiley and Sons, 2012.
[5] Dietel, Dietel and Choffnes, “Operating Systems”, 3rd
edition, Pearson education, 2009.
[6] Yogesh Niranjan and Shailendra Tiwari, “Design and
Implementation of Page Replacement Algorithm for
Web Proxy Caching”, IJCTA, Volume 4, April 2013.
[7] Ali Khosrozadeh, Sanaz Pashmforoush, “Presenting a
novel Page Replacement Algorithm based on LRU”,
Journal of Basic and Applied Scientific Research,
2012.
[8] Pooja Khulbe, Shruti Pant, “Hybrid (LRU) page
Replacement Algorithm”, IJCA, Volume 91, April
2014.
[9] Anany Levitin, “Introduction to the Design and
Analysis of Algorithms”, second edition, Pearson,
2008.

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