Evaluate fixed execution time, Computer Engineering

Assignment Help:

The statement of Gustafson's law can be described with the help of an illustration. Let us take a problem, say P, which has to be solved using a parallel computer. Let Ts be the time taken which is in use as constant for implementing sequential operations. Let Tp (N, L) be the time taken for running the parallel operations with L as total load on a parallel computer with N processors. The total time taken for finding the answer of problem is T=Ts + Tp. Thus, S (N) can be calculated as under:

2037_Gustafsons Law1.png

 

Also, Tp (1, L)= N* Tp (N, L) i.e. time taken to implement parallel operations having a load of L on one processor is equivalent to the N multiplied by the time taken by one computer having N processor. If α be the fraction of sequential load for a given problem i.e.

α =          Ts / Ts + T p ( N , L)

Substituting Tp (1, L)= N* Tp (N, L) we find,

 

S (n) =   Ts + N * T p ( N , L) / Ts +T p( N , L)

150_Gustafsons Law2.png

Fixed Execution Time for Gustafson's Law

1440_Gustafsons Law3.png

Now, let us change the total equation of S(N) in the form of X. We get

S(N) = α +N * (1-α)

S (N) = N -α * (N-1)

Now, let us put some values of α and compute the speed up factor for increasing values of α i.e. sequential factor of work load for a fixed number of processors say N.  Figure shows a pictorial view of effect of Gustafson's Law on the speed up factor. The graph illustrate as the value of α increases, the speed up factor increases. This decrease is because of overhead caused by inter-processor communication.

1773_Gustafsons Law4.png

α  (Sequential Operations)

Figure: S (N) vs. α (Graph is not to scale)


Related Discussions:- Evaluate fixed execution time

Qwerty-based keyboards, QWERTY-based keyboards In addition the standard...

QWERTY-based keyboards In addition the standard alphabet keys having QWERTY arrangement, a computer keyboard also comprises the control (alt, Del, Ctrl etc. keys) and function

Source and destination are named the same, What happens if the both source ...

What happens if the both source and destination are named the same? Ans) The import operation present in MS Access does not overwrite or change any of the existing tables or obj

Show list files by dir command, Q. Show list files by Dir command? The ...

Q. Show list files by Dir command? The Dir command can also be used to list files from the exacting directory. For example, the list of files present in the WORD directory in d

OS, why we say OS is a resource allocator and control program

why we say OS is a resource allocator and control program

Parallelism based on granularity size-granularity, Parallelism based on G...

Parallelism based on Granularity size Granularity:  Granularity or Grain size is a determine which measure how much computation is devoted in a process.Granularity size is

Features of read-only memory, Q. Features of read-only memory? ROMs are...

Q. Features of read-only memory? ROMs are memories on which it's not possible to write data when they are on-line to computer. They can only be read. This is reason why it is k

Define the state and instance of properties of object, Define the state and...

Define the state and instance of properties of object A state encompasses all properties of object along with values of each of these properties. An instance is a concr

What is access latency and rotation speed, Q. What is Access latency and Ro...

Q. What is Access latency and Rotation Speed? Access latency: A disk access basically moves the arm to selected cylinder and waits for rotational latency that may take less t

Communications between r/3 and external applications, What is the means of ...

What is the means of communications between R/3 and external applications? The means of communication among R/2,R/3 and external applications is by the CPI-C handler or SAP Gat

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd