Efficiency vs. number of processors, Computer Networking

Assignment Help:

Efficiency:-

The other main metric used for performance measurement is efficiency of parallel computer system i.e. how the resources of the parallel systems are being utilized. This is known as degree of effectiveness and the efficiency of a program on a parallel computer with k processors can be defined as the ratio of the relative speed up achieved as shifting the load from one processor machine to k processor machine where the multiple processors are being used for achieving the result in a parallel computer. This is denoted by E(k).

Ek is defined as follows:

E(k) = S (k )/ k

The value of E (k) is directly proportional to S (k) and inversely proportional to number of processors employed for performing the computation. The relation between E (k) vs. Number of processors is shown in Figure.

1947_Efficiency vs. Number of Processors.png

   Efficiency vs. Number of Processors

Assuming we have the multiplication problem as discussed above with k processors, then the efficiency is as under:

E(k) = T(1)/T(n)*K = N/log n*N

E(n) =1/log(n)

Now, supposing we have X processors i.e. X < K and we have to multiply n numbers, in such a condition the processors may be overloaded or might have a few overheads. Then the efficiency is as under:

E(X)= T(1)/T(X)*X

Now, the value of T(X) has to be computed. As we have n numbers, and we have X processors, thus firstly each processor will multiply n/X numbers and consequently process the X partial results on the X processors according to the method discussed in Figure. The time complexity is equal to the sum of the time to compute multiplication of k/X numbers on every processor i.e., O(k/X) and time to compute the answer of partial results i.e. log (X)

E(X) =K/(K/X +log(X))*X

E(X) = (K/X)/(K/X +log(X))

Dividing by X/K we get

E(X) = 1/ (1+(X/K)* log(X))

It can be concluded from the above statement that if N is fixed then the efficiency i.e. E(X) will reduces as the value of X increases and becomes equivalent to E(N) in case X=N.  Likewise, if X is fixed then the efficiency i.e., E(X) will increase as the value of X i.e. the number of computations increases.

The other performance metrics engage the standard metrics like MIPS and Mflops. The term MIPS (Million of Instructions Per Second) shows the instruction execution rate. Mflops (Million of Floating Point Operations per Second) shows the floating-point execution rate.


Related Discussions:- Efficiency vs. number of processors

What is peripheral connect interface, Q. What is Peripheral Connect Interfa...

Q. What is Peripheral Connect Interface? PCI signify Peripheral Connect Interface. It's the revolutionary high speed expansion bus presented by Intel.  With the growing signifi

Process of securing an intranet, Process of Securing an Intranet Secur...

Process of Securing an Intranet Securing an Intranet is not a simple task. Mere installation of firewall hardware and software would not help the Intranet to protect itself. P

Why it is necessary to have layering in a network, Why it is necessary to h...

Why it is necessary to have layering in a network? A computer network is a very complex system. It becomes very difficult to execute as a single entity. The layered approach di

Firewall architectures-screened host architecture, Screened Host Architectu...

Screened Host Architecture This architecture consists of two host machines: a Screening Router and a Screening Host. Screening Router is placed between a local network and the

Fault tree analysis, FAULT TREE ANALYSIS Reliability engineering, in a ...

FAULT TREE ANALYSIS Reliability engineering, in a nutshell is concerned with failures.   How failures occur, how often they occur, and how to minimize them are the basic proble

Define the backbone networks, Q. Define the Backbone Networks? Backbon...

Q. Define the Backbone Networks? Backbone Networks - Allows several LANs to be connected - Non of station is directly connected to the backbone - Stations are part

Install, how to install xp via network

how to install xp via network

Merit and drawback of mpi, Merits of MPI Runs on any shared or dist...

Merits of MPI Runs on any shared or distributed memory architectures; Can be used on a wider range of troubles than OpenMP; Every process has its own local variabl

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