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

What is process control block, What is process control block?  Each pro...

What is process control block?  Each process is shown in the OS by a process control block. It having many pieces of information associated with a specific process.

Complicated question, Hi I need a help in this question : A telephone sw...

Hi I need a help in this question : A telephone switchboard handles ? calls on average during a rush hour, and the switchboard can at most make k connections per minute. Write a

Interaction goals, Most interactive products aim to satisfy a variety of us...

Most interactive products aim to satisfy a variety of usability and user experience goals. Fully satisfying all of these goals is rarely, if ever, feasible, either because of pract

Define congestion and grade of service, Define congestion and grade of serv...

Define congestion and grade of service. Congestion : This is uneconomic to give sufficient equipment to carry all the traffic which could possibly be offered to a telec

Where virtual memory is used, Where Virtual memory is used ? Ans. Virtu...

Where Virtual memory is used ? Ans. Virtual memory is utilized in all main commercial operating systems.

What is race condition, What is Race condition? Race condition: The c...

What is Race condition? Race condition: The circumstances where several processes access - and manipulate shared data-concurrently. The last value of the shared data depends

Explain Not recently used page replacement algorithm, Not Recently Used Pag...

Not Recently Used Page Replacement Algorithm The not recently used abbreviated as NRU page replacement algorithm works on the subsequent principle: while a page is referenced,

What is the need of modem in data communication, What is the need of MODEM ...

What is the need of MODEM in data communication? Need of Modem: Modems are utilized to interface computer networks, computers and other terminal equipment for radio channels

Moral and ethical implications, • Moral and Ethical Implications o Will ...

• Moral and Ethical Implications o Will this be safe to have on the road    Will the computers on board be able to handle extreme circumstances • Hazardous conditions o Ex

Illustrate about the single inheritance, Illustrate about the single inheri...

Illustrate about the single inheritance During inheritance, superclass feature may by override by a subclass defining that feature with the same name. The overriding features (

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