What is gustafsons law, Computer Engineering

Assignment Help:

Q. What is Gustafsons Law?

Amdahl's law is appropriate for applications where response time is significant. On the other hand there are numerous applications that necessitate that accuracy of resultant output must be high. In present situation computing power has raised considerably because of increase in number of processors connected to parallel computer. So it is probable to raise size of problem that implies workload can be raised. How does this operate? Gustafson's Law relaxed limitation of fixed size of problem as well as aimed at employing notion of constant execution time in order to conquer sequential bottleneck encountered in Amdahl's Law. This condition that doesn't suppose a fixed workload is analysed by Gustafson.  So Gustafson's Law presumes the workload can increase considerably with number of processors however total execution time must remain same as highlighted in Figures below.

1373_What is Gustafsons Law2.png

Figure: Parallel Load Increases for Gustafson's Law

As said by Gustafson's Law if number of parallel operations for a problem raises satisfactorily then sequential operations would no longer be a bottleneck. The declaration of Gustafson's law should be illustrated with help of given example. Let's discuss a problem let's say P that has to be solved with the help of a parallel computer. Let Ts be time taken that is considered as constant for executing sequential operations. Let Tp (N, L) be time taken for running parallel operations with L as whole load on a parallel computer with N processors. The complete time taken for finding solution of problem is T=Ts + Tp. Consequently S (N) can be computed as under:

1264_What is Gustafsons Law1.png               

As well Tp (1, L)= N* Tp (N, L) it implies that time taken to execute parallel operations having a load of L on one processor is equal to N multiplied by time taken by one computer having N processor. If α be fraction of sequential load for a provided problem it implies that:

2132_What is Gustafsons Law3.png

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

1466_What is Gustafsons Law4.png

Figure: Fixed Execution Time for Gustafson's Law

19_What is Gustafsons Law5.png

Let's change complete equation of S(N) in form of X. Now we get

            S(N) = α +N * (1-α)

S(N) = N -α * (N-1)

Now let's put a number of values of α as well as compute speed up factor for rising values of α it implies that sequential factor of work load for a fixed number of processors let's say N.  Figure explains a pictorial view of effect of Gustafson's Law on speed up factor. The graph illustrates as value of α rises speed up factor increases. This reduce is due to overhead caused by inter-processor communication.

405_What is Gustafsons Law6.png

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


Related Discussions:- What is gustafsons law

Resetting the computer, Sometime you may have to reset your computer (i.e.,...

Sometime you may have to reset your computer (i.e., Reboot DOS) when it is still running because DOS does not work accurately. To reset your computer you have two choices: 1. P

Write a program to input an address, Write a program to input an address i....

Write a program to input an address i.e. 20 Hex and read the byte (char) contents of that address   Answer   include void main() { char prompt; Date: 26th August 2012

Segment combinations, Segment Combinations In 8086 assembler provides a...

Segment Combinations In 8086 assembler provides a means for combining segments declared in various modules. Some typical combine types are: 1.   PUBLIC: This combine directi

Write an algorithm for deadlock detection, Write an algorithm for deadlock ...

Write an algorithm for deadlock detection. An algorithm for deadlock detection: 1. Assume that Work and Finish be vectors of length m and n, correspondingly. Initialize:

Problem solving in parallel-, Problem Solving In Parallel Introduction ...

Problem Solving In Parallel Introduction to Parallel Computing This section examines how a particular task can be broken into minor subtasks and how subtasks can be answer i

Flowchart, How to calculate the flowchart

How to calculate the flowchart

What do you meant by a multimedia authoring system, Problem : a) What d...

Problem : a) What do you meant by a Multimedia Authoring System? b) Compare the verbose syntax to the dot syntax in Lingo. c) Explain each of the following terms: i) L

Illustrate minimization of gates, Q. Illustrate Minimization of Gates? ...

Q. Illustrate Minimization of Gates? The generalization of Boolean expression is much useful for combinational circuit design. The subsequent three techniques are used for this

Explain working of intranet, Intranets are mainly "small" Internets. They u...

Intranets are mainly "small" Internets. They use same network facilities that Internet does, though access is restricted to a limited sphere. For example, a company can set up an i

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