20AIM52A Module operating system - Memory management

Operating System – 20AIM52A
Module 4
Memory Management
20AIM52A, Operating System 1

• Have seen how CPU can be shared by a set of
processes
– Improve system performance
– Process management
• Need to keep several process in memory
– Share memory
• Learn various techniques to manage memory
– Hardware dependent
Memory management

Memory management
What are we going to learn?
• Basic Memory Management: logical vs.
physical address space, protection, contiguous
memory allocation, paging, segmentation,
segmentation with paging.
• Virtual Memory: background, demand paging,
performance, page replacement, page
replacement algorithms (FCFS, LRU), allocation
of frames, thrashing.

Background
• Program must be brought (from disk) into
memory
• Fetch-decode-execute cycle
• Memory unit only sees a stream of
addresses + read requests, or address + data
and write requests
• Sequence of memory addresses generated
by running program
CPU

Logical vs. Physical Address Space
Logical address – generated by the CPU; also
referred to as virtual address
Physical address – address seen by the memory
unit
• Logical address space is the set of all logical
addresses generated by a program
• Physical address space is the set of all
physical addresses generated by a program
CPU

• Protection of memory required to ensure
correct operation
Background
Multiple processes resides in memory
1. Protect OS
2. Protect user processes

Base and Limit Registers
• A pair of base and limit registers define
the logical address space

Hardware Address Protection with Base and Limit Registers
• OS loads the base & limit reg.
• Privileged instruction

Address Binding
• Process resides in main memory
• Associate each data element with memory address
• Further, addresses represented in different ways at
different stages of a program’s life
– Source code addresses usually symbolic
– Compiled code addresses bind to relocatable addresses
• i.e. “14 bytes from beginning of this module”
– Linker or loader will bind relocatable addresses to absolute
addresses
• i.e. 74014

Multistep Processing of a User
Program

Binding of Instructions and Data to
Memory
• Address binding of instructions and data to memory
addresses can happen at three different stages
– Compile time: If memory location known a priori,
absolute code can be generated; must recompile code if
starting location changes
– Load time: Must generate relocatable code if memory
location is not known at compile time
– Execution time: If the process can be moved during its
execution from one memory segment to another
• Binding delayed until run time
• Need hardware support for address maps (e.g., base and limit
registers)

Logical vs. Physical Address Space
Logical address – generated by the CPU; also referred to
as virtual address
Physical address – address seen by the memory unit
• Logical and physical addresses are the same in
compile-time and load-time address-binding
schemes;
• logical (virtual) and physical addresses differ in
execution-time address-binding scheme
• Logical address space is the set of all logical
• Physical address space is the set of all physical
CPU

Memory-Management Unit (MMU)
• Hardware device that at run time maps virtual to physical address
• Many methods possible
• To start, consider simple scheme where the value in the
relocation register is added to every address generated by a user
process at the time it is sent to memory
– relocation register
– MS-DOS on Intel 80x86 used 4 relocation registers
• The user program deals with logical addresses (0 to max); it
never sees the real physical addresses (R to R+max)
– Say the logical address 25
– Execution-time binding occurs when reference is made to location
in memory
– Logical address bound to physical addresses

Dynamic relocation using a
relocation register
Relocatable
code
14000

Multiple processes resides in memory
Contiguous Allocation

Contiguous Allocation
• Main memory usually divided into two
partitions:
– Resident operating system, usually held in low
memory
– User processes then held in high memory
– Each process contained in single contiguous
section of memory

Contiguous Allocation (Cont.)
• Multiple-partition allocation
– Divide memory into several Fixed size partition
– Each partition stores one process
– Degree of multiprogramming limited by number of
partitions
– If a partition is free, load process from job queue
– MFT (IBM OS/360)

Contiguous Allocation (Cont.)
• Multiple-partition allocation
– Variable partition scheme
– Hole – block of available memory; holes of various size are
scattered throughout memory
– Keeps a table of free memory
– When a process arrives, it is allocated memory from a hole large
enough to accommodate it
– Process exiting frees its partition, adjacent free partitions
combined
– Operating system maintains information about:
a) allocated partitions b) free partitions (hole)
OS
process 5
process 8
process 2
OS
process 5
process 2
OS
process 5
process 2
OS
process 5
process 9
process 2
process 9
process 10
OS
Hole

Dynamic Storage-Allocation Problem
• First-fit: Allocate the first hole that is big enough
• Best-fit: Allocate the smallest hole that is big enough; must search
entire list, unless ordered by size
– Produces the smallest leftover hole
• Worst-fit: Allocate the largest hole; must also search entire list
– Produces the largest leftover hole
How to satisfy a request of size n from a list of free holes?
Dynamic storage allocation problem

Hardware Support for Relocation
and Limit Registers
• Relocation registers used to protect user processes from each other, and from changing
operating-system code and data
• Relocation register contains value of smallest physical address
• Limit register contains range of logical addresses – each logical address must be less
than the limit register
• Context switch
• MMU maps logical address dynamically

Fragmentation
• Processes loaded and removed from memory
– Memory is broken into little pieces
• External Fragmentation – total memory space
exists to satisfy a request, but it is not contiguous
• First fit analysis reveals that given N blocks
allocated, 0.5 N blocks lost to fragmentation
– 1/3 may be unusable -> 50-percent rule

Fragmentation (Cont.)
• Reduce external fragmentation by compaction
– Shuffle memory contents to place all free memory
together in one large block
– Compaction is possible only if relocation is dynamic,
and is done at execution time
• Change relocation reg.
– Cost
• Internal Fragmentation – allocated memory may
be slightly larger than requested memory; this size
difference is memory internal to a partition, but
not being used 20AIM52A, Operating System 22

Paging
• Physical address space of a process can be noncontiguous;
– process allocates physical memory whenever the latter is available
• Divide physical memory into fixed-sized blocks called frames
– Size is power of 2, between 512 bytes and 16 Mbytes
• Divide logical memory into blocks of same size called pages
– To run a program of size N pages, need to find N free frames and load
program
• Backing store likewise split into pages
• Set up a page table to translate logical to physical addresses
• System keeps track of all free frames

Paging Model of Logical and Physical Memory
page table to translate logical to physical
addresses

Address Translation Scheme
• Address generated by CPU is divided into:
– Page number (p) – used as an index into a page table
• which contains base address of each page in physical memory
– Page offset (d) – offset within a page
• combined with base address to define the physical memory address that
is sent to the memory unit
– For given logical address space 2m and page size 2n
page number page offset
p d
m - n n
offset
page

Paging Hardware

Paging Example
n=2 and m=4 32-byte
memory and 4-byte pages
Logical address = 16
Page size=4
Physical memory=32
User’s view
Logical address 0
(0*4+0)
Physical address:
(5*4+0)=20
Logical address 3
(0*4+3)
Physical address:
(5*4+0)=23
Logical address 4
(1*4+0)
Physical address:
(6*4+0)=24
Logical address 13
(3*4+1)
Physical address:
(2*4+1)
Run time address binding

Paging
• External fragmentation??
• Calculating internal fragmentation
– Page size = 2,048 bytes
– Process size = 72,766 bytes
– 35 pages + 1,086 bytes
– Internal fragmentation of 2,048 - 1,086 = 962 bytes
• So small frame sizes desirable?
– But increases the page table size
– Poor disk I/O
– Page sizes growing over time
• Solaris supports two page sizes – 8 KB and 4 MB
• User’s view and physical memory now very different
– user view=> process contains in single contiguous memory space
• By implementation process can only access its own memory
– protection 20AIM52A, Operating System 29

• Each page table entry 4 bytes (32 bits) long
• Each entry can point to 232 page frames
• If each frame is 4 KB
• The system can address 244 bytes (16TB) of
physical memory
Virtual address space 16MB.
Page table size?

• Process P1 arrives
• Requires n pages => n frames must be
available
• Allocate n frames to the process P1
• Create page table for P1

Free Frames
Before allocation After allocation
Frame table
RAM RAM
Use’s view
System’s view

Implementation of Page Table
• For each process, Page table is kept in main memory
• Page-table base register (PTBR) points to the page table
• Page-table length register (PTLR) indicates size of the
page table
• In this scheme every data/instruction access requires two
memory accesses
– One for the page table and one for the data / instruction
• The two memory access problem can be solved by the
use of a special fast-lookup hardware cache called
associative memory or translation look-aside buffers
(TLBs)

Associative memory

Associative Memory
• Associative memory – parallel search
• Address translation (p, d)
– If p is in associative register, get frame # out
– Otherwise get frame # from page table in memory
Page # Frame #

Implementation of Page Table
• For each process, Page table is kept in main memory
• Page-table base register (PTBR) points to the page table
• Page-table length register (PTLR) indicates size of the page table
• In this scheme every data/instruction access requires two memory accesses
– One for the page table and one for the data / instruction
• The two memory access problem can be solved by the use of a special fast-lookup
hardware cache called associative memory or translation look-aside buffers (TLBs)
• TLBs typically small (64 to 1,024 entries)
• On a TLB miss, value is loaded into the TLB for faster access next time
– Replacement policies must be considered (LRU)
– Some entries can be wired down for permanent fast access
• Some TLBs store address-space identifiers (ASIDs) in each TLB entry – uniquely
identifies each process (PID) to provide address-space protection for that process
– Otherwise need to flush at every context switch

Paging Hardware With TLB

Effective Access Time
• Associative Lookup =  time unit
– Can be < 10% of memory access time
• Hit ratio = 
– Hit ratio – percentage of times that a page number is found in the
associative registers; ratio related to size of TLB
• Consider  = 80%,  = 20ns for TLB search, 100ns for memory access
• Effective Access Time (EAT)
EAT = (100 + )  + (200 + )(1 – )
• Consider  = 80%,  = 20ns for TLB search, 100ns for memory access
– EAT = 0.80 x 120 + 0.20 x 220 = 140ns
• Consider better hit ratio ->  = 98%,  = 20ns for TLB search, 100ns for
memory access
– EAT = 0.98 x 120 + 0.02 x 220 = 122ns

Memory Protection
• Memory protection implemented by associating protection bit
with each frame to indicate if read-only or read-write access is
allowed
– Can also add more bits to indicate page execute-only, and so on
• Valid-invalid bit attached to each entry in the page table:
– “valid” indicates that the associated page is in the process’ logical
address space, and is thus a legal page
– “invalid” indicates that the page is not in the process’ logical
address space
– Or use PTLR
• Any violations result in a trap to the kernel

Valid (v) or Invalid (i)
Bit In A Page Table
14 bit address space (0 to 16383)
Page size 2KB
Process P1 uses only 0 to 10468
Internal fragmentation Use of PTLR (length)
Page 0
Page 1
Page 2
Page 3
P1
P2

• System with 40 users
– Use common text editor
• Text editor contains 150KB code 50KB data (page size 50KB)
– 8000KB!
• Shared code
– One copy of read-only (reentrant) code shared among
processes (i.e., text editors, compilers, window systems)
• Code never changes during execution
• Only one copy of the editor in the memory
• Total memory consumption
– 40*50+150=2150KB
Shared Pages Example

Shared Pages Example

Data share: example
int main()
{
int shmid,f,key=3,i,pid;
char *ptr;
shmid=shmget((key_t)key,100,IPC_CREAT|0666);
ptr=shmat(shmid,NULL,0);
printf("shmid=%d ptr=%un",shmid, ptr);
strcpy(ptr,"hello");
i=shmdt((char*)ptr);
}
int main()
{
int shmid,f,key=3,i,pid;
char *ptr;
shmid=shmget((key_t)key,100,IPC_CREAT|0666);
ptr=shmat(shmid,NULL,0);
printf("shmid=%d ptr=%un",shmid, ptr);
printf("nstr %sn",ptr);
}
writer.c
reader .c
ptr
Shared
memory

Structure of the Page Table
• Memory requirement for page table can get huge using straight-
forward methods
– Consider a 32-bit logical address space as on modern computers
– Page size of 4 KB (212)
– Page table would have 1 million entries 220 (232 / 212)
– If each entry is 4 bytes -> 4 MB of physical address space / memory for
page table alone
• That amount of memory used to cost a lot
• Don’t want to allocate that contiguously in main memory
• Hierarchical Paging
• Hashed Page Tables
• Inverted Page Tables

Hierarchical Page Tables
• Break up the page table into multiple
pages
• We then page the page table
• A simple technique is a two-level page
table

Two-Level Page-Table Scheme

Two-Level Paging Example
• A logical address (on 32-bit machine with 4KB page size) is
divided into:
– a page number consisting of 20 bits
– a page offset consisting of 12 bits
• Since the page table is paged, the page number is further
divided into:
– a 10-bit page number
– a 10-bit page offset
• Thus, a logical address is as follows:
• where p1 is an index into the outer page table, and p2 is the
displacement within the page of the inner page table
page number page offset
p1 p2 d
10 10 12

Two-Level Page-Table Scheme
p1
p2
d
Each divided page table
size=210 *4bytes=4KB
=Page size
Pentium II

Address-Translation Scheme
Pentium II

64-bit Logical Address Space
• Even two-level paging scheme not sufficient
• If page size is 4 KB (212)
– Then page table has 252 entries
– If two level scheme, inner page tables could be 210 4-byte entries
– Address would look like
– Outer page table has 242 entries or 244 bytes
– One solution is to add a 2nd outer page table
– But in the following example the 2nd outer page table is still 234
bytes in size
• And possibly 4 memory access to get to one physical memory location
outer page page offset
p1 p2 d
42 10 12
inner page

Three-level Paging Scheme
SPARC (32 bits), Motorola 68030 support three and four level paging respectively

Hashed Page Tables
• Common in virtual address spaces > 32 bits
• The page number is hashed into a page table
– This page table contains a chain of elements hashing to the same
location
• Each element contains (1) the page number (2) the value of the
mapped page frame (3) a pointer to the next element
• Virtual page numbers are compared in this chain searching for a
match
– If a match is found, the corresponding physical frame is extracted

Hashed Page Table

Inverted Page Table
• Rather than each process having a page table and
keeping track of all possible logical pages, track all frames
• One entry for each frame
• Entry consists the page number stored in that frame, with
information about the process that owns that page
• Decreases memory needed to store each page table,
– but increases time needed to search the table when a page
reference occurs

Inverted Page Table Architecture
64 bit UltraSPARC, PowerPC,
Address space ID

Segmentation
• Memory-management scheme that supports user view of
memory
• A program is a collection of segments
– A segment is a logical unit such as:
main program
procedure
function
method
object
local variables, global variables
common block
stack
symbol table
arrays
Compiler generates the
segments
Loader assign the seg#

User’s View of a Program
User specifies each address
by two quantities
(a) Segment name
(b) Segment offset
Logical address contains the
tuple
<segment#, offset>
• Variable size segments without order
• Length=> purpose of the program
• Elements are identified by offset

Logical View of Segmentation
1
3
2
4
1
4
2
3
user space physical memory space
• Long term scheduler finds and allocates memory for all segments of a program
• Variable size partition scheme
Logical
address
space
Logical address <segment-number, offset>

Memory image

Executable file and virtual address
Virtual address
space
a.out
Symbol table
Name address
SQR 0
SUM 4
0 Load 0
4 ADD 4
<CODE, 0> Load <ST,0>
<CODE, 2> ADD <ST,4>
Paging view
Segmentation view

Segmentation Architecture
• Logical address consists of a two tuple:
<segment-number, offset>
• Segment table – maps two-dimensional logical address
to physical address;
• Each table entry has:
– base – contains the starting physical address where the
segments reside in memory
– limit – specifies the length of the segment
• Segment-table base register (STBR) points to the
segment table’s location in memory
• Segment-table length register (STLR) indicates number
of segments used by a program;
segment number s is legal if s < STLR

Example of Segmentation

Segmentation Hardware

Example of Segmentation

Segmentation Architecture
• Protection
• Protection bits associated with segments
– With each entry in segment table associate:
• validation bit = 0  illegal segment
• read/write/execute privileges
• Code sharing occurs at segment level
• Since segments vary in length, memory allocation is
a dynamic storage-allocation problem
– Long term scheduler
– First fit, best fit etc
• Fragmentation

Segmentation with Paging
Key idea:
Segments are splitted into multiple pages
Each page is loaded into frames in the memory

Segmentation with Paging
• Supports segmentation with paging
– Each segment can be 4 GB
– Up to 16 K segments per process
– <selector(16), offset (32)>
– Divided into two partitions
• First partition of up to 8 K segments are private to process (kept in local
descriptor table LDT)
• Second partition of up to 8K segments shared among all processes (kept in
global descriptor table GDT)
• CPU generates logical address (six Segment Reg.)
– Given to segmentation unit
• Which produces linear addresses
– Physical address 32 bits
– Linear address given to paging unit
• Which generates physical address in main memory
• Paging units form equivalent of MMU
• Pages sizes can be 4 KB
Intel 80386
IBM OS/2
S(13) G(1) P(2)

Logical to Physical Address
Translation in Pentium
Page table=220
entries

Example: The Intel Pentium
8 bytes Segment register

Intel Pentium Segmentation

Pentium Paging Architecture

Virtual Memory

Background
• Code needs to be in memory to execute, but
entire program rarely used
– Error code, unusual routines, large data structures
• Entire program code not needed at same time
• Consider ability to execute partially-loaded
program
– Program no longer constrained by limits of physical
memory
– programs could be larger than physical memory
– More processes can be accommodated

Virtual Memory That is
Larger Than Physical Memory
Large virtual
space
Small memory

Classical paging
• Process P1 arrives
• Requires n pages => n frames must be
available
• Allocate n frames to the process P1
• Create page table for P1
Allocate < n frames

Background
• Virtual memory – separation of user logical memory from
physical memory
– Extremely large logical space is available to programmer
– Concentrate on the problem
• Only part of the program needs to be in memory for
execution
– Logical address space can therefore be much larger than physical
address space
– Starts with address 0, allocates contiguous logical memory
– Physical memory
• Collection of frame
• Virtual memory can be implemented via:
– Demand paging
– Demand segmentation

Demand Paging
• Bring a page into memory only when it is needed
• Lazy swapper – never swaps a page into memory
unless page will be needed
– Swapper that deals with pages is a pager
• Less I/O needed, no unnecessary I/O
– Less memory needed
– More users
• Page is needed  reference to it
– invalid reference  abort
– not-in-memory  bring to memory
Valid address
information is available
in PCB

Transfer of a Paged Memory to
Contiguous Disk Space
• When we want to
execute a process, swap
in
• Instead of swap in entire
process, load page
• Pager

Page Table When Some Pages
Are Not in Main Memory
Pager loads few necessary pages in
memory

Valid-Invalid Bit
• With each page table entry a valid–invalid bit is associated
(v  in-memory – memory resident, i  not-in-memory)
• Initially valid–invalid bit is set to i on all entries
• Example of a page table snapshot:
• During address translation, if valid–invalid bit in page table entry
is i  page fault
v
v
v
v
i
i
i
….
Frame # valid-invalid bit
page table
Disk
address

Page Fault
• If the page in not in memory, first reference to that page will trap to
operating system:
page fault
1. Operating system looks at PCB to decide:
– Invalid reference  abort
– Just not in memory (load the page)
2. Get empty frame
3. Swap page into frame via scheduled disk operation
4. Reset page table to indicate page now in memory
Set validation bit = v
5. Restart the instruction that caused the page fault

What Happens if There is no Free Frame?
• Example
– 40 frames in memory
– 8 processes each needs 10 pages
– 5 of them never used
• Two options
– Run 4 processes (10 pages)
– Run 8 processes (5 pages)
• Increase the degree of multiprogramming
– Over allocating memory
• Page fault
– No free frame
– Terminate? swap out? replace the page?
• Page replacement – find some page in memory, not really in use, page it out
– Performance – want an algorithm which will result in minimum number of page faults
• Same page may be brought into memory several times

Steps in Handling a Page Fault
Check
PCB

Pure Demand Paging
• Extreme case – start process with no pages in memory
– OS sets instruction pointer to first instruction of process, non-
memory-resident -> page fault
– Swap in that page
– Pure demand paging
• Actually, a given instruction could access multiple pages
(instruction + data) -> multiple page faults
– Pain decreased because of locality of reference
• Hardware support needed for demand paging
– Page table with valid / invalid bit
– Secondary memory (swap device with swap space)
– Instruction restart after page fault

Steps in the ISR
• In Demand Paging
1. Trap to the operating system
2. Save the user registers and process state
3. Determine that the interrupt was a page fault
4. Check that the page reference was legal and determine the location of the page on the disk
5. Get a free frame
6. Issue a read from the disk to a free frame:
1. Wait in a queue for this device until the read request is serviced
2. Wait for the device seek and/or latency time
3. Begin the transfer of the page to a free frame
7. While waiting, allocate the CPU to some other user
8. Receive an interrupt from the disk I/O subsystem (I/O completed)
9. Save the registers and process state of the running process
10. Determine that the interrupt was from the disk
11. Correct the page table and other tables to show page is now in memory
12. Wait for the CPU to be allocated to this process again
13. Restore the user registers, process state, and new page table, and then resume the interrupted
instruction 20AIM52A, Operating System 87

Performance of Demand Paging
• Page Fault Rate 0  p  1
– if p = 0 no page faults
– if p = 1, every reference is a fault
• Effective Access Time (EAT)
EAT = (1 – p) x memory access
+ p (page fault overhead
+ swap page out
+ swap page in
+ restart overhead
)
Demand paging affects the performance of the computer systems

Demand Paging Example
• Memory access time = 200 nanoseconds
• Average page-fault service time = 8 milliseconds
• EAT = (1 – p) x 200 + p (8 milliseconds)
= (1 – p ) x 200 + p x 8,000,000
= 200 + p x 7,999,800
• If one access out of 1,000 causes a page fault, then
EAT = 8.2 microseconds.
This is a slowdown by a factor of 40!!
• If want performance degradation < 10 percent
– 220 > 200 + 7,999,800 x p
20 > 7,999,800 x p
– p < .0000025
– < one page fault in every 400,000 memory accesses
Better utilization of swap space
Swap space

Allocation of Frames
• How do we allocate the fixed amount of
memory among various processes?
• Single user system
– Trivial

Allocation of Frames
• Each process needs minimum number of frames
• Minimum number is defined by the instruction set
• Page fault forces to restart the instruction
– Enough frames to hold all the pages for that instruction
• Example:
– Single address instruction (2 frames)
– Two address instruction (3 frames)
• Maximum of course is total frames in the system
• Two major allocation schemes
– fixed allocation
– proportional allocation

Fixed and proportional Allocation
• Equal allocation – m frames and n processes
– Each process gets m/n
• For example, if there are 100 frames (after allocating frames
for the OS) and 5 processes, give each process 20 frames
– Keep some as free frame buffer pool
• Unfair for small and large sized processes
• Proportional allocation – Allocate according to the size of
process
– Dynamic as degree of multiprogramming, process sizes
change
m
S
s
p
a
m
s
S
p
s
i
i
i
i
i
i







for
allocation
frames
of
number
total
process
of
size
m  64
s1 10
s2 127
a1 
10
137
 64  5
a2 
127
137
 64  59

Priority Allocation
Allocation of frames
• Depends on multiprogramming level
• Use a proportional allocation scheme using
priorities along with size

Need For Page Replacement
P1
P2
K

Need For Page Replacement
P1
P2
PC
K

Basic Page Replacement
1. Find the location of the desired page on disk
2. Find a free frame:
- If there is a free frame, use it
- If there is no free frame, use a page replacement algorithm to
select a victim frame (of that process)
- Write victim frame to disk
3. Bring the desired page into the (newly) free frame; update the page
and frame tables
4. Continue the process by restarting the instruction that caused the trap
Note now potentially 2 page transfers for page fault – increasing Effective
memory access time

Page Replacement
5
6
5
6

Page Replacement
5
6
6
5

Evaluation
• Evaluate algorithm by running it on a particular string
of memory references (reference string) and
computing the number of page faults on that string
– String is just page numbers, not full addresses
– Repeated access to the same page does not cause a page
fault
• Trace the memory reference of a process
0100, 0432, 0101, 0612, 0102, 0104, 0101, 0611, 0102
• Page size 100B
• Reference string 1, 4, 1, 6, 1, 6
• In all our examples, the reference string is
7,0,1,2,0,3,0,4,2,3,0,3,0,3,2,1,2,0,1,7,0,1

Graph of Page Faults Versus
The Number of Frames

Associates a time with each frame when the page was brought
into memory
When a page must be replaced, the oldest one is chosen
Reference string: 7,0,1,2,0,3,0,4,2,3,0,3,0,3,2,1,2,0,1,7,0,1
First-In-First-Out (FIFO) Algorithm
Limitation:
A variable is initialized early and constantly used

FIFO Page Replacement
• How to track ages of pages?
• Just use a FIFO queue to hold all the pages in memory
• Replace the page at the head
• Insert at tail
3 frames (3 pages can be in memory at a time)
15 page faults

Optimal Algorithm
• Replace page that will not be used for longest
period of time
• How do you know this?
– Can’t read the future
• Used for measuring how well your algorithm
performs

Optimal Page Replacement
9 page faults

Least Recently Used (LRU)
Algorithm
• Use past knowledge rather than future
– Past is the proxy of future
• Replace page that has not been used in the most of the
time
• Associate time of last use with each page
• 12 faults – better than FIFO but worse than OPT
• Generally good algorithm and frequently used
• But how to implement?

LRU Algorithm-Implementation
• Counter implementation
– CPU maintains a clock
– Every page entry has a Time of use;
• every time page is referenced, copy the clock into the time of
use
– When a page needs to be replaced, look at the “Time of use” to
find smallest value
• Search through table needed
CPU
Clock
address
Time of
Use
Page table
0
1
2
3

• Stack implementation
• Keep a stack of page numbers in a double linked list form:
• Page referenced:
• move it to the top
• Victim page is the bottom page
LRU Algorithm-Implementation

LRU Approximation Algorithms
• LRU needs special hardware and still slow
• Reference bit
– With each page associate a bit, initially = 0
– When page is referenced bit set to 1
• Additional reference bit algorithm
– Record the reference bits in regular interval
– Keep a 8 bit string for each page in memory
– At regular interval, timer copies the reference bit
to the high order bit (MSB) of the string.
– Shift the other bits right side by one bit

Period Period Period
0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5
Reset
reference

• LRU needs special hardware and still slow
• Reference bit
– With each page associate a bit, initially = 0
– When page is referenced bit set to 1
• Additional reference bit algorithm
• Second-chance algorithm
– Generally FIFO, plus hardware-provided reference bit
– Clock replacement
– If page to be replaced has
• Reference bit = 0 -> replace it
• reference bit = 1 then:
– set reference bit 0, leave page in memory (reset the time)
– replace next page, subject to same rules

Second-Chance (clock) Page-Replacement Algorithm
{Reference bit, Dirty bit} combination

Counting Algorithms
• Keep a counter of the number of references
that have been made to each page
• LFU Algorithm: replaces page with smallest
count
• MFU Algorithm: based on the argument that
the page with the smallest count was
probably just brought in and has yet to be
used
Least and most frequently used

Graph of Page Faults Versus
The Number of Frames

1
2
3
1 2 3 4 1 2 5 1 2 3 4 5
1 1
2
4
2
3
4
1
3
4
1
2
5
1
2
5
1
2
5
1
2
5
3
2
5
3
4
5
3
4
        
9
faults
FIFO Example –
Program - 5 pages,
3 frames of Memory allocated
Increase in page frame decreases page fault rate?

1
2
3
1 2 3 4 1 2 5 1 2 3 4 5
1 1
2
4
2
3
4
1
3
4
1
2
5
1
2
5
1
2
5
1
2
5
3
2
5
3
4
5
3
4
1
2
3
4
1 1
2
1
2
3
1
2
3
4
1
2
3
4
5
2
3
4
5
1
3
4
5
1
2
4
5
1
2
3
4
1
2
3
4
5
2
3
         
10
faults
FIFO Example –
Program - 5 pages,
4 frames of Memory allocated

116
Belady's Anomaly
#
of
Page
Faults
Number of Frames
20AIM52A, Operating System

Belady’s Anomaly
• This most unexpected result is known as
Belady’s anomaly – for some page-
replacement algorithms, the page fault rate
may increase as the number of allocated
frames increases
• Is there a characterization of algorithms
susceptible to Belady’s anomaly?

Stack Algorithms
• Certain page replacement algorithms are more “well
behaved” than others
• (In the FIFO example), the problem arises because the set of
pages loaded with a memory allocation of 3 frames is not
necessarily also loaded with a memory allocation of 4 frames
• There are a set of paging algorithms whereby the set of pages
loaded with an allocation of m frames is always a subset of
the set of pages loaded with an allocation of m +1 frames.
This property is called the inclusion property
• Algorithms that satisfy the inclusion property are not subject
to Belady’s anomaly. FIFO does not satisfy the inclusion
property and is not a stack algorithm

3
5
6
6
3
5
4
6
3
5
3
4
6
5
9
3
4
6
5
3
5
6
6
3
5
4
6
3
5
3
4
6
5
9
3
4
6
5
6 4 3 9
6 5 3
In memory
Outside
memory
In memory
3 frames
4 frames
LRU algorithm

Global vs. Local Allocation
• Frames are allocated to various processes
• If process Pi generates a page fault
– select for replacement one of its frames
– select for replacement a frame from another process
• Local replacement – each process selects from only its own set of
allocated frames
– More consistent per-process performance
– But possibly underutilized memory
• Global replacement – process selects a replacement frame from the
set of all frames; one process can take a frame from another
– But then process execution time can vary greatly
– But greater throughput ----- so more common
• Processes can not control its own page fault rate
– Depends on the paging behavior of other processes

Thrashing
• If a process uses a set of “active pages”
– Number of allocated frames is less than that
• Page-fault
– Replace some “active” page
– But quickly need replaced “active” frame back
– Quickly a page fault, again and again
– Thrashing  a process is busy swapping pages in and out
• OS monitors CPU utilization
– If low? Increase the degree of multiprogramming

• Global page replacement
– Process enters new phase (subroutine call) execution
– Page fault
– Taking frames from other processes
• Replace “active” frames of other processes
– These processes start page fault
– These faulting processes wait on the device queue for disk
• Ready queue empty
– CPU utilization decreases
• CPU scheduler increases the degree of multiprogramming
– More page faults
– Drop in CPU utilization
• Page fault increases tremendously
Disk
Thrashing

Thrashing (Cont.)

Thrashing
• Solution
– Local replacement
– One process cannot steal frames from other
processes
• Provide a process as many frames as needed
– Able to load all active pages
– How do we know?
– Locality model

Demand Paging and Thrashing
• Why does demand paging work?
Locality model
– Process migrates from one locality to another
– Localities may overlap
• Allocate enough frames to a process to accommodate its
locality
• Why does thrashing occur?
 size of locality > total allocated frames
– Limit effects by using local or priority page replacement

Locality In A Memory-Reference Pattern

Working-set model

Working-Set Model
•   working-set window  a fixed number of page references
Example: 10,000 instructions
• WSSi (working set of Process Pi) =
total number of pages referenced in the most recent  (varies
in time)
– if  too small will not encompass entire locality
– if  too large will encompass several localities
– if  =   will encompass entire program
• D =  WSSi  total demand frames
– Approximation of locality
• if D > m  Thrashing
• Policy if D > m, then suspend or swap out one of the
processes

Page-Fault Frequency
• More direct approach than WSS
• Establish “acceptable” page-fault frequency (PFF)
rate and use local replacement policy
– If actual rate too low, process loses frame
– If actual rate too high, process gains frame

20AIM52A Module operating system - Memory management

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