Efficiency vs. number of processors, Computer Networking

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.

Posted Date: 3/4/2013 6:00:29 AM | Location : United States







Related Discussions:- Efficiency vs. number of processors, Assignment Help, Ask Question on Efficiency vs. number of processors, Get Answer, Expert's Help, Efficiency vs. number of processors Discussions

Write discussion on Efficiency vs. number of processors
Your posts are moderated
Related Questions
what are the terms CSU, DSU and TSU?

Normal 0 false false false EN-IN X-NONE X-NONE MicrosoftInternetExplorer4

Question: (a) Explain the usage of the following parts of the IPv4 datagram format. i. VERS ii. HLEN iii. TOTAL LENGTH iv. SERVICE TYPE v. HEADER CHECKSUM (b) Na


A default route is analogous to a default gateway. It is used to decrease the length of routing tables and to give complete routing capabilities when a router may not know the rout

Q. Data Link Layer Responsibilities? - Defines frames into manageable data units - Physical addressing - Flow control - Error control - Access control Nod

QUESTION (a) Figure 3 below shows a reference model of the Foundations of Intelligent Physical Agents (FIPA). Explain the roles of the following components (i) Agent platfor

Can you define the difference among trusted and untrusted networks?

Q. Unshielded Twisted Pair - transmission media? - A most common kind suitable for both voice and data transmission - Categories are determined by chain quality - Cat 3 c

Q. Comparing Transport for TCP/IP and osi model? - The features of TCP and UDP defined at TCP/IP Transport Layer correspond to many of the requirements of the OSI Transport Lay