Chapter 6, Problem 23E

a)

Program Plan Intro

Given:

TLB hit=5ns

Cache hit =12ns

Main memory=25ns (Memory reference)

Hard drive=200ms (Disk reference)

Hit ratio TLB=90%

Hit ratio cache=98%

Rate of Page fault=0.001%

Explanation of Solution

TLB (Translation Look aside Buffer) hit and cache Hit:

• Translation Look aside buffer is special type of cache that is used to store the contents of the page table.
• The content of the TLB cache includes pairs of virtual page number, physical frame numbers.
• The page number that is required can be looked up inside the TLB.
  • If the requested page number is found it is considered to be a hit and it indicates that the page number is being mapped with the frame number that is present in the main memory.
• The contents of the cache will also be accessed to find whether the data is present in the cache as well and if the same contents are present it is meant to be a hit.

Therefore, this type of access is possible and the total access time is calculated as shown below:

$\begin{array}{c}\text{Access}\text{Time}\text{=}\text{TLB\_access}\text{time+Cache\_accesstime}\\ \text{=5+12}\\ \text{=17ns}\end{array}$

Therefore, the total access time is 17ns.

b)

Program Plan Intro

Given:

TLB hit=5ns

Cache hit =12ns

Main memory=25ns (Memory reference)

Hard drive=200ms (Disk reference)

Hit ratio TLB=90%

Hit ratio cache=98%

Rate of Page fault=0.001%

Explanation of Solution

TLB (Translation Look aside Buffer) miss, page table hit and cache Hit:

• Translation Look aside buffer is special type of cache that is used to store the contents of the page table.
• The content of the TLB cache includes pairs of virtual page number, physical frame numbers.
• The page number that is required can be looked up inside the TLB.
  • If the requested page number is found it is considered to be a miss, then the page number that is required is searched in the main memory’s page table.
  • If the page entry is found in the page table, the address of the virtual memory is mapped with the main memory.
• The contents of the cache will also be accessed to find whether the data is present in the cache as well and if the same contents are present it is meant to be a hit.

Therefore, this type of access is possible and the total access time is calculated as shown below:

$\begin{array}{c}\text{Access}\text{Time}\text{=}\text{TLB\_access}\text{time+MainMemory\_accesstime+Cache\_accesstime}\\ \text{=5+25+12}\\ \text{=42ns}\end{array}$

Therefore, the total access time is 42ns.

c)

Program Plan Intro

Given:

TLB hit=5ns

Cache hit =12ns

Main memory=25ns (Memory reference)

Hard drive=200ms (Disk reference)

Hit ratio TLB=90%

Hit ratio cache=98%

Rate of Page fault=0.001%

Explanation of Solution

TLB (Translation Look aside Buffer) miss, page table hit and cache Miss:

• Translation Look aside buffer is special type of cache that is used to store the contents of the page table.
• The content of the TLB cache includes pairs of virtual page number, physical frame numbers.
• The page number that is required can be looked up inside the TLB.
  • If the requested page number is found it is considered to be a miss, then the page number that is required is searched in the main memory’s page table.
  • If the page entry is found in the page table, the address of the virtual memory is mapped with the main memory.
• The contents of the cache will also be accessed to find whether the data is present in the cache as well and if the same contents are not present it is meant to be a miss, then the access is being transferred to main memory and the block that is required is transferred again to the cache.

Therefore, this type of access is possible and the total access time is calculated as shown below:

$\begin{array}{c}\text{Access}\text{Time}\text{=}\text{TLB\_access}\text{time+MainMemory\_accesstime+Cache\_accesstime}\\ \text{+MainMemory\_accesstime}\\ \text{=5+25+12+25}\\ \text{=67ns}\end{array}$

Therefore, the total access time is 67ns.

d)

Program Plan Intro

Given:

TLB hit=5ns

Cache hit =12ns

Main memory=25ns (Memory reference)

Hard drive=200ms (Disk reference)

Hit ratio TLB=90%

Hit ratio cache=98%

Rate of Page fault=0.001%

Explanation of Solution

TLB (Translation Look aside Buffer) miss, page table miss and cache hit:

• Translation Look aside buffer is special type of cache that is used to store the contents of the page table.
• The content of the TLB cache includes pairs of virtual page number, physical frame numbers.
• The page number that is required can be looked up inside the TLB.
  • If the requested page number is found it is considered to be a miss, then the page number that is required is searched in the main memory’s page table.
  • If the page entry is not found in the page table, there occurs a page fault .
  • The access is made with the hard drive to bring the required data into the main memory.
• There is no possibility of the cache being hit in this scenario because the address is not present in the main memory itself

Therefore, this type of access is not possible.

e)

Program Plan Intro

Given:

TLB hit=5ns

Cache hit =12ns

Main memory=25ns (Memory reference)

Hard drive=200ms (Disk reference)

Hit ratio TLB=90%

Hit ratio cache=98%

Rate of Page fault=0.001%

Explanation of Solution

TLB miss and page table miss:

• Translation Look aside buffer is special type of cache that is used to store the contents of the page table.
• The content of the TLB cache includes pairs of virtual page number, physical frame numbers.
• The page number that is required can be looked up inside the TLB.
  • If the requested page number is found it is considered to be a miss, then the page number that is required is searched in the main memory’s page table.
  • If the page entry is not found in the page table, there occurs a page fault.
  • The access is made with the hard drive to bring the required data into the main memory.
  • The access will be getting restarted at this stage.
• The page number that is required can be looked up inside the TLB.
  • If the requested page number is found it is considered to be a miss, then the page number that is required is searched in the main memory’s page table.
  • Now the request page number is found at the page table of the main memory.
  • There occurs a page hit.
  • The value that is requested and found in the main memory may not be reflected at the cache.
  • There occurs a cache miss.
  • Then the main memory is accessed to bring the block to the cache.

Therefore, this type of access is possible and the total access time is calculated as shown below:

$\begin{array}{c}\text{Access}\text{Time}\text{=}\text{TLB\_access}\text{time+MainMemory\_accesstime+Harddrive\_accesstime}\\ \text{+TLB\_access}\text{time+Cache\_accesstime}\\ \text{=5+25+200+5+12}\\ \text{=200}\text{.047ms}\end{array}$

Therefore, the total access time is $\text{200}\text{.047}\text{ms}$.

Effective Access time (EAT):

• EAT is a measure of Hierarchal memory performance.
• A weighted average that utilizes the hit ratio and the relative access time of the levels present in successful order of the memory hierarchy is called as effective access time.
• The actual time of the access is based on the technology that is utilized to access the contents present at each level of the hierarchy.

Formula for the effective access time:

The formula for effective access time where the memory contains two levels that includes a main memory and the cache memory is obtained as shown below:

$\text{EAT}\text{=}{\text{H×Access}}_{\text{c}}\text{+}\left(\text{1-H}\right){\text{×Access}}_{\text{MM}}$

In the above formula,

$\begin{array}{c}\text{H}\text{=}\text{cache}\text{hit}\\ {\text{Access}}_{\text{c}}\text{=}\text{cache}\text{access}\text{time}\\ {\text{Access}}_{\text{MM}}\text{=}\text{Main}\text{Memory}\text{access}\text{time}\end{array}$

Any access that is made is being split up into following ways:

• Virtual access
• Main memory access

If the contents are present in the TLB then it is called as hit, and if the element is not present in the TLB then the element is accessed at the page table.

If the element is present at the page table then it is a hit, if the contents are not present then the access is made at the main memory to bring the elements to the cache.

Now again the contents are searched at the cache now the data found is considered as a hit.

$\begin{array}{c}\text{EAT}\text{=}\text{Virtual}\text{access}\text{+}\text{Main}\text{Memory}\text{access}\\ \text{Virtual}\text{access=TLBHit×TLB\_accesstime+}\left(\text{1-TLBHit}\right)\text{×PageTable}\text{access}\text{time}\\ \text{Main}\text{Memory}\text{access}\text{=cachehit×cache\_accesstime+}\left(\text{1-cachehitrate}\right)\text{×MainMemory\_accesstime}\end{array}$

$\begin{array}{c}\text{Virtual}\text{access=0}\text{.9×5+}\left(\text{1-0}\text{.9}\right)\text{×}\left(\text{0}\text{.001×200+0}\text{.999×25}\right)\\ \text{Main}\text{Memory}\text{access}\text{=0}\text{.98×12+}\left(\text{1-0}\text{.98}\right)\text{×25}\\ \text{EAT}\text{=0}\text{.9×5+}\left(\text{1-0}\text{.9}\right)\text{×}\left(\text{0}\text{.001×200+0}\text{.999×25}\right)\text{+0}\text{.98×12+}\left(\text{1-0}\text{.98}\right)\text{×25}\end{array}$